Years of Life Lost due to coronavirus

This post is by Phil Price, not Andrew.

A few days ago I posted some thoughts about the coronavirus response, one of which was that I wanted to see ‘years of life lost’ in addition to (or even instead of) ‘deaths’. Mendel pointed me to a source of data for Florida cases and deaths, which I have used to do that calculation myself for that dataset. The plots below show:
(Top) Histogram of deaths as a function of age, colored by sex because why not, although I would rather color them by ‘number of comorbidities’ or something else informative, since the difference by sex isn’t all that big.
(Middle) Points are expected years of life remaining for a person of a given age, from the Social Security Administration; and the lines are from a model that I fit to the points in order to get a continuous function of age that runs from birth to…well, to any age, although it predicts the same number of remaining years of life (or rather months of life) for anyone over 108 years old.
(Bottom) Histogram of ‘expected years of life lost’, calculated using the functions shown in the middle, i.e. a function of age and sex only. This is presumably an overestimate because the people dying of COVID-19 were probably already sicker (and thus set to be shorter-lived on average) than their same-age peers, although perhaps not as much as news reports might suggest: sure, most COVID-19 deaths of people over 80 are of people who have several “co-morbidities”, but most people over 80 have some health issues so it would be very surprising if that weren’t true.

The data through 5/12 include 1849 deaths, which the model predicts to represent 23177 years of life lost; that’s an average of about 12.5 years lost per death, but see the caveat in the explanation of the bottom plot. Is this a lot or a little? Daniel Lakeland has suggested dividing the years of life lost by 80 to get an equivalent number of lifetimes, where ‘equivalent’ just means equivalent in terms of life-years lost; in this case that gives us about 290, so the deaths of these 1849 people represent about the same loss of life-years as the death of 290 infants. This is not meant to imply that the tragedy is equal either way, it’s just a way to put this in terms that are easier to understand.

It will be interesting to see if the YLL distribution (and the deaths distribution) shift towards lower ages as the pandemic progresses. At least in California most of the new cases are among workers. If better hygiene and social distancing have reduced the spread of the virus among the old, but it continues among the young, then we would expect to see fewer cases become deaths, but each death will represent more years of life lost.

This post is by Phil.

1. jim says:

Seems like Florida is a great place to get a very strong age skew.

Possible way to extract a more accurate age distribution is looking at churches or other point-source outbreaks where the age distribution more closely approximates that in society as a whole. Or maybe just subtract out the nursing home fatalities and see the distribution with them removed.

2. Thanks Phil!

If someone wanted to take this further, what you could do is put a prior on “relative life years lost”, a number between [0,1] which would multiply your function in the 2nd graph. The assumption being that there’s a definite bias downward due to “comorbidities” but that it could be a wide range of biases. Something like a beta(6,3) distribution which has a 95% high probability region between .35 and .91

The next further step would be to make the bias a function of age. You could do that with a nonlinear function inv_logit(f(age)) where f represents the effect of comorbidities averaged over patients of a given age… if you somehow had information to inform such a choice of function.

If you have any enthusiasm for it, you might try to apply this model to the CDC national numbers https://data.cdc.gov/api/views/9bhg-hcku/rows.csv?accessType=DOWNLOAD

3. John Cavnar-Johnson says:

You should talk to these guys
https://opensafely.org

They have the data for this analysis (for the UK).

4. Joseph Candelora says:

If you want to get a good estimate of impact of comorbidities, and you have data on prevalence, talk to life insurance actuaries.

Still not sure what you’re trying to do with this info. It’s odd to see life-years as completely fungible like this implies.

I mean, why not extend your analysis and say that if they’ve gotten 300 bonus quarantine babies out of the deal, then Florida has actually come out _ahead_ from a life-years perspective. Or put differently, a fertility doctor making a baby a day does more in fighting Covid than a doctor who somehow prevents 44 Covid deaths?

Life-years lost is mildly interesting, but it gets you to some obviously absurd value judgments, as illustrated above. Does it really take 5+ 80 year-olds to equal one 30 year-old? I mean come on, I’ve gotta think one good healthy 30-year-old is worth _at least_ a dozen babies, but only like 2 or 3 geezers. But that’s just my set of preferences.

• Joshua says:

Joseph –

> Life-years lost is mildly interesting, but it gets you to some obviously absurd value judgments, as illustrated above.

+1

I still have yet to see anyone explain in any way how this metric might be used. Closest I’ve seen, that kind of makes sense to me, is that it helps measure the virulence of the virus, but even there I don’t see how that’s actually a usable piece of knowledge.

• See statflash comment below. As the pandemic wears on the population that’s exposed changes, and this measure is sensitive to that.

• Joshua says:

> fewer cases become deaths, but each death will represent more years of life lost”),

Seems pretty speculative. Some studies now suggesting that earlier on, infections will be more prevalent among the young and they’ll be developing immunity – meaning the pattern would actually go the other way.

But even if you could identify a shift in years lost as this metric might show – how would that information be useful?

• Phil says:

Joshua and Joseph,
If ‘life-years lost’ is uninteresting or only mildly interesting to you, that’s fine, you don’t have to look at it.

As for ‘how is it useful’, it’s useful for helping to quantify the severity of the pandemic. You could also ask ‘how is the number of deaths useful’, so why don’t you ask that? Neither the number of deaths nor the number of life-years lost is some magic parameter that tells us how to act, as you seem to desire. If you think you can come up with such a parameter, that’s great, go for it. If you think all lives are fungible and thus the death of a 90-year-old with dementia and pancreatic cancer should count exactly the same as that of an otherwise-healthy 30-year-old, that’s fine, nobody is making you look at anything other than the death count.

And ‘this implies absurd value judgments’ is less true of this metric than just counting deaths. If all you look at is deaths then you are saying a year in the life of someone who is currently 90 years old should count the same as 50 years in the life of someone who is currently 30 years old. Talk about an absurd value judgment!

In point of fact neither deaths nor life-years lost encapsulates a ‘value judgment’ other than the judgment that both of them are valuable for understanding the impact of the pandemic. Or at least, they are valuable for _my_ understanding of the impact of the pandemic. If you want to say they don’t tell _you_ anything because you don’t care whether the people dying are 30 or 60 or 90 years old, that’s fine; as I said, you don’t have to look at this stuff.

• Joshua says:

Phil –

Thanks for the response.

> If ‘life-years lost’ is uninteresting or only mildly interesting to you, that’s fine, you don’t have to look at it.

I didn’t really weigh in on whether I think it’s interesting. Just because I’m somewhat dubious about it’s value, and somewhat trep·i·da·tious about it’s implications, doesn’t imply that I don’t find it interesting.

> As for ‘how is it useful’, it’s useful for helping to quantify the severity of the pandemic. You could also ask ‘how is the number of deaths useful’,

Sure. Which I think is also a valid question.

> so why don’t you ask that?

I do, and I think as a society we are doing that a lot. There is a lot of questioning going on as to how much we should weight an increase in deaths as we think of social policies.

> Neither the number of deaths nor the number of life-years lost is some magic parameter that tells us how to act,

Right – and I never thought they they would.

> as you seem to desire.

? Where did you get that from?

> If you think you can come up with such a parameter, that’s great, go for it.

Actually, I don’t. Part of my criticism is that it may be a futile exercise to think that we can find a metric that really answers these questions. Part of my critique is against going for a metric just because you can measure something without actually assessing the validity of your metric – in other words, does it actually measure what you want to be measuring. I am specifically questioning this metric in the sense that I’m skeptical about the notion that it somehow measures value to society in a useful way. I’m kind of convinced that as Twain says, it could measure the virulence of a disease, but beyond that???

Again, my point is that it is a very crude measure if it doesn’t incorporate aspects like severity of co-morbidities, or the predictive value of specific co-morbidities (I think you’d have to do some kind of sensitivity analysis for co-morbidities to make this metric useful), or lifestyle/health behaviors, or race/ethnicity, or employment, etc. And then, on top of trying to evaluate years lost on a one-dimensional metric like age of death, I think that the whole notion of “years lost” as somehow measuring value is very dubious. It rests almost entirely on a value judgement that I’m not sure that I accept. For example, the value of “old-age” is very different across different cultures.

> If you think all lives are fungible and thus the death of a 90-year-old with dementia and pancreatic cancer should count exactly the same as that of an otherwise-healthy 30-year-old, that’s fine, nobody is making you look at anything other than the death count.

That’s an ad absurdum that makes it hard to have this discussion. That isn’t, at all, what I’m saying. Not even close.

> And ‘this implies absurd value judgments’ is less true of this metric than just counting deaths.

Less true? I don’t think so at all.

> If all you look at is deaths then you are saying a year in the life of someone who is currently 90 years old should count the same as 50 years in the life of someone who is currently 30 years old. Talk about an absurd value judgment!

I’m not saying it should. But again, you’re going the ad absurdum route. So it’s hard to respond. I’ll notice that here you add in the co-morbidity aspect – which actually is exactly the type of criticism I have because it does add in an additional factor to make it more complete…but still ignores a whole host of other predictive factors.

My question would be something more along the lines of why should we have some intrinsic value that’s greater for a 50 year old smoker who never exercises and works in a coal mine and drinks like a fish and beats his wife and abandoned three kids from each of his previous three wives and regularly dumps his garbage in a local reservoir that is the water supply for thousands of people, than a 60 year old who exercises daily and never smokes and drinks one cup of wine a day and donates tens of thousands of dollars to charities and takes care of the families of three of his neighbors and…well, you get my point. I don’t like going all ad abusrdum – but the thing is you haven’t really addressed my criticisms previously so maybe this will actually help?

> In point of fact neither deaths nor life-years lost encapsulates a ‘value judgment’ other than the judgment that both of them are valuable for understanding the impact of the pandemic.

Yah…well I don’t actually agree with that. I think they both have embedded value judgement – which in itself doesn’t make them invalid or not useful – but I think that it’s worth discussing whether they do embed value judgments and if so, what those value judgments might be.

But I might turn your earlier comment around, and say that if you don’t want to discuss what the embedded value judgments of your proposed metric might be, then why do you put up a blog post on the topic on a public forum where people will likely weight-in on the various implications of your proposed metric?

The “my country right or wrong” mentality isn’t, imo, terribly useful here.

> Or at least, they are valuable for _my_ understanding of the impact of the pandemic. If you want to say they don’t tell _you_ anything because you don’t care whether the people dying are 30 or 60 or 90 years old, that’s fine; as I said, you don’t have to look at this stuff.

Yah. I agree with that. If you find it useful, go for it.

I’m still curious as to what kinds of decisions you might use this metric to implement. I mean something relatively specific rather than just a handwave to an absurdum construct such as the 20 year old to 90 year old comparison.

And one last bit – in your construct, I’ll notice that even if you went absrudum, you didn’t quite go all the way. You stopped at 20 years at the one end of the comparison. I would suggest that is precisely because you didn’t want to really take on the embedded value aspects. You didn’t compare to a 1 year-old because of the value implications of doing so – because in some sense your construct necessarily implies a greater value for a 20 year-old than a 1 year-old – but that gets pretty tricky in terms of the implied values, and so you naturally didn’t go there.

• Joshua says:

PHil –

Sorry for the overly long, gish-gallopish response (stuck in moderation at the moment) ….but there was a lot of stuff packed into your comment that I wanted to address. If you want to respond and want to pick only one particular element, I’m cool with that.

• Joshua, your insistence seems to be that we not calculate something unless and until we have the *perfect* something that “does it all”. I reject this entirely out of hand. we never at one go, jump from nothing to the perfect thing.

Nevertheless you may find it interesting to evaluate the flexible family of measures that I mention in a different comment which is currently held in moderation.

• Joshua says:

Daniel –

> Joshua, your insistence seems to be that we not calculate something unless and until we have the *perfect* something that “does it all”. I reject this entirely out of hand. we never at one go, jump from nothing to the perfect thing.

That’s a fair point to the extent that it’s true. I recognize the danger of going there – largely from the perspective of someone who sees that line of thinking often put forth by climate “skeptics” in ways that I consider ultimate non-productive.

But I don’t really think that’s where I’m coming for here. I’m not expecting perfection. My basic questions, on top of the specifics, is rather simple. How is this metric useful? By which I mostly mean to rather simply ask someone to present a scenarios where they think a decision space will be enhanced by this information.

> Nevertheless you may find it interesting to evaluate the flexible family of measures that I mention in a different comment which is currently held in moderation.

Will check it out.

• Phil says:

Joshua,
I’m becoming increasingly frustrated with the five or six people who have been responding to this post and my previous post with what I see as unhelpful passive-aggressive commentary and rhetorical questions.

