The Symmetry Error - are the benefits of healthspan extension offset by extended disease-span?

Simply put, the erroneous symmetry assumption is that lifespan extension merely delays aging, hence it will not benefit the economy or reduce the net burden of disease and suffering to society. This makes intuitive sense if we think about it, under most assumptions an extended lifespan (and healthspan!) means you will be younger for longer and older for longer. A longer healthspan implies a longer "disease-span" as well.

The symmetry error is closely related to the Tithonus fallacy. Many people imagine that an extension of lifespan only leads to more time spent old and ill. The main difference is one of degree. While the Tithonus fallacy claims a net negative effect or outright inefficacy of lifespan extension efforts, the symmetry error merely suggests that the benefits are zero at worst and at best offset by extended "disease-span". Both imply that the benefits of lifespan extension are not as large as expected.

Tithonus was a Trojan prince in Greek mythology, son of King Laomedon of Troy and the water nymph Strymo. Eos, the Titan goddess of dawn, kidnapped Tithonus along with Ganymede, in order to make them her lovers. She then asked Zeus to grant Tithonus immortality, but did not think of asking to grant him eternal youth too. As a result, Tithonus aged and did not die, resulting in his strength wilting away to the point that he could no longer move his arms.

Source: &

Usually, the Tithonus fallacy will be committed by laypeople and our political enemies (e.g. bioluddites and primitivists), whereas the symmetry error is likely to be encountered with experts and policymakers, who are not well versed in biogerontology.

With this post I do not want to single anyone out and, if anything, I am happy to be confronted with some (snide) remarks that challenge me to blog again. I've had a bit of a writing dry spell recently! I would say this post on twitter is pretty run-off-the-mill and a good starting point (15):

TL;DR abstract
Delaying aging saves money under most assumptions, even relatively conservative ones. This is not settled science but I would defend it as the strongest hypothesis available. The reasons are as follows. Delaying aging will likely lead to "compression of morbidity" into later life stages, thus reducing healthcare expenditure. Delaying aging is more efficient than delaying cancer, cardiovascular disease or diabetes and this is known as Taeuber's paradox, because "if one does not kill you, the other will". Even if we "just" delay the burden of age-related disease we gain a lot because today's dollar is worth more in the future and because we will have better treatments for those diseases in the future! What is more, in a society with more old people and adults, more people are working in their prime rather than being replaced by children undergoing costly training and education (dependency ratio); and fewer people, at any point in time, are attending funerals and mourning their beloved ones. That does not even begin to cover the ethical aspects, as once we value human life, we are obliged to extend it.

What are the benefits of lifespan extension? What do we mean when we use the word benefits?
The importance of shortcuts (rambling introduction)

  • The dependency ratio
  • Is there symmetry in lifespan - "disease-span" extension?
  • Compression of morbidity - the taxpayer's magic potion?
  • The bereavement quotient
  • Taeuber's paradox does apply
  • Extending the QUALY concept to aging
  • Compound interest and opportunity cost 

Key References & Notes

What are the benefits of lifespan extension? What do we mean when we use the word benefits?
The cost to the tax payer is not a good standard because it is entirely dependent on the pension system and totally malleable. If people live a healthier life, then they can work somewhat longer, because they are able to do so. We should definitely think bigger, perhaps in terms of world GDP and total, net human well-being. Not easy to measure, not easy to define the impacts, but certainly on the right track. So let us ask if delaying aging is a net-benefit to world GDP, how it would affect disease burden and overall human well-being.

The importance of shortcuts (rambling introduction)
The problem is too difficult to understand completely, too complex to discuss thoroughly without using some heuristic, some intuition. Personally, I believe developing said intuition is extremely beneficial both for us aging researchers, policymakers, and other experts, as well as for interested laypeople. I sincerely hope people can think more deeply about this topic, point out additional issues and engage in constructive debate. 

When you extend lifespan you are changing the age pyramid and the demography of the whole society which is a dynamic process. This would have to be considered if we wanted to build a complete model. Even if we revert to "just" looking