The only statistic that is regularly reported about the medical impact of the pandemic, or at least the only one in the sources that I see, is the number of deaths. For reasons I have stated previously I do not like that summary. What I would prefer is simply to see more parameters, but if I did have to pick a single parameter for some reason it would not be ‘deaths.’

I am proposing another parameter that I am more interested in: years of life lost. And what is the response? Some people think I’m saying that’s the only parameter that matters, in spite of my clear statement that that is not the case. Others say they don’t like this one, but they don’t propose another. It’s frustrating.

Perhaps in your case I have made the mistake of not taking your ‘what good is it’ question literally. It’s hard for me to believe you, or anyone, doesn’t think we should try to quantify the impact of the pandemic in any way. Since you haven’t been complaining about people quantifying it with ‘deaths’ I have assumed you are OK with using deaths as a way of quantifying the impact of the pandemic, but maybe that’s not the case.

I think quantifying the impact of the pandemic is important for many reasons, including (but not limited to) figuring out what resources are appropriate to respond; how to allocate those resources; how to determine whether our efforts are or are not successful; extrapolating to see what we can reasonably expect the near future to look like.

• Joshua says:

Phil –

> I’m becoming increasingly frustrated with the five or six people who have been responding to this post and my previous post with what I see as unhelpful passive-aggressive commentary and rhetorical questions.

Ok. I can see where they might have seem like rhetorical questions.. They aren’t, but if you see them that way there’s not much room to go further. I will respond to one more of your comments and then just drop it.

> The only statistic that is regularly reported about the medical impact of the pandemic, or at least the only one in the sources that I see, is the number of deaths.

But even if that is true – the question of the impact of age is a rather constant aspect of the question at hand, and my question is whether your metric actually addresses the impact of age in a truly meaningful way given all the elements that are left out.

And with that, I’ll drop it.

• Phil says:

Joshua,
I’m not asking you to ‘drop it’ if you have something to contribute! Now that I understand that your question was not in fact rhetorical I will try to answer it.

Let’s consider the next month or two. It is possible that we will get better at protecting the very old — certainly we should be able to do better in long-term care facilities — so deaths per week among the old will go down. But as people start to resume normal activities, including work, we might see more working-age people get sick, and some small fraction of them will die. Putting these together, possibly we will see deaths per week decline, but years of life lost per week increase. If decisions about ratcheting down the shutdown are based only on deaths, we might keep relaxing the rules even though, by the years of life lost (YLL) metric, things are actually getting worse. I’m OK with that if that is what we collectively decide we want, but I want us to recognize that that is what is happening and make an affirmative decision that we are willing to accept the increasing YLL.

So there’s an example of something you can do with YLL that you can’t do with ‘deaths’.

I’m not predicting that we will see weekly deaths decline while YLL increases, but it’s obviously possible. And if it happens I want to know about it.

• Joshua says:

Phil –

> But as people start to resume normal activities, including work, we might see more working-age people get sick, and some small fraction of them will die. Putting these together, possibly we will see deaths per week decline, but years of life lost per week increase. If decisions about ratcheting down the shutdown are based only on deaths, we might keep relaxing the rules even though, by the years of life lost (YLL) metric, things are actually getting worse. I’m OK with that if that is what we collectively decide we want, but I want us to recognize that that is what is happening and make an affirmative decision that we are willing to accept the increasing YLL.

Ok, that kind of makes sense to me…

I’m still pretty critical of the practicality, robustness, and real world likely of how this metric might be used…but it doesn’t seem that there’s much value in continuing with that critique. So I’ll just leave it there.

• Carlos Ungil says:

So does the median age of those who die, which is easy to calculate and interpret.

• Phil says:

The median age of the dead is a fine statistic to look at, and one I am also interested in. But two age distributions could have a median of 78 years but have histograms that look quite different. One of the striking things about the age distribution that we see is that there is pretty much no tail below 35 years or so, and not really much below 45.

• Carlos Ungil says:

Two distributions could also have the same years-lost-weighted average and be very different. My point was that as far as single-number statistics go, the median is also sensitive to the expected shifts in the distribution.

I do find your analysis interesting. The second distribution is a good complement to the first one. The initial reaction of “only very old people are affected” and is somewhat adjusted with “but I’d rather die at 80 than at 60, so in fact the impact is not so different”. As you discuss, the second distribution require some not-so-mild assumptions and is an overestimate so the “truth” (whatever it means for a visualization that is intended to be informative but not in a precise sense) may be somewhere in the middle.

Like other commenters, I don’t like the fact that newborns (and fetuses) score higher than anyone else on that metric. After all, the ultimate plague was to kill firstborns, not lastborns. But in this case the distributions essentially start at 30-40 so that’s not a problem.

• Phil says:

Years ago I mentioned on this blog that I think the most tragic deaths are those of people in their late teens or early twenties, since they have spent their whole lives to that point becoming fully realized people but now they and society are deprived of all of that built-up potential.

But I don’t understand why people assume I’m interested in ‘years of life lost’ as if it’s supposed to be a sufficient statistic that completely captures the impact of the pandemic. I certainly never said that, indeed I have repeatedly said the contrary. I find it very frustrating.

• Phil, a lot of people are made uncomfortable by the mere concept of discussing values and making ethical decisions through calculations. They see such things even far off in the distance and immediately begin attacking those who even set foot down the path.

For you and me, what we want is to start looking at a spectrum of measures, and begin through seeing what that spectrum looks like, to understand where our responsibilities may lie, what we should do about them so to speak. But you can’t figure that out until you’ve seen such a spectrum and had a bunch of discussions. Many people simply are made SUPER uncomfortable by that entire concept and want to shut it down as soon as possible. For them, any quantification seems to be a rock out from which they can never wriggle, that pins them down inexorably and therefore keeps them from arriving at the ethical endpoint they think is best.

Lots of People have *super strong* ethical priors. Ones that can essentially NEVER be budged by data. And this kind of thing they just hate.

For me, I agree with your assessment of people in their late teens and twenties being the ones we have to protect most. I have a way to quantify that but of course that’d be super uncomfortable for the anti-ethical-quantifiers… but what the heck, I’ll go for it.

Clearly a life should be worth more than the sum of the economic productivity, but also clearly the economic productivity is worth something… So as a way of handling this, we can imagine a given year of life as worth Productivity(t) + Intangible(t) where Intangible is just some measure of how much we like to be around that person. Now, clearly, in infancy almost all of the worth is in Intangible, because unless you’re the Gerber baby you’re not getting paid much, and in fact babies cost a lot to take care of (childcare, food, loss of productivity of the parents, etc). Yet, there are a few of us who still have children amazingly…

So, one way to evaluate social value of a life is integrate(exp(-r*t) * (Productivity(t) + Intangible(t)),t,0,inf) where “inf” can be truncated at death since productivity and intangibles go to zero at that point.

If we do this, it automatically weights infants less valuable than their life years because their productivity is negative and because their years of positive productivity are farther out so the discount factor exp(-rt) is larger for those productive years.

Again, I DON’T think this the be-all end-all measure. It is a very flexible integral measure of some kind of “value” but also note that intangible is an infinite dimensional parameter you can fiddle with… Those who really like the stories about the way things used to be can feel free to amplify the intangibles of the 80 year olds, and those who really really like the cuteness of babies can amplify those intangibles… so it’s an extremely flexible family of measures.

Nevertheless, you can’t even begin to calculate it until you put in the infinite dimensional parameter = Intangibles so if you decide you want to do something like that, you’ll have to have a stand-in for that intangible, and then everyone will jump down your throat. I’d recommend a broad prior on the behavior of Intangible and have the measure be a kind of “conditional” thing… From the enormous MCMC sample, subset the samples that have intangible curves you can get on board with, and then look at the measure of value lost under that range of intangibles…

Or let’s be honest here, this is the internet, some nutcase will probably call in a fake SWAT call on you if you even try this because it just makes them so angry to even talk about numbers and ethics. :-(

• Joshua says:

Daniel –

> Phil, a lot of people are made uncomfortable by the mere concept of discussing values and making ethical decisions through calculations. They see such things even far off in the distance and immediately begin attacking those who even set foot down the path.

[…]

Many people simply are made SUPER uncomfortable by that entire concept and want to shut it down as soon as possible.

[…]

> Or let’s be honest here, this is the internet, some nutcase will probably call in a fake SWAT call on you if you even try this because it just makes them so angry to even talk about numbers and ethics. :-(

++++++++++++

I hope that I could be forgiven for being paranoid if I”m wrong, but I’m getting the impression that those characterizations are being targeted towards what I’ve written in these threads?

If you do think such characterizations of me apply, I don’t imagine that me telling you that they don’t will make much of a difference. C’est la vie

Either way, that’s fine. It doesn’t really bother me if people want to characterize me in such a way, but I just wanted to check. Are those characterizations that you think apply to me based on what I’ve written in these threads? FWIW, I’m not at all “uncomfortable by the mere concept of discussing values and making ethical decisions through calculations.” Nor to I harbor any illusion that I might be able to shut the conversation down, let alone have any desire to do so. Nor do I have any interest in calling a SWAT team because I”m so angry about talking about numbers and ethics.

• Joshua, not specifically you, I have had multiple conversations in which people get angry when discussing calculations of life years lost or other metrics of badness used to discuss ethical issues (like, for example suicide prevention, the opioid crisis, or gun control issues). Many of those have been Facebook discussions and they usually go way off the rails rather quickly, so I’ve just stopped doing ethical / political discussions there.

The bit about the SWAT team was supposed to be hyperbole, but of course *it does happen on the internet* that people call in SWAT on people they dislike.

• Joshua says:

Daniel –

Ok. Thanks.

• Twain says:

Joshua,

IMO, the value of using LYL is twofold:
– It forces you to make explicit potential factors that could skew data, like age and comorbidity, that you do not have to make explicate per se when calculating CFR/IFR/similar.
– It makes explicit the shift in mortality among sub-populations with time as the more vulnerable populations deplete or some behavior change (such as ending shutdowns) begins exposing more to infection.

But as I’ve said, it is another measure to consider — but not the only one, either.

• Joshua says:

Twain –

> – It forces you to make explicit potential factors that could skew data, like age and comorbidity, that you do not have to make explicate per se when calculating CFR/IFR/similar.

Well, you/I have been doing that for weeks now, without such a measure – and I don’t particularly think having such a metric would improve our ability to do so, so much as just being able to look at data on the morbidity and mortality of CV stratified by age. Do you think that having had this metric would have improved our ability to discuss these issues?

I will also point out that this metric largely essentially works completely independently of the impact of morbidity – which may be equally if not impactful long term. So this metric, as described, misses a very important part of the picture.

– It makes explicit the shift in mortality among sub-populations with time as the more vulnerable populations deplete or some behavior change (such as ending shutdowns) begins exposing more to infection.

Yah, I have to think about that more but I’m not sure it really does – largely because it doesn’t take into account morbidity – which is what will likely be the largest signal that shifts over time if more younger people get sick as a % of the # of people who get sick. Also, I think it’s rather speculative to think that there’s going to be an actually significant signal in terms of more vulnerable populations depleting. I’m thinking of the implications of those studies that show that as more and more less vulnerable people get sick and recover, in their view, we will get to HIT relatively quickly.

• Twain says:

Joshua,

> Do you think that having had this metric would have improved our ability to discuss these issues?

IMO, yes. I hypothesize that a major reason LTCFs were hit so hard (in some states) was because policymakers there only examined overall CFR/IFR and did not see how heavily the severe outcomes skewed with age/morbidity. If they instead used LYL, the analysis would have forced them to make these factors explicitly and perhaps the immediate risk to elderly and morbid would have been more apparent.

But again, this is a hypothesis; I’m not privy to what happens behind-closed-doors, so perhaps policymakers considered LYL when making decisions and did the best they could.

> Yah, I have to think about that more but I’m not sure it really does – largely because it doesn’t take into account morbidity – which is what will likely be the largest signal that shifts over time if more younger people get sick as a % of the # of people who get sick.

See my post below and link. Integrating morbidity (and varying severity thereof) is simple using Standardized Mortality Ratios; from my understanding, this is common practice actuaries use. (You just need to find the values for SMR.) You could even generate SMRs for high-exposure locations, living, or occupation.

• Joshua says:

Twain –

Thanks for the response. A quick comment and then I’ll stop cluttering the recent comments column.

> IMO, yes. I hypothesize that a major reason LTCFs were hit so hard (in some states) was because policymakers there only examined overall CFR/IFR and did not see how heavily the severe outcomes skewed with age/morbidity. If they instead used LYL, the analysis would have forced them to make these factors explicitly and perhaps the immediate risk to elderly and morbid would have been more apparent.

I would think it might run the other way…that one of the reasons for such a high concentration of deaths and illness in LTCFs is that it’s a bunch of old people living somewhere – and that gets to the heart of my question about the usefulness of this metric. I’m not suggesting that any one person in particular is going this route, but I would be reluctant to embrace a metric that could potentially accelerate the aspect where people are less likely to value someone’s life on the basis of advanced age.

Given that I’m not getting any younger – perhaps there’s a bias in play there? :-)

• Twain says:

Joshua,

> I’m not suggesting that any one person in particular is going this route, but I would be reluctant to embrace a metric that could potentially accelerate the aspect where people are less likely to value someone’s life on the basis of advanced age.

If I were a policymaker (which I’m not) viewing the results of Phil’s or another LYL analysis, my response would be the following: “Oh no. This clearly will ravage the elderly and morbid much much more than other demographics. Let us focus as many resources as reasonable to secure, reinforce, and isolate these populations. We still want the healthy and young to be careful (masks, distancing, etc.), but their risk of severe outcome is much less.” Granted, one could come to this conclusion from looking at stratified IFR; but for me, it is more obvious using LYL.

This rationale seems to have happened in some states, like NY, MA, and NJ. There, the governors essentially let LTCFs each have their own plan, secure their own supplies, and enforce themselves … which had disastrous results. LTCFs were quickly short on PPE (anecdotally); infected patients were sent BACK to LTCFs from hospitals; employees were still allowed to work at multiple facilities; etc.

Because these policymakers acted in a way to protect *everyone* equally, they did not allocate enough resources to protect those who were far more vulnerable, causing more deaths among those populations than perhaps should have occurred.

• Twain says:

Joshua,

All of my above analysis is, of course, hypothetical. I cannot know for sure what policymakers considered besides what they make available publicly.

• Carlos Ungil says:

> Granted, one could come to this conclusion from looking at stratified IFR; but for me, it is more obvious using LYL.

Twain, I don’t get it. If by LYL you mean a number it’s not obvious which groups are more affected, wether you make it 10 years per death patient, or 1 month per infected person or 3 vietnams per quarter or anything else. And if you mean the curve, the difference between the naive death-count plot above and the life-years-lost plot below is that the former says “This clearly will ravage the elderly and morbid much much more than other demographics” and the latter tunes down the message to just “more” instead of “much much more” by given more weight to the younger victims.

• Twain says:

Carlos,

The prior for my statements is LYL analysis including comorbidities. LYL is useful because it allows you to deconvolve age from morbidity (see Table 1 in the linked report). In fact, it is not common to use LYL analysis without factoring for comorbidities because they have pronounced influence the outcomes for a given disease or injury.

If you include comorbidities, say using SMR like the linked report, the skewing toward elderly and morbid patients would become much more clear. Say most of those hospitalized and dying had SMR>=3. That would be a major finding: it would show COVID-19 only poses a danger to those who are most morbid in the population, while everyone else has little risk of severe outcomes. Say death is independent of SMR (so independent of morbidity). That would also be a major (and scary) finding: it would show COVID-19 poses a danger to the *entire* population, not just those who are morbid.

Since ~90%+ of deaths in most locations (NYC, Italy, Spain, etc.) have 1+ comorbidity, including them when calculating LYL is necessary. But such data is not available, so we can’t know for sure what “level” or morbidity those dying have.

• Carlos Ungil says:

I don’t say that a more complex analysis is not interesting!

But if policymakers had somehow missed [*] that severe outcomes are skewed towards the elder people, an easy way to push them to the “This clearly will ravage the elderly and morbid much much more than other demographics” enlightment would be to say things like

“Half the of the victims are over eighty”

or the slightly more complex

“In NYC 1.4% of those older than 75 have died of COVID-19, and the mortality decreases rapidly with age: 0.55% in the 65-75 range, 0.17% in the 45-64 range, and 0.02% in the 18-44 range”

which still fits in a single sentence. If I need to read a report full of acronyms to get the context to understand how a naive policymaker would interpret your analysis… then maybe it’s not so obvious.

[*] Of course they didn’t, because as far as I remember the almost universal governmental position when the first deaths happened was to stress how old those people were and how many previous pathologies they had so the usual four-stage crisis response policy was in order: “In stage one we say nothing is going to happen. Stage two, we say something may be about to happen, but we should do nothing about it. In stage three, we say that maybe we should do something about it, but there’s nothing we can do. Stage four, we say maybe there was something we could have done, but it’s too late now.”

• Twain says:

Carlos,

I understand your point now, thank you for clarifying.

You may be misunderstanding: My quote was to illustrate my immediate mental dialogue would be upon seeing the results of the LYL analysis; it is not what I would say to another policymaker. I would never use “much much more” when communicating to others a difference in magnitude (or even myself beyond an immediate reaction); I’d use precise values and statistics, like those you provided.

> Of course they didn’t, because as far as I remember the almost universal governmental position when the first deaths happened was to stress how old those people were and how many previous pathologies they had so the usual four-stage crisis response policy was in order […]

I’m not sure what you are claiming here. Do you think that the mass infections and deaths from LTCFs were not more preventable and that policymakers did the best they could?

• Carlos Ungil says:

I say that they always knew that the weak and old were the most affected. And that they explained to the public, at least in the places I know better, that there was no need to worry because it was the old and the weak who were being affected.

• Twain says:

Thank you for clarifying. What I heard for the first month-or-so in my locale was more dire; of course, my own biases and priors could have made it seem that way.

• jim says:

“I still have yet to see anyone explain in any way how this metric might be used.”

Well, if you were to get a group of laid off 32 yr olds together, they might – justifiably, in my opinion – ask why so much is being sacrificed for so few life years.

• Joshua says:

jim –

> Well, if you were to get a group of laid off 32 yr olds together, they might – justifiably, in my opinion – ask why so much is being sacrificed for so few life years.

Not only might they – but I have seen that happening all over the media and all over the Interwebs already. No years lost metric needed. They’re doing it now and the years lost metric, as far as I can tell, would not particularly inform the discussion.

Is it justifiable? I don’t know. But one aspect that I think is relevant is that a lot of it is based on a simplistic notion that it is only the “lockdowns” that are causing the problem. And, IMO, a lot of that reasoning is tribally and ideologically based more so than reality based.

• All ethical assessments lead eventually to absurd conclusions, whether measures of life-years lost or measures that weigh every life equally. That doesn’t make them useless: we should think not about the extremes, but in general about what these different approaches mean to us. We do this all the time — in an even more extreme example that weighs convenience against life, we set speed limits on highways to lethal levels (65 mph) rather than a more sedate 20 mph, because we assign value to the quality of life associated with getting places fast. (I’m fine with this, but that’s another story.)

As for “what you’re trying to do with this” — this is exactly what we *should* be doing, to weigh different approaches. Whether we like it or not, we always weigh the deaths of groups against each other, for example the millions of poor at risk of dying from economic-collapse-induced hunger versus the relatively well off in Europe and the US. More conventionally, we decide which disease to allocate funding towards researching based on these sorts of issues — we don’t just throw our hands up and say decision-making is impossible, or ignore numbers (like lives lost or years of lives lost).

Yes, ethics is hard. It’s a fascinating and deep subject to read about. It’s relevance now is of course striking, though I’ve been sad to see how the present pandemic makes it clear that people *really don’t* want to think about ethical choices.

• +1 to all of this, especially the “sad to see” part.

• Joseph Candelora says:

Again I ask, what is anyone going to do with this info? You still haven’t done anything with it.

You’ll note that I’ve weighed the considerations and rendered my value judgments — on record in the comment you’re responding to. In particular, I think counting years before someone can even form a coherent thought and weighing them equally against others is perverse, and that valuing the life of one infant even at parity with a 30-year old (much less at roughly double) is absurd. And also that weighing the life of a 30-year old.

If you’re going to weight the value of lives, a simple accounting of years is, in my opinion, entirely the wrong approach, and the above chart obscures more than it enlightens. A simple display of deaths by age would be more useful, as we can each then plug in our own weights and proceed.

So one more time, with feeling: What do you want to do with this info?

• I don’t understand what “you” means in “What do you want to do with this info?”

If “you” is generic, meaning “what should anyone do with this information,” then the answer has already been stated: it should inform the decisions we make about policies in the same way that data on traffic fatalities inform our policies. There’s not a simple mapping between data and policies — as mentioned, ethics is hard — but that doesn’t mean the information is meaningless.

If “you” is specific to me or other commenters: personal action is not a prerequisite for writing on a blog. I’m not planning on “doing” anything about Andrew’s favorite mid-twentieth-century authors, or some particular p-hacked psychology study, but that needn’t stop me from thinking about them or writing about them. I do, in fact, spend very packed days “doing things”, so I’m not opposed to being results-oriented, but if this is your criticism of blog comments I think it’s misplaced.

• Joseph Candelora says:

I never said the information is meaningless. Mildly interesting, to quote myself.

My question was originally posed to Phil. I’m still interested in knowing what he wants to do with this info. To extend your metaphor, it’s all well and good to multiply the number of traffic fatalities by miles each driver was going to drive, but what does it tell him? You have the data, now what does it mean?

Since you jumped in, I pose the same question to you. What meaning do you glean from this, what policies does it inform, what new or existing courses of action do you recommend? Or even simpler what random insights does it provide you?

I think life years is a terrible measure. Yes, the life of a healthy, productive young adult is worth more than someone on death’s doorstep. But the weights that life-years provides are absurd. We as a society don’t find murdering a sick older person who wants to live any less heinous than murdering the young adult, so clearly our preferences don’t scale with life years. Personally, I think the appropriate weight is some linear combination between death count and QALYs, with the QALY weight being a very minor term, with the QALY term providing no more than 50% of the total value.

Why do you think life years is a useful measure? How would you use it? For someone who claims to be sad that _other_ people don’t want to think about ethical choices, you sure seem to be unwilling to enter that territory yourself.

• Phil says:

Joseph,
See my response to your previous comment. But basically I say what Raghuveer has said.

I hope there are other blogs where you comment that you think ‘deaths’ is a terrible measure, because how would you ever use such a metric, what policies does it inform, what new or existing courses of action would you recommend because of the ‘deaths’ metric.

Eh, I’m going to find that I’m repeating myself. See what I said above.

• Joseph Candelora says:

Phil,

You seem to be taking personally what was an honestly asked question. I’m still trying to understand what you mean to _do_ with this information.

As I revealed above, I personally think it’s a bad metric. I don’t want to get too bogged down in my explanation of why (although I gave it a few times above in my responses to Raghuveer), because I’m judging the metric on my gut feeling of how you would use it, and not on how you are actually using it, because you still haven’t shared that.

Let me give an example. Deaths is a fairly easy to grasp metric, and we have data on it across a whole variety of risks. My go-to in the course of this pandemic has been driving deaths per year. Now before I had anything good to base a Covid death estimate, I was figuring that a reasonable estimate of deaths in unmitigated outbreak would be about 200k*. And I compared that against another easily measured statistic, which is annual deaths from driving of about 35,000. To me, 200,000 deaths is a tragedy, but it was a real stretch to think it made sense to “cancel everything” — shut down work indefinitely, causing suffering to our most vulnerable — to save the equivalent of 7 years of driving deaths. I mean, I’d bet that that the thought has never even crossed any American’s mind that we should shut our economy to save the deaths from driving, so the idea we would do it for something less than an order of magnitude higher seemed less than rational and overly focused on the newness of the threat. Not entirely crazy like it would be if we were talking, say, 20k Covid deaths from unmitigated outbreak, but still to me personally it wouldn’t be worth it. When you layer on top of that the fact that the 200,000 lives would mostly be from our sickest people, it’s even less justified; you can’t value those lives at the same level as the lives lost from car accidents, since the accidents pretty much don’t discriminate on health status (and actually are overrepresented in younger-aged males).

Then the ICL report came out, much more expert than I, and put the number of lives lost in an unmitigated epidemic at 2,200,000, of which we can save about 90% if we shut down. Okay, that changes my thinking. Now, for me personally, the cost-benefit lands on the side of shutting down — I mean we’re talking a whole order of magnitude more than my 200k estimate, and 70 times the death toll from one year of driving. [I have more to say here in that I found ICL’s mitigation approach that saved 1m of those lives while not shutting anything down to be quite compelling, but that’s a different topic.]

So that’s why I keep asking what y’all intend to do with this life-year number now that you have it. I think if you were to do a comparison against driving deaths, re-worked for life years, you end up way overcompensating in your reweighting, and the problem of overvaluing old lives somewhat when just counting deaths ends up way worse in the other direction by dramatically overvaluing young lives with life-years. Additionally, moving to life-years makes it much more difficult to share the conclusions with others, because I can’t think of a good reference point for what a lost life-year means (most people have no idea how many life years they have outstanding, but they know they have exactly one life.)

But see, I’m just arguing with myself here. Maybe you’re going to do something completely different with it. I don’t know what meaning you’re gleaning from these numbers, and that’s why I keep asking for someone to assign some meaning to them. I think I can convince you that this is a bad metric once I see how you use it, but I’m certainly open to correction myself. Maybe you’re thinking about it in a way that I’m not, or comparing against some reference value that I’m not thinking of, or whatever.

So please, use it for something… compare it against other sources of life-years lost, compare it to other interventions that could extend life-years, surprise me. Otherwise it’s just trivia, and the answer to your question from last post of “Why isn’t [anyone reporting life-years lost]” is “Because nobody cares.”

———
*My original, completely uninformed guess of about 200k deaths was based on the fact that reported CFR was 3.4%, then looking up reporting from during the 2009 swine flu outbreak and finding that the final IFR was about one tenth of the CFR reported mid-outbreak, and also figuring that about 20% of the people could get (if it’s like a bad year of influenza). So, 3.4%/10*20%*330m = 200k. I have since learned that the “novel” part of “novel” coronavirus is the critical thing — there’s no in-built immunity in the population (and apparently we all carry some level of influenza immunity from prior infection) so the likely unmitigated prevalence is much higher than the 20% of a bad flu year — more like 80%. And also that actual experts had studied the Wuhan et al fatalities and were using that to project a population specific IFR of more like 0.8%. So now I’m thinking a much more reasonable death projection would be 0.8%*80%*330m = 2m. I’m fine with being wrong on these things — just trying to learn more.

• confused says:

>> We as a society don’t find murdering a sick older person who wants to live any less heinous than murdering the young adult, so clearly our preferences don’t scale with life years.

I don’t think you can compare how society views death from *murder* to how society views death from natural causes or accidental causes, though.

This is due to moral instincts and/or because because committing murder shows that someone is not a suitable member of civil society (I’d argue those are two ways of saying the same thing; our moral instincts are “calibrated” the way they are because having murderers around is dangerous to society). This is why we prosecute people for attempted murder even if zero actual harm is done; because someone who tried to commit murder once is likely to try again.

I *would* say that a 20-year-old dying in a car accident is significantly more tragic than a 90-year-old dying in a car accident, and I don’t think that’s an unusual position.

• +1, you said it so I don’t have to, thanks

• Zhou Fang says:

I dunno, we accept 20 year olds driving too fast and getting themselves killed much more than some beloved grandma. Andrew wrote a blog about John Conway. He’s not doing that for many 20 year olds.

• I’m now imagining Martha Smith drag racing her mustang through the streets of Austin.

There is a time asymmetry involved here. retrospectives on things people actually did are different from fictional accounts of things people might have done in the future if they hadn’t died.

• Phil says:

Zhou Fang,
If Conway has died forty years earlier it would have been even more of a loss, wouldn’t it?

• Martha (Smith) says:

Daniel Lakeland said,
“I’m now imagining Martha Smith drag racing her mustang through the streets of Austin.

He’s got a better imagination than I do — I don’t seem to be able to imagine myself even owning a mustang, let alone driving one, let alone drag racing.

• confused says:

I guess I should have said “dying in a car accident *that isn’t their own fault*”. If someone is driving crazy, that definitely changes people’s opinion.

• Zhou Fang says:

Phil: From the perspective of objective utilitarian ethics perhaps (though there’s an argument here about whether we subscribe to Great Men theory too much when a different person could have risen up in their place…) but I just wanted to make the point that this isn’t how we subjectively really act. There’s at least some sense in which societies value people for the sum of their achievements and connections, instead of what they are *yet* to achieve.

Perhaps this is not entirely illogical, if the idea is that this expectation of future reward helps motivate in the present? Thus the cost of a Conway dying is not the cost of the lost work Conway would have done in his remaining lifetime, but rather the cost of a young would-be Conway seeing the social contract being broken and not being motivated to achieve. In this way an old esteemed person dying avoidably can be more socially costly than a young person.

• confused says:

>>the cost of a young would-be Conway seeing the social contract being broken and not being motivated to achieve.

This sounds good, and clearly comes from the right place ethically (re: not ignoring the elderly), but I don’t know if this really makes sense with how young people think. People mostly don’t really start thinking about retirement & their quality of life then particularly early – else we would see a lot better financial planning, a lot fewer unhealthy behaviors, etc.

I guess it depends on what you mean by “young” though. If you just mean “working-age instead of retirement-age” then it makes sense.

But also… I think most really high-achieving people, especially in intellectual and creative fields (as opposed to say politics or business), are more internally motivated than by external reward, except perhaps recognition (especially in their own and related fields).

• Zhou Fang says:

I think you need something like that with respect to what young people think *about covid* though. It’s clear that people’s concern about covid is not at all proportional to their personal exposure to risk. Far from young people being peeved at what is done to save the old, it is the old who prefer more relaxed policies. See e.g.

https://theconversation.com/coronavirus-survey-reveals-what-swedish-people-really-think-of-countrys-relaxed-approach-137275

https://docs.cdn.yougov.com/h6nwhcsrrv/GMBResults_200511.pdf

Perhaps there’s a distinction between young persons thinking about their personal retirement plans, and thinking about long term societal breakdown. This is why I phrased it in terms of the social contract – it is not so much the reward itself that is enticing, it’s the trust in a system that *rewards*.

• confused says:

I think that effect is for a different reason, though: most young people overestimate their own risk because it is new and scary, and because they’ve never had to think about infectious diseases (other than maybe AIDS) before; while elderly people have seen more bad things happen in the world in their lifetime, and may even remember the 50s and 60s when a lot of diseases now very rare in the US because of vaccination were prevalent.

It’s much like how people think of nuclear power as super scary when kills orders of magnitude less people than coal, or why flying is scarier than driving – unusual and flashy accidents are more frightening than baseline things that are ‘normalized’ by experience, even if the latter are far worse.

>>This is why I phrased it in terms of the social contract – it is not so much the reward itself that is enticing, it’s the trust in a system that *rewards*.

I’m not sure that changes the question very much. I don’t think (anecdotally) all that many young people *do* trust the system at all, and even if they did, that would only matter if they actually thought about the issue (of retirement, etc.)

• Zhou Fang says:

confused:

I don’t think that’s true. Polling also shows that young people are less scared of personally contracting the virus than older people:

https://theconversation.com/coronavirus-lockdown-fresh-data-on-compliance-and-public-opinion-135872

And also more cogniscent of long term economic damage.

Nevertheless they favour tougher lockdown action.

For me I think it’s hard to not come to the conclusion that there is a broader social perspective young people are adopting here.

> I’m not sure that changes the question very much. I don’t think (anecdotally) all that many young people *do* trust the system at all, and even if they did, that would only matter if they actually thought about the issue (of retirement, etc.)

The fact that young people do not *trust* the system does not mean they do not consider building a trustworthy system to be important – rather I’d argue their criticism is actually based on a deep concern about those systems.

• confused says:

Hmm. OK. That’s interesting.

I find that quite odd, because it seems to me that from a dispassionate, what’s best for society “as a whole” perspective, lockdowns are very risky.

We have clear historical examples of pandemics, and even fairly deadly ones don’t really impact society or economy all *that* much. (1918-19, for example; that killed 2% or more of the entire world population – not IFR, but 2%-4% of *everyone*.)

We have no historical example of trying lockdowns like this in a modern economy with all its delicate, complex, inter-related supply chains. That seems far riskier to me.

Even if the risk of a supply chain collapse is considered too low to matter (and I think even a 1% risk would be far too high to accept), it’s not at all clear that the lockdowns would really save any lives “overall”, once you include delayed cancer surgeries, people too afraid to go to the ER for heart attack/stroke symptoms until it’s too late [ER visits for these sort of things are

If I really believed the lockdowns might be saving, say, 2 million lives, that would be different. But given that states that didn’t do stay-at-home orders aren’t doing worse than ones that did, I think the effect is going to be a lot smaller than “expected”. (Partially because I think experience from high-density places like Wuhan, Lombardy, Madrid, New York City, etc. led people to expect a higher R0 than most of the “non-New-York”, low-density, cars-rather-than-mass-transit US actually had.)

5. statflash says:

Phil,

Nicely done! This is an elegant data analysis and set of plots. I really appreciate you expanding on your previous post and using the feedback from the comments there.

I don’t have much to add except to say that the 12.5 years of life lost per death seems hard to interpret, I mean without comparisons or other context. In the 1918 flu, what would it have been — 30 YLL per death? How would we adjust for the fact that people didn’t live nearly as long back then? I do like this idea though, just hard to interpret since it’s a metric I’ve never seen or thought about before. It would be interesting to get the total YLL and the YLL per death for US casualties in Vietnam, for example.

Other potentially useful metrics could be the YLL per capita (to compare state to state for COVID-19) or the YLL per people infected (once we have good/widespread serological testing).

You’re point at the end is really important. I doubt the news media will be able to pick up on the plot if the mortality shifts in that direction (“fewer cases become deaths, but each death will represent more years of life lost”), but this metric would be a useful way to measure that shift.

• Phil says:

statflash,
I, too, am not exactly sure what to make of the average 12 YLL. On the one hand, _if_ we think it’s a fair estimate, i.e. these deaths are among people who are fairly typical of their cohort and not already at death’s door, then one take-home for me is that it’s a pretty big number. I can’t return to my state of ignorance from before I calculated this number — also, someone on the comment thread of the last post said it’s about 10 years lost per death, which is about right — but I feel like I might have looked at the large number of deaths among people over 80, and the small number among people under 60, and guessed more like 5 or 8 years lost per death. 10 or 12 is substantially bigger than that, so I guess I’d say the situation seems a little worse than I thought.

If people were dying 0.5 years ‘early’ or 1 year ‘early’, well, that would still be very sad but if you got to live out 69/70 of the measure of your days, or whatever, well, you had some bad luck but it’s not a terribly raw deal. But to lose out on a dozen years, even if they’re not your absolute best dozen years, that’s fairly tragic. Even a modest decrease in the estimate because on average these were presumably somewhat less robust than others of their age cohort would still leave it on the order of a decade of lost life per person.

The U.S. is heading for 100,000 deaths and if we were betting on the number by the end of the calendar year I would take the over on 150K. If it really is about 10 years of life lost for each death, that’s 1.5 million years of life lost. Comparing that to Vietnam: about 60K Americans died in Vietnam, at maybe 55 YLL for each one, so that’s 3.3 million years of life lost. Those numbers (1.5M and 3.3M) are close enough that I think one could argue either way as far as which is worse in terms of the death toll. On the one hand, Vietnam cost more years of life lost; on the other hand, years of life are not necessarily all that matters and if someone’s favored metric is more like Badness = YLL + b * Deaths, then there are reasonable choices of b that would say the U.S. death toll of the pandemic is, or soon will be, worse than the U.S. death toll in Vietnam. And of course the number for Vietnam is not going to change, whereas for the pandemic there is a lot of potential to get a whole lot worse.

• Phil, one of the values to me of doing this kind of analysis is that in fact it helps people calibrate their expectations. If you don’t do the calculation, people in general are apt to say “the typical person dying is 80, and 80 is already past the life expectancy at birth, so they probably were only going to live another few months to a year anyway” (or something like that)

But the people who are 80 today don’t live a few months, they live quite a few years (life expectancy is ~10 years for a random 80 year old according to your curve). So, one way to say that this metric is useful is that it just explodes the innumeracy inherent in many people’s understanding of life expectancy. Of course, comorbidity is still a thing, and so another way this metric is useful is that it points out that we really need more comprehensive data on who is dying and what kinds of comorbidities they have, and how badly those comorbidities affect their life expectancy.

People seem to want these analyses to provide answers. To me, they’re at least as important in terms of providing questions.

• confused says:

Yeah, I’ve seen the argument that “the median age at death from COVID is greater than the life expectancy, so therefore basically these people were all dying anyway, hardly anyone actually dies *from* COVID” a lot, and that is total nonsense.

This also makes me think that maybe 2009-10 H1N1 was a bit worse than we think (I’d always seen it as practically a “false alarm”, probably largely because when I had it the symptoms were extremely mild). Sure, still much less severe than other pandemics, but given how it didn’t have a sharp increasing-with-age curve to its mortality, whereas very few people who aren’t *extremely* elderly die of infectious disease in the modern US absent a pandemic…

• Thanks! I am not surprised people are finding massive imbalance in glutathione among severe COVID patients. Basically the immune system is one enormous oxidative stress machine.

• Anoneuoid says:

If you check the comments there is also this interesting info:

The concentrations of both ascorbate and glutathione in bronchoalveolar lavage in smokers are double those in nonsmokers (36, 37).[…] Finally, it is important to cite the study of a 45-mo-old girl with hereditary glutathione synthetase (EC 6.3.2.3) deficiency and severe glutathione deficiency (41). After receiving vitamin C supplementation, she had dramatic increases in the concentrations of plasma (8-fold) and lymphocyte (4-fold) glutathione. Indeed, the observed increases in glutathione after vitamin C supplementation were greater than those observed with high doses of N-acetylcysteine.

I had no idea about this, but it makes some sense. Usually smokers are reported to have lower *blood* vitamin C levels, so its surprising to learn it is higher in the lungs.

• Joshua says:

Anoneuoid –

FYI, there was more discussion over at ATTP related to your thoughts on the findings on the range of climate change sensitivity. I have no idea if you felt it was any more on point, but FWIW I did find the discussion interesting.

• Anoneuoid says:

I commented in the other thread about it. I didn’t see a single person address the point that the 1.5-4.5 C range is due to variability instead of uncertainty by definition. It is like a standard deviation, not a confidence interval. The entire discussion there still assumes it is like a confidence interval.

• Joshua says:

Anoneuoid –

I’ll defer to your technical expertise, but it looked to me like they discussed the question of variability vs. uncertainty.

If you’d like, I’ll post what “my friend” had to say and see if tbete ate any more bites.

• Anoneuoid says:

Well link to where you think it was discussed, maybe I missed it.

But I want to emphasize there is nothing theoretical or philosophical about it… The response I am looking for is “here is how it is actually calculated, you got confused” and some code or equations are shown yielding the correct range that do not depend the amount of scatter around the forcing vs deltaT line (which is a descriptive property of the data, and will not change unless the underlying process that generates the data changes).

I don’t think anyone in that discussion has ever looked into how that range is actually arrived it.

• Joshua says:

If you could combine your two comments there into one, I could more easily post how you think they missed the point.

• Anoneuoid says:

The 1.5-4.5 C range is due to variability instead of uncertainty *by definition*. It is like a standard deviation, not a confidence interval.

There is nothing theoretical or philosophical about it… The response I am looking for is “here is how it is actually calculated, you got confused” and some code or equations are shown yielding the correct range that do not depend the amount of scatter around the forcing vs deltaT line (which is a descriptive property of the data, and will not change unless the underlying process that generates the data changes).

• Joshua says:

Anoneuoid –

> (which is a descriptive property of the data, and will not change unless the underlying process that generates the data changes)

I’m confused because it seemed to me there was general agreement (albeit more for some than others) that the range of the estimate may well be a property of the data, and might not change.

What am I missing?

• Anoneuoid says:

You’ll have to quote where you saw that. I saw the exact opposite. Discussion of hypothetical earths, aleatory uncertainty, thinking the range will get smaller as more data is collected, etc.

I’d also say link the original post, which I admit is hard to follow without equations (which can be seen in the paper I cute though) and a graph: https://gelmanstatdev.wpengine.com/2015/12/10/28302/#comment-254706

• Anoneuoid says:

“But I want to emphasize there is nothing theoretical or philosophical about it… ”

err, no, defining what type of uncertainty you are talking about is central to the question.

[…]

I think it would be more correct to say that the range will get smaller as our understanding improves (which will be partly due to the collection of data, but only partly – you have to extract knowledge from the data first).

Thanks for trying but I expect it to go on like this. This is why I didn’t bother.

• Joshua says:

Anoneuoid –

> Thanks for trying but I expect it to go on like this. This is why I didn’t bother.

Well, FWIW, he an I butt heads quite often. That said, he has a style, but so do we all, including you. To the extent that you have expectations, you may well help lay the groundwork to meet them.

He has relevant expertise. Others might have something to say. If you’re looking to answer a question rather than push an conclusion (e.g., that climate models are fatally flawed) you might wait a bit. You might be able to learn something – if even only to learn how to explain your viewpoint in a way that leads to better communication on the topic. You might consider rephrasing your reaction in a way that might promote a more satisfactory response – it could be worth a try. I anticipated that your reaction might not be the most conducive to give and take (part of the reason I was asking you to rephrase). And the indirect channel seems inherently sub-optimal. All up to you, of course.

Dhogaza suggested James Annan. He might have a more receptive framework to your question. I gave you his blog URL. He has a more technical blog also, but I sense he’s less responsive at that one. Isaac Held used to have a blog, and would be a possible person to reconcile your question – but I don’t know how available he is anymore. Science of Doom was a technical website that entertained such discussions (from a relatively “skeptical” angle) – but I noticed that it seems to be defunct.

• Anoneuoid says:

@Joshua, from what ive seen so far there is no hope of a useful response from there. Looks like a bunch of people who want to endlessly argue in the abstract to me.

• Joshua says:

Anoneuoid –

> Looks like a bunch of people who want to endlessly argue in the abstract to me.

That hasn’t been my experience. FWIW, person who runs the blog is a quantitative scientist, as are the others that have commented (including the person who commented most recently)

> @Joshua, from what ive seen so far there is no hope of a useful response from there.

That’s unfortunate. I wonder if that isn’t to some degree a function of your expectations? At any rate, you might try the other scientists I mentioned. I mentioned them in particular because I think that among those I’ve seen, they might be ones who would respond in a way you’d be most receptive to. And I have no reason to push it any further.

• Anoneuoid says:

@Joshua

Agreed, iys not our job to stop them from tilting and windmills. If they cant recognize useful info that deserves a proper critique or acceptance so be it.

• Anoneuoid says:

Oops. *its *tilting at

6. Joshua L Brooks says:

Another reason why, imo, this metric seems not close to comprehensive.

Many, many more people are getting ill from this disease than dying. Many of those who have gotten ill may well have their lives shortened as a result of complications from their illness. But that could never actually be measured.

What is the magnitide of years lost from the complications from illness compared to the magnitude of years lost from deaths? Since you font know, you might be significantly underestimating the actual years lost from this virusvv

• Phil says:

Joshua,
I’m not sure where you got the idea this metric (Years of Life Lost) is supposed to be ‘comprehensive.’ I don’t see it that way at all.

Since you want a comprehensive metric, I suppose QALYs — ‘quality-adjusted life years’ — might be closer to what you’re looking for: it attempts to take into account the loss of quality of life (e.g. if people develop long-term lung problems) in addition to just the number of life-years lost. I certainly wouldn’t object if people look at QALYs too; as for me I always sort of worry about the quality-adjustment and I’d rather see multiple individual numbers than have someone boil it down for me into a single number, but that might just be from not being familiar enough with the adjustment to really grok it.
If I did have to pick a single number I’d probably go with Years of Life Lost, on the assumption that the other bad outcomes more or less scale with it, but since I don’t have to pick a single number and in fact I’m comfortable thinking about several things at once, I’d rather see Years of Life Lost, and Deaths, and People with Permanent Lung Damage, and Weeks of Severe Illness, and a bunch of other stuff too, and if I want to combine it I will. But that doesn’t help you since you really want a single number. Take a look at QALYs, maybe that will do it for you. Twain (immediately below) has posted a useful and timely link.

• confused says:

I don’t think that is knowable yet.

There are reports of lung damage after recovery, and I’ve seen at least one report of heart damage after recovery, but those were media reports (not medical) so I don’t know how reliable, and they are all *shortly* after recovery. Is there evidence that these things are likely to be permanent or last years? I don’t know. Maybe no one does, since no one’s been recovered for longer than a few months.

7. Twain says:

Phil,

Nice work and thank you for taking the time to do this!

You may find the link posted in a previous post useful: https://avalonecon.com/estimating-qaly-losses-associated-with-deaths-in-hospital-covid-19/.

It provides another way of stratifying by comorbities (in addition to what Daniel states above) using Standardize Mortality Ratios (but you would have to find those tables…which seem to be proprietary to insurers from my searching).

8. confused says:

>>This is presumably an overestimate because the people dying of COVID-19 were probably already sicker (and thus set to be shorter-lived on average) than their same-age peers, although perhaps not as much as news reports might suggest: sure, most COVID-19 deaths of people over 80 are of people who have several “co-morbidities”, but most people over 80 have some health issues so it would be very surprising if that weren’t true.

I think the really big question here is, how much does *severity* of comorbidities affect a person’s risk from dying of COVID (assuming a certain age)? Yes, almost everyone 80+ has some comorbidity. But many of the things considered comorbidities are quite common conditions that people can live with for decades if well-controlled, and things like hypertension have a wide continuum of severity.

The huge proportion of total COVID deaths occurring in long-term care facilities does suggest that “patients of age group X who die of COVID” are likely to be much less healthy on average than “people of age group X in general”, even when X is very elderly.

• Joshua says:

confused –

Severity of comorbidities might be more informative than absolute number as you say, but even there you’re probably missing very important predictors like health behaviors (e.g., exercise it smoking), diet, race/ethnicity, SES, access to healthcare, where the person lives, what they do for a living, etc.

• intercostal says:

Sure.

Although I think some of the things you mention are basically different ways of getting at the same confounding factors: SES is probably just a proxy for access to healthcare, diet, and some other health-related behaviors (e.g. smoking prevalence) – how else could it affect health outcomes? Race/ethnicity is probably the same way, since US definitions of those categories don’t really line up with anything biological.

• You have to disentangle the fact that when you’re in a LTCF you are a sitting duck for COVID to spread rapidly with no way out. Whereas when you’re a 78 year old living alone at home in a single family home sheltering in place, there’s no sudden mechanism for you and 37 other people to all get this disease from each other in a period of 3 days.

The fact that LTCFs have been hit hard is due to *both* the higher risk of exposure, and the higher risk of mortality. It’s hard to disentangle those. But as we move forward, with more openness, more people will get exposed in “everyday life”… this metric can help us think about how the pandemic is proceeding. In fact, it’s fine for that purpose even if it doesn’t try to adjust comorbidity.

• Phil says:

• jim says:

I’m not sure LTCFs are a higher risk of exposure. They surely are a higher risk of *transmission* due to confined conditions. With respect to society as a whole LTCFs are walled communities and seem likely a lower overall risk of exposure.

But another factor affecting exposure in LTCFs is that they are commonly staffed by immigrants, also known to be hard hit apparently bcz they tend to live in larger families and smaller quarters. So there is an intersection of two segments of the population at high risk of transmission.

• Twain says:

My understanding is that, in general, LTCFs have sub-par sanitizing, HVAC, hygiene, etc., due to under-funding and under-staffing. As a result, once an infection enters the facility, it can proliferate (because of the many vulnerable hosts) unfettered. This can, in principle, increase the likelihood of increased routine exposure to virus.

Your point about immigrant-heavy staffing is also another likely source; especially since many of these staff work at 2-3 facilities (at least in my locale).

• Joshua says:

Twain, jim –

I saw a video with a heavy-hitter Swedish epidemiologist who largely tried to explain their high death rate at LTCFs on the fact that they’re largely staffed by immigrants.

Hmmm.

• jim says:

People that emigrate to Western countries often leave countries with low standards of living, and many of them have little education. Therefore, LTCF jobs, have low pay by Western standards, are attractive to immigrants because the pay is good by the standards of their home country and they are accessible to people with limited education.

They also have a tendency to live in larger family groups in smaller quarters, both because this is normal for them in their home countries and because it allows them to have a higher standard of living in their host countries. But it also dramatically increases the likelihood that infections will spread rapidly among them, and it’s probably part of the reason immigrant communities are getting hit harder than non-immigrant communities.

• jim says:

It may be that poor Westerners also work in LTCFs, but they don’t have the same risk factor for crowding up in home conditions as many immigrant groups because they’re adapted to a more spacious living conditions and possibly have more familial wealth to support them.

• Phil says:

I saw an article about a month ago about workers at Swedish LTCFs who were complaining that they weren’t being given the tools they needed to keep the residents safe: no gloves, no face shields, no masks. The article quoted staffers who said something like “We know how the virus is reaching these people: we are giving it to them. It’s a disgrace.” (That’s not a verbatim quote, it’s a paraphrase of what I remember). The article may have mentioned immigrant workers in the facilities, but if I did it wasn’t a major element of the article.

• Twain says:

Phil,

While it is likely that SARS-CoV-2 can transmit via air per clinical evidence, there is still much virology left to perform to determine *how* transmissible it is via air versus via surfaces.

• Twain says:

Whoops! Replied to the wrong comment. Meant to reply to “jim, do you have a source you can direct me to? All of the news reports seem to say you can easily get infected by touching an infected surface and then touching your mouth or eye…”

• Twain says:

Joshua,

I was using “immigrant-heavy” staffing to follow Jim’s phrasing. “Multi-LTFC-employed” would likely be a better adjective, since many of the staff working at multiple facilities are not immigrants, minorities, etc.

IMO, the problem depends much more on under-staffing and under-funding — well known issues that result in poor sanitation, resident infections, and delayed care.

It would take time, but you could stratify deaths in LTCFs by using the cost of living in said LTCFs as a proxy for quality of conditions/care; higher-cost LTCFs usually have higher-quality care.

• Joshua says:

Twain –

> IMO, the problem depends much more on under-staffing and under-funding — well known issues that result in poor sanitation, resident infections, and delayed care.

Bingo.

• jim says:

I’m surprised so many people are stuck on sanitation and cleaning as a method of preventing transmission. It can’t possibly be more than a marginal factor. The key factor is atmospheric concentration of virus. You can scrub and wipe nursing homes all day long and do little or nothing to prevent transmission of the infection. That’s why you have to isolate people.

Recently one of our hospitals here had an outbreak among staff. The key factor was improper social distancing in break rooms – ie, one infected person breathing in a small room with others present. The environment is plenty sanitary. So general sanitation is mostly ineffective.

This tragic misunderstanding is wasting immense resources on ineffective measures.

• Twain says:

jim,

I do not focus on sanitation alone. That is one among many issues with LTCFs that increase probability of severe outcomes.

LTCFs are rife with secondary-infections that residents can contract with COVID-19 that exacerbate their symptoms. LTCFs are under-staffed, which can lead to symptoms going unnoticed and thus denying crucial early care. LTCFs are under-funded, which means they may have been unable to purchase or stockpile necessary PPE and other equipment to mitigate transmission.

See here: https://www.kff.org/medicaid/issue-brief/key-issues-in-long-term-services-and-supports-quality/
And here: https://psnet.ahrq.gov/primer/long-term-care-and-patient-safety
And here: https://www.ncbi.nlm.nih.gov/books/NBK222681/ (from 1986 but many of these issues have barely improved, if at all)

• jim says:

Twain,

Yes, I’m sure all that is true. Many many issues are converging in LTCFs that make them off the charts for fatalities.

Anyway, I’m not claiming that sanitation has no effect. What I’m suggesting is that it isn’t effective against the primary mode of transmission.

• jim says:

Yes, I’m sure all those are true, but IMO the HVAC and small building confines are the most important of these.

I really don’t think this virus is significantly transmitted through surfaces. almost everything suggests it’s primary mode of transportation is aerosol, so the key element is being in room with an infected person, where the air volume is small and the rate of air replacement is poor, and the concentration of communicable particles in the air can rise quickly.

• Phil says:

jim, do you have a source you can direct me to? All of the news reports seem to say you can easily get infected by touching an infected surface and then touching your mouth or eye. I’m sure it is indeed possible to get infected that way, and it is clearly also possible to get infected by inhaling droplets containing the virus, but I have seen nothing quantitative about how many infections are due to one or the other of these routes. I’d certainly like to know more about it.

• jim says:

Phil,

Aerosol transmission is where the data very very strongly point, but it’s also generally accepted among many epidemiologists.

See this interview with Michael Osterholm, director of the Center for Infectious Disease Research and Policy at the University of Minnesota:

“This really is acting like an influenza virus, something that transmits very very easily through the air…in some cases just breathing is all you need to do”

My views are also influenced by John Barry’s exhaustive book on the 1918 pandemic. I accept Osterholm’s comments at face value because they agree so strongly with what I read in Barry’s book – and because it’s very sensible to me.

It’s fine that media are reporting that it can be contracted via surfaces. I’m sure that’s accurate. But it doesn’t mean it’s an major mode of transmission much less even a significant one.

For all I’ve seen and read it almost certainly can’t be very important for two reasons. First because surfaces allow transfer across distance, meaning social distancing policies wouldn’t be very effective if it was an important mode of transmission; and second just the simple numbers: it just wont’ transmit nearly as fast across surfaces as it would through the air.

• Joshua says:

Phil –

Good timing. Not what you’re looking for, but related info nonetheless.

https://www.nytimes.com/2020/05/14/health/coronavirus-infections.html

• jim says:

Joshua – yep, now imagine that one infected person goes to an apartment party with 25 people; they’re all in the same 2-3 rooms with 8ft ceilings and little ventilation (its’ winter after all) for 4-6 hours.

• Twain says:

Jim and Joshua,

Be careful to not over-simplify airborne transmission.

The term “airborne” belies a complicated process that can have high variance and depend on multiple factors: location of the infection (upper or lower respiratory track); viral load per droplet as a function of infection (e.g., does it vary between those who are asymtomatic or symptomatic); viability of viral load in droplet; humidity (droplets travel less far with increasing humidity), volume and circulation of ambient air in the location; and more.

I’m sure SARS-CoV-2 transmits through air. But the key is to what degree as a function of the above, and that seems TBD. This article provides a nice summary of the current situation: https://www.scientificamerican.com/article/how-coronavirus-spreads-through-the-air-what-we-know-so-far1/

• Joshua says:

Twain –

I was out for a hike and didn’t see Jim’s response ’till now. My first thought wast the single study syndrome.

• jim says:

Twain,

Great piece!

For me that confirms everything I’ve already discussed. Places with poor air circulation, small air volume, and larger numbers of people, and/or (in the case of the choir practice) people loudly vocalizing – have drastically higher transmission rates. That just screams aerosol transmission.

During the 1918 pandemic, there are documented instances of entire barracks contracting the infection in a period of hours. The only sensible way that can occur is via aerosol transmission.

The fact that it hasn’t been directly measured doesn’t bother me. it’s a difficult thing to measure. We don’t have virus alarms analogous to smoke alarms.

• Regardless of whether the facility itself is dramatically more at risk of an initial outbreak, once the outbreak occurs the people in that facility are at high risk of it sweeping through the facility rapidly. So, it’s like a person living in a log cabin in a dry pine forest vs a person in a log cabin in a damp meadow. Sure, maybe lightning is somewhat more likely to strike one place vs another, maybe its even more likely to strike the meadow by a factor of 2 or 3, but once it strikes the forest it’ll burn the entire dry pine forest to the ground… leaving the person there more at risk of fire than the meadow dweller who is less likely to be caught up in the spread.

• jim says:

“the people in that facility are at high risk of it sweeping through the facility rapidly. ”

Right. High risk of *transmission*. As best I can see transmission is a function of concentration in the atmosphere, not of presence in the atmosphere; we can all be exposed at home depot, but the concentration is low so we don’t contract the disease. OTOH in small buildings with poor circulation, people are much more likely to contract from a given exposure.

It’s a matter of properly understanding and representing the process.

Let’s change your analogy a bit. Lets have a community of log cabins and a community of Home Depot stores. If an infectious individual goes to the cabin community and spends 2hrs in one cabin then goes to the Home Depot community and spends 2 hrs in one Home Depot, which community is more likely to experience a rapid spread of the virus? both have been equally exposed.

• I don’t think both are equally exposed, but it’s clear we need some definitions of words to come to an agreement.

Normally, in industrial hygiene we’d define exposure as something like time integrated average concentration.

“The lead standards establish a permissible exposure limit (PEL) of 50 μg/m3 of lead over an eight-hour time-weighted-average for all employees covered. The standards also set an action level of 30 μg/m3, at which an employer must begin specific compliance activities, including blood lead testing for exposed workers.”

So very clearly, the family in the log cabin will get *much more exposure* to the virus than if the infected person wandered randomly around a Home Depot.

• jim says:

That definition definitely makes sense for aerosol. HOw would it work for the irregular exposure related to surfaces? You could have virtually no exposure all day then put your hand in a proverbial pile of shit – on a big droplet on a surface – and your exposure would shoot up. So highly discontinuous.

• Twain says:

confused,

> But many of the things considered comorbidities are quite common conditions that people can live with for decades if well-controlled, and things like hypertension have a wide continuum of severity.

+1. “Comorbidity” is a blanket term that often belies the variance between and within comorbidities. For example, the morbidity posed by controlled grade-1 hypertension is usually much less than uncontrolled grade-3 hypertension. But we don’t have fine enough data to ascertain exactly how severity of a given comorbitity correlates with severity COVID-19 infection (which is frustrating).

• Joshua says:

Somehow comment got eaten by ethernet.

Yes, severity of comorbidities might be more informative than the absolute number, but so we would so many other factors be important to consider relative to the impact of comorbidities on life expectancy, such as health behaviors (physical activity), diet, access to healthcare, race/ethnicity, employment, etc. Seems to me that each of them would need to be part of the calculation to make years of life lost a valid measurement.

9. Dr. Eric Wornhoff says:

The quality (value) of the lost years of life should be included. That can be assessed as is often done in psychology, by asking people to rate how they feel about something or other, in this case, the number years they expect to live in excess of the years they have already lived. A more economically oriented way would be to charge a fee for each extra year (which could be collected retroactively, after the excess years are consumed, assuming anything is left over. If nothing is left over, the corpse could be converted into cat food or some such, which should have some, albeit small, economic value. Surely no one would object to that. It’s not like depriving them of anything they’d otherwise have.) Social value could be evaluated by counting academic publications and blog posts/comments, etc. Or by having a panel rate the value of an individual’s social contribution (with an “expected future contribution value”, aka EFCV, extrapolated from that). As a proxy, net worth could be used. People who decline to think ethically should be lined up and shot.

10. Keith E. says:

This could be a useful gauge of the lasting human impact of the virus. Five years from now, ten years, how big of a loss will we still be experiencing, demographically? World war one killed off a substantial portion of European men aged 18-30, and that had large effects for many decades afterwards. This analysis might indicate that COVID’s effects will be more limited, mostly resolved within a decade. (The cultural and political impact might be longer-lasting.)

I’d like to see the curves for a different disease. Would cancer be very different? Traffic accidents would be.

• intercostal says:

Historical flu pandemics have had very little cultural and political impact, even the very deadly 1918-19 one (though it may have been somewhat overshadowed by the impacts of WWI). The ubiquity of social media and the current fraught political situation in the US and some other places may make this one a bit different, but those things may also mean a *shorter* cultural memory (we’ll all be on to the next big issue a year and a half from now).

11. David Young says:

Another perhaps more interesting number is months of equivalent expected risk of death. According to this, it ranges from a couple months to a couple of years. It’s based on Fergusons numbers which I believe are too high by a factor of at least 2.

https://medium.com/wintoncentre/how-much-normal-risk-does-covid-represent-4539118e1196

12. Joshua says:

Phil –

You might find this intersting.

–snip–

Findings In this study with a development cohort of 1590 patients and a validation cohort of 710 patients, a risk score was developed and validated to predict development of critical illness. We identified 10 independent predictors and developed a risk score (COVID-GRAM) that predicts development of critical illness. The risk score predictors included: chest radiography abnormality, age, hemoptysis, dyspnea, unconsciousness, number of comorbidities, cancer history, neutrophil-to-lymphocyte ratio, lactate dehydrogenase, and direct bilirubin.

13. Rick G says:

This is still an overestimate since E(years left | age, covid kills) < E(years left | age), i.e. the kind of person of age X who dies of COVID surely in expectation had fewer years remaining (in the absence of COVID) than the average person of age X. We can think of this in terms of comorbidities (and in the New York data they are dominant: https://www1.nyc.gov/assets/doh/downloads/pdf/imm/covid-19-daily-data-summary-deaths-05142020-1.pdf; or do we think that the marginal proportion of individuals with comorbidities by age in that data is typical of the population at large, by age?) or any unobservables that render one at greater risk for death by COVID *and* greater risk for other things that kill.

And y'all need to lay off Phil here. This is a totally reasonable line of inquiry, and the moral intuition that the death of a child or a young adult is more tragic than that of a nursing home resident is basically universal, so why shouldn't our quantification of this tragedy reflect it?

• Carlos Ungil says:

You’re right that the people who die of covid is, on average, not as healthy as the age-adjusted general population. Probably a worse health condition is correlated to higher exposure to infection and surely it will lead to worse outcomes. But comorbidity stats like those from NYC don’t really give us much information about that. Even if all of the deaths were in people with underlying conditions, one should consider that 85% of the people older than 65 have them (that figure includes also arthritis, which is not considered relevant in the NYC stats): https://www.cdc.gov/nchs/health_policy/adult_chronic_conditions.htm

• Joshua says:

Is treating comorbities and even # of comorbidities as some kind of uniform condition of limited value? It might average out, but the type and severity of comorbidities, and associated factors like health behaviors, access to healthcare, SES, etc., it seems to me, should be consideted as important moderators between comorbidities and outcomes.

• confused says:

Type and severity of comorbidities – absolutely, especially in elderly populations where having *no* comorbidities is incredibly rare.

I’d argue that SES is essentially a proxy for health behaviors + access to healthcare (the latter depending on what country/state is being discussed, and probably less important in the 65+ US population because of Medicare) in this case.

14. Björn Högberg says:

I don’t know of any American studies of this sort, but according to this study – Schön et al. (2016) “Rapid decrease in length of stay in institutional care for older people in Sweden between 2006 and 2012: results from a population‐based study” – the median (not mean) survival time (length of stay until death) for long term care residents in Stockholm, Sweden, was 595 days, or about 1.5 years. About 1/3 of residents died within six months. Assuming that there is some selection also within the population of LTC-residents, such that the most fragile are most likely to die, the expected years of life lost for this population is not very high, perhaps not more than one year.

According to official statistics – https://www.socialstyrelsen.se/globalassets/sharepoint-dokument/dokument-webb/statistik/statistik-covid19-avlidna.pdf – LTC-residents constitute 48 % of Swedish Covid-deaths so far. Non-institutionalised with public assistance (for cooking, cleaning, hygien etc.) constitute 25 % of deaths (I don’t have any data on life expectancy for this population).

Btw, I’m not advocating euthanasia of old people, and I am rather critical of the current Swedish policy. But I think it is important to put this in perspective. Current guidelines for public policy in Sweden (Should we subsidize this drug? Should we reconstruct this road to reduce accidents?) state that one year lived in good health is worth about 1 million SEK (around 100 000 \$). The UK use similar numbers.
Now, decisions regarding infectious disease pandemics are not directly comparable to decisions regarding infrastructure investments, but with limited resources no government can put an infinite value on life, and expected life years was already before the Corona pandemic one metric that governments consider when designing policy.

15. Joshua says:

Phil –

I don’t know if you can get past the inane notion that you can just calculate the “cost” of lockdowns by calculating GDP loss (as if there would be no losses from a raging epidemic w/o “lockdowns”), you might find this interesting:

> First the costs. The ultimate dollar value of costs will eventually be relatively easy to calculate. Until then, rough estimates are the best numbers available.

[…]

> But all such benefit claims remain doubtfully based on an equation linking two artificial constructs: Total benefit = number of lives saved x value of a life. The Value of a Statistical Life, while accepted in official circles, remains uncomfortably high through many age groups. The Chicago economists even broke down the average estimated value of each statistical life saved by age. A 12-year-old has a statistical value of US\$15.3 million, a 40-year-old \$13.8 million, and a 77-year-old libertarian columnist would have a value of \$3.7 million.

• Dale Lehman says:

If you follow the link, you will see an interesting debate between Viscusi (one of the leading value of statistical life economists) and Broughel (a more conservative free-market type economist). Non-economists may not realize the underlying tension between these two schools of thought. In places where values of statistical lives are usually applied (environmental policy, occupational safety standards, and now COVID), the numbers get very large. Broughel’s critique represents a view (which he does not state – so I am reading into it, perhaps incorrectly, but I suspect not) that a more societal view would reject these high values (consider his example of the potential value placed on the last 2 months of an elderly person’s life – very high to the individual, perhaps not to society).

I submit that the debate is really about the results, not really the methodology, although it is couched in terms of the latter. I am suggesting that economists argue about methodological issues associated with the value of a statistical life because they have different priors on whether the value should be large or small. Then they score methodological points according to these views they already hold.

I am not against valuing statistical lives. The exercise can be informative and the methodologies are interesting. But to the extent that these debates are merely playing out prior beliefs that the values are large or small, they are a diversion from what is essentially an ethical question. What I object to is transforming an ethical issue into a technical issue. Just imagine that the methodological arguments could be settled persuasively (this includes things like marginal vs non-marginal changes in risk, external costs/benefits, appropriate use of market wages, etc.) – would you really want that to dictate decisions we make on how much we should shut down the economy to limit the danger of COVID?

If you are uncomfortable with that dictating the policy, then I’d suggest that there are ethical considerations that transcend such calculations. I don’t know how we should address such messy issues and I have no particular expertise in doing so. But I think the first step might be an acknowledgement that policy may be more than an issue of cost-benefit analysis. Perhaps even philosophers might have something to contribute to the discussion.

• I fully agree with you when you say “I am not against valuing statistical lives. The exercise can be informative and the methodologies are interesting. But to the extent that these debates are merely playing out prior beliefs that the values are large or small, they are a diversion from what is essentially an ethical question. ”

There can NOT be a “one true objective value” of a life year. It is *inherently* a value decision. One needs to argue for why the chosen valuation method is the right one, and this is an ethical argument, NOT a technical one (though I guess what it comes down to is a mixture of ethical and technical, like “this technique is the ethical one to use for x reason”)

• Martha (Smith) says:

+1

• Joseph Candelora says:

Personally, I think the “right” answer is for each individual to develop their own rating of the value of life at each age and level of illness, and use that against expected/observed death toll to render a judgment on the cost in terms of death. I think if we did that, we’d get something much closer to a unity weighting than we would to a life-year weighting, given that I think most people see any death as a tragedy regardless of other considerations, whereas I don’t think they see a year lost in the same terms. But of course it would vary substantially across each person. So while imperfect, I think the better default is simply death count because it’s easy to calculate and correspondingly easy to understand and to convey.

If I read Dale correctly, he’s cautioning against getting too caught up in the technical details of one valuation approach vs another, out of concern that if we make that our prime focus, then we can feel once we’ve “solved” it and gotten the right metric, we no longer have any responsibility to the ethical considerations. A fair point.

• Joshua says:

Daniel –

> I am suggesting that economists argue about methodological issues associated with the value of a statistical life because they have different priors on whether the value should be large or small. Then they score methodological points according to these views they already hold.

I certainly wouldn’t single out economists in that regard. Seems like pretty much the human condition to me. What I try to focus on is the extent to which people accept what you describe as a baseline condition, and take then steps to mitigate the pattern. Of course, there are significant limitations to how much any of us can mitigate the patter. However, IMO, transparency is the key issue there. To the extent that someone is transparent about that process, they can get feedback.

> But to the extent that these debates are merely playing out prior beliefs that the values are large or small, they are a diversion from what is essentially an ethical question.

That is very consistent, actually, with what I have been trying to argue on this thread. Except I don’t actually think of it as an ethical question – but as an operational values question can be largely predicted by (but not caused by) political ideology.

> would you really want that to dictate decisions we make on how much we should shut down the economy to limit the danger of COVID? […] But I think the first step might be an acknowledgement that policy may be more than an issue of cost-benefit analysis.

What you describe there is why I’ve been asking how people see specific ways to use YLL calculations to make decisions. I’m kind of scratching my head here because as near as I can tell we are much less far apart than how it played out in the discussion?

• Dale Lehman says:

I think you have confused Dale and Daniel, so perhaps you don’t need to scratch your head.

• Joshua:

Here are just a few things you could do if you had a decent LYL metric:

You could ask whether it makes sense to use young people as “soldiers” in the fight against COVID-19, as is being done in Israel…. perhaps we should encourage young people ages 20-30 to go get the virus, and then after recovering, go back to work, and also donate a lot of blood for serum… we could create a kind of “health corps” or something.

But, if COVID has a lowish death rate but turns out still relatively high LYL among the young. this might be a terrible idea.

You could track whether as we reopen the deaths are going down but the LYL are going up… so perhaps things aren’t as rosy as people seem to think because of the decline in deaths.

You could look at the impact on health care workers to see if LYL among them is outlandishly higher, to see whether PPE is actually working well for them, or perhaps we’re fooled by the low incidence of death.

etc etc

• Joshua says:

Daniel –

> But, if COVID has a lowish death rate but turns out still relatively high LYL among the young. this might be a terrible idea.

Ok. So I accept that could be a use. And that’s helpful to some degree to see that described. And I don’t have any particular ethical problem with it if that’s what a given society chooses to use as a rationale.

But…

My guess is that it might seem like a terrible idea to send young people out as COVID warriors if you accept the LYL metric as a means to make decisions, but that in the real world most people wouldn’t utilize that metric.

Already, there seems to be a lot of momentum towards having younger people take on more risk under the assumption that they’re less likely to die or get seriously ill. For example, Trump today was talking about how older teachers should be staying home and letting younger teachers work in the classrooms. I just think that there is a very tiny % of people who wouldn’t buy into that logic that Trump was using.

> You could track whether as we reopen the deaths are going down but the LYL are going up… so perhaps things aren’t as rosy as people seem to think because of the decline in deaths.

Yeah, you could – but I think that it wouldn’t play out that way, because of the values that people bring to the questions that won’t conform to calculation. Of course, I could well be wrong, but I seriously doubt it. And I, for one, even if I were inclined to see it on paper that in the long run in terms of years lost it would make more sense to put the older people in the classroom, wouldn’t go along with it because essentially, I don’t accept the implicit value orientation that a simple calculation of years lost is a good basis on which to assess value. For me, it’s way to messy.

16. Joshua says:

Sorry – I got confused… I thought Daniel had written that comment and actually it was Dale. And that, actually, clarifies my earlier confusion as to why it seemed that “Daniel” and I were so far apart.

17. Joshua says:

A general question for the blog (hoping that I don’t trigger any trip wires).

It seems to me that people here use the term “prior” in pretty much the same way as I would use “bias.” Now I guess that there’s probably a technical distinction between the two terms, but in a more practical or conversational sense I’m wondering if there’s really any conceptual difference? Maybe it’s just more of a semantic difference?

• Zhou Fang says:

Bias has negative connotations (being generally connected with error), but more importantly prior can capture a sense of honest uncertainty. Like if I really don’t know about a quantity, my prior could be flat within a certain range or whatever.

• confused says:

I think this is the difference, yes.

For example, if I see a scientific result published that seems to contradict tons of known data/well-established principles (faster than light neutrinos for example), I’m going to expect really good-quality data to back that up.

(And I think prior is more of a Bayesian thing vs. frequentist. For example p < .05 by itself isn't going to convince me if you've claimed to disprove fundamental principles that have been supported by hundreds of experiments…)

It's kind of the principle of "extraordinary claims demand extraordinary evidence" – but how do you determine what's "extraordinary", and thus avoid that principle becoming just an argument from incredulity? I think that ideally a prior is based on known data, whereas a bias is more emotional.

But I'm not a statistician, so I could be a bit off.

• Martha (Smith) says:

confused said: “(And I think prior is more of a Bayesian thing vs. frequentist….)

Yes, “prior” is an important concept in the Bayesian approach to inference. A very brief summary to give the vague idea if you’re not familiar with it: In addition to being based on specific data, the Bayesian approach incorporates a “prior distribution” which tries to describe (based on previous information — hence “prior”), and combines data plus prior (via Bayes’ Theorem) to obtain a “posterior” distribution that takes into account both the data and prior information.

• Joshua says:

I once read a climate “skeptic” paper where he kept talking about “objective priors.” And my first thought was “bullshit, that’s an oxymoron.”

Reminded me of when judges on SCOTUS talk about interpreting “original intent.”

• No, an objective prior is NOT an oxymoron.

Objectively, my prior for your height is that the only region of height space I need consider is between say 2 and 13 feet.

Is it objectively a fact that *essentially every adult* is between 2 and 13 feet? Yes.

• Zhou Fang says:

It is however a subjective choice to argue that these are *all* you truly know about this, to assert that it is equally as likely for someone’s height to be between 2 and 3 feet as it is to be between 5 and 6 feet.

• Zhou Fang says:

Perhaps in some cases this claim is relatively harmless. But in some analyses it absolutely is not. The technical consequence of all of this is that trying to find a truely “objective” prior can be a much more complicated and risky endeavour than using some reasonable weakly informative one.

• Joshua says:

With the understanding that my technical understanding is nil…

And that my colloquial usage reflects my lack of understanding…

My previous exposure to the term of “objective prior” was when it seemed to me that someone was trying to use that technical term to avoid the subjectivity of their prior. And actually, some technical folks argued as much.

With all of that, you say:

> Objectively, my prior for your height is that the only region of height space I need consider is between say 2 and 13 feet.

>> Is it objectively a fact that *essentially every adult* is between 2 and 13 feet? Yes.

Yes, it is objectively a fact. It is also a prior that is built on your experience in the world. Someone else might have a different experience. Say if they lived in a village where no one was over 5′. Then they would say that it’s an objective fact that my height is between 2′ and 5′.

So lately I’ve been working on incorporating an understanding of how two things that seem mutually exclusive can both be true.

But mostly I was just talking about a colloquial usage…where it seems to me that the notion of an objective prior is an oxymoron because our priors are necessarily built upon our life experiences and our observations over our lifetime.

And it annoys the hell out of me when I see situations like judges on the SCOTUS ignore the subjectivity of their “priors” to argue that they are objectively true.

I think that Zhao captured well what I was going for, within a colloquial framework:

> The technical consequence of all of this is that trying to find a truely “objective” prior can be a much more complicated and risky endeavour than using some reasonable weakly informative one.

• Andrew says:

Joshua:

I use “prior” in pretty much the same way as I use “model,” as representing a set of mathematical assumptions which, when combined with data, yield inferences.

• Joshua says:

Andrew –

I was thinking about what Zhou wrote above. It’s funny because I don’t think of bias as having a negative connotation. I think it’s because I’ve been very focused on “bias” and motivated reasoning for a long time and view it as a basic human trait. I frequently say that I have a “bias” abut something to basically mean that I have an opinion about something that I recognize must be subjective and affected by my “motivations.”

But sure, I also recognize that bias in the common vernacular has a negative connotation.

• Curious says:

I would argue that bias is exactly opposite to prior in that bias moves inference away from reality and a prior is intended to move inference closer to reality.

• Curious says:

** In combination with modeled data that is.

• Joshua says:

> bias moves inference away from reality

I get that’s a common usage, but that’s just not how I think of bias. I think of bias as recognition that an “reality” is necessarily rooted in opinion and perspective.

• confused says:

I’m not sure I see that – at least in the physical sciences, where objective reality is what it is, and our perspective may give get in the way of determining what it is, or may give us insights into what it is, but can’t change what it is. (Except indirectly, in the sense that our perspective can affect our actions which can actually change the state of things.)

Social science, policy, etc. of course is different.

• Joshua says:

confused –

See above, my 7:45 comment.

• confused says:

Ah, ok, if you mean our *knowledge of reality* is rooted in perspective, rather than *reality itself* being shaped by perspective, I can certainly agree with that.

I do think there is still an important difference — again, at least in the physical sciences — between a prior based on previous empirical knowledge, gathered in at least an attempt to objectively observe reality, vs. a personal bias based largely on emotion, anecdote, confirmation bias etc.

It’s more two ends of a spectrum than two radically different things, though… obviously personal bias does tend to creep in.

18. David Young says:

I really think Phil, that there is very little solid evidence on years of life lost. Ferguson says that for most age groups covid19 deaths would be roughly 6 months to 2 years expected morality risk. If we divide by 2 for Ferguson’s IFR being too high, that’s 3 months to a year excess mortality. However, especially for those over 80, 8% are going to die within the year. If covid mortality is 8% and if those who are seriously ill are vastly more affected, then one could argue that indeed most of the fatalities are among those with a limited life expectancy. Using the average life expectancy of this group does not take account of the differential risk.

But we need better data to put some real numbers to these effects.

• Phil says:

Agreed that we need more data and better data.

I don’t think I’m following exactly what you’re saying. If the suggestion is that the average death only costs 3 months to a year of life lost, that seems really low to me, I don’t think the low end of this range could be right and even the high end seems probably too low. This story https://www.nytimes.com/interactive/2020/04/10/upshot/coronavirus-deaths-new-york-city.html is quite old now, updated figures would show even more mortality in New York (indeed a lot more); unless the death rate dips way below normal for the coming months, New York is going to have way more excess deaths this year than is consistent with old people dying 3 or 4 months early…and it’s not like every old person in New York was infected. Also, we know the disease has killed some seemingly otherwise-healthy young people, and it would be odd if it weren’t capable of killing otherwise-healthy older people in even larger numbers.

The ‘years of life lost’ estimates that I calculated are probably too high, but I don’t see how they could be too high by the magnitude I think you’re implying.

• Carlos Ungil says:

What he says is that, roughly,

if you are 50: your probability of dying in one year is 0.5%, your probability of dying if you get COVID-19 is between 0.25% and 1%

if you are 80: your probability of dying in one year is 10%, your probability of dying if you get COVID-19 is between 5% and 20%

• Carlos Ungil says:

I was too lazy to look it up before, but now that I’ve seen a mortaility table, the second example would be more like

if you are 80: your probability of dying in one year is 5%, your probability of dying if you get COVID-19 is between 2.5% and 10%

• Zhou Fang says:

He’s misquoting. The original statement is that a covid *infection* is about a year’s worth of risk.

• David Young says:

I think Phil that Carlos’ numbers are about right based on Ferguson’s age cohort IFR’s and expected mortality statistics. It all hinges on your assumption that those who die from covid actually had the average life expectancy of their age cohort. That seems quite wrong to me. We know those who are seriously ill and likely to die in the short term are also much more likely to get very ill if they get covid. Those who are healthy have a much bigger margin in lung function and other measures to be able to survive covid. This is already true for other infections. 380K will die in US nursing homes from infections in a normal year (out of 1.3 million residents). About 440K die each year of all causes.

• Zhou Fang says:

No, the assumption is that people die proportionate to their non-covid death rates. So if you are a 60 year old with a death probability of 0.9%, you now have a 1.8% chance of dying, if you are a health 60 year old with a death probability of 0.1% (these numbers plucked out of a hat), you now have a 0.1% chance of dying etc.

• Phil says:

Ah, I had misunderstood the original estimate, or maybe it’s a cognitive error on my part to not recognize that “a year’s worth of risk” is very different from “shortening life by a year.” I’m not really sure how to think about a year’s worth of risk, but I will try thinking about it and see where it gets me!

• confused says:

Yeah, I can’t really see it being less than 1 year even in places like Massachusetts where well over half the deaths are in LTCFs.

I *would* expect the death rate to dip below normal for a while after the pandemic is over in really hard-hit places … except that missed cancer treatments, etc. might raise it enough to counter that effect, or more.

19. Alex says:

Does anyone know if you can get the distribution of life remaining instead of just the expected life remaining (as a function of age)? I.e. Prob(lives exactly T more years | person is age A right now) as a function of both A and T. Is this published by the gov in some form?

• Carlos Ungil says:

This gives probability of dying at every age https://www.ssa.gov/oact/STATS/table4c6.html

From those numbers it’s easy to calculate the probability of surviving from age A to age B.

• Brent Hutto says:

I believe Alex wants the entire distribution of survival times, conditioned on a specific age. Not just the probability of dying in an age range.

That’s probably going to be hard to find in the general public health or epi literature but perhaps some actuarial reference provides it.

• Carlos Ungil says:

He asked for Prob(lives exactly T more years | person is age A right now) = Prob(dies at age A+T | person is age A) = Prob(dies at age A+T| reaches age A+T) Prob(reaches age A+T | person is age A) = Prob(dies at age A+T|age A+T) (1-Prob(dies at age A+T-1 | age A+T-1) … (1-Prob(dies at age A+1 | age A+1) (1-Prob(dies at age A | age A)) and all the required probabilities are on that table.

• Carlos Ungil says:

A couple of parenthesis were missing, but I think the idea is clear:

Prob(dies at age A+T|age A) = Prob(dies at age A+T|age A+T) [1-Prob(dies at age A+T-1 | age A+T-1)] … [1-Prob(dies at age A+1 | age A+1)] [1-Prob(dies at age A | age A)]

• Sort of… you’re assuming a stationary survival curve. But as technology and medicine have advanced, the shape of the curves has changed through time.

Like for example think of the probability that a person born in 1900 lived to age A vs the same curve for a person born in 2000

• Carlos Ungil says:

Any calculation requires assumptions, of course. One reasonable way to estimate the probability that a 65 years-old has of reaching 75 is to assume that his probability of dying at 66, 67, 68, 69, 70, 71, 72, 73 or 74 (given that he reaches those ages) is the estimated probability that a 66, 67, 68, 69, 70, 71, 72, 73 or 74 years-old has of dying today.

For example. from the link I sent: “Note: The period life expectancy at a given age for 2017 represents the average number of years of life remaining if a group of persons at that age were to experience the mortality rates for 2017 over the course of their remaining life.“

But I don’t think a calculation based on historical cohorts will give a better answer to the question that was asked.

• Phil says:

A stationary survival curve seems like a good start. Carlos is right, obviously, that any calculation requires assumptions: empirically there is no way to know the distribution for anyone who is alive right now, because all of their future is unobservable.

I only learned a few years ago that the official ‘life expectancy at birth’ is calculated by assuming that someone born today has the empirically determined probability of living until age 1 (based on the most recent cohort of children to reach age 1); then the probability that, if they are still alive, they will live to age 2, is determined from the most recent cohort of children to reach age 2; and so on.

20. Patrick Heuveline says:

Thanks for this, this is really interesting. Relatedly, my colleague Mike Tzen and I have calculated a related indicator: decline in life expectancy at birth. This requires a benchmark life table so we took projected life tables for 2020 in a number of countries from the UN and IHME projections for the same countries.
Our result for the U.S. is -.6 year, which is quite compatible with your estimate of 12.5 years of LL on average: as a first approximation, the decline in life expectancy at birth would be that LL average times the ratio of covid to total death. The IHME projections (up to August 2020) amount to roughly 5% of the annual number of deaths in the U.S. (about 150,000 to about 3M).
This approximation is only valid under stationary conditions that are not met, but it still works pretty well (.05*12.5 years v. .6 year)! You can find more about our estimation approach here:
https://www.medrxiv.org/content/10.1101/2020.04.29.20085506v2

21. Alexander Palti says:

I have some surprising statistics for you. A lot of COVID-19 deaths happened in Europe this spring. I tried to compare the average age of death for COVID-19 victims with the Life Expectancy at Birth for the same country. For example, Netherlands:
https://en.wikipedia.org/wiki/COVID-19_pandemic_in_the_Netherlands
There is a table with all deaths until May 12, partitioned by ages, every 5 years. What is missing is average age for every period bracket. For the 266 cases over age 95 I supposed crowding close to age 95, so the average I considered is 96. For 90-95 ‘ I considered average 92, closer to lower limit, a.s.o.
The average age of COVID-19 fatalities is:
(96*266 + 92*724 + 87*1224 + 83*1162 + 78*943 + 73*573 + 68*301 + 63*148 + 58*90 + 53*40 + 48*20 + 43*5 + 38*7 + 33*3 + 28*3 + 18*1)/5510 = 81.53
The average Life Expectancy at Birth in Netherlands is 81.7 years. So, the life expectancy was shortened by 0.17 years, about 2 months. Unless the COVID-19 victims were a special category of people, with higher life expectancy than average, the data suggest most victims were close to their life expectancy. Diabetes, blood circulation problems, hyper-tension are probably not prerequisites for a longer than average life span, but they are said to conduct to a larger percentage of COVID-19 deaths. So, the result is very surprising. More than this, other countries exhibit exactly the same pattern. You may look at Germany, with age brackets of 10 years, with 50 COVID-19 victims over age of 100. A similar computation for Germany:
(101*50 + 93*1496 + 85*3688 + 76*1844 + 66*761 + 56*279) / 8216 = 80.77 years , average age of illness fatalities , compared to 81.1 years life expectancy. You may look also for Sweden:
https://experience.arcgis.com/experience/09f821667ce64bf7be6f9f87457ed9aa
“Avlidna” means death in Swedish.
As source for life expectancies I used:
https://www.cia.gov/library/publications/the-world-factbook/geos/nl.html

22. Like a lot of studies you take the average YLL and then apply that to COVID fatalities with 2.7 comorbidities with average age 80 (UK), with a caveat that of course it could be a bit lower. The CDC now has a best estimate of IFR of 0.26% so 99.74% infected survive – its difficult to link that figure with idea that average YLL is about right. You need to know about severity of comorbidities to say something sensible about YLL, but given very high survival rate even amongst elderly it seems safer to assume YLL will be well below average for those tragically dying of COVID-19.

23. Dr.Bob Meek says:

I think the years of life lost is a very important concept. In the trauma world it has been used for years. The thought is that more years of life (usually productive) are lost due to trauma than to heart disease and stroke combined. With the surge in cases in Florida, Texas, California and other states, there can be a false sense of security because raw the death rates might not rise or even could go down compared to the ‘bad old days in March/April”. It is relatively easy to lock down the old folks homes and to save the old folks by having the personnel be careful, use PPE, restrict visitors etc. However, if at the same time there is a surge in cases among young people and some of the 20 -40 year olds die, as they will, then the loss of years of life will still be very high and could surpass that of the bad old days even though the raw death rate is lower. For instance, the loss of life of a 20 year old might give a number of years of life lost of 64 years, it would take the loss of 32 82 year olds to have the same 64 years of loss of life. The death rate would look very good if all those 82 year olds were saved (which, of course is a good thing). There would only be 1 death (the 20 year old). The death rate would be 1/x instead of 33/x. The years of life lost change would be 64/x as compared to 128/x and this wouldn’t look as impressive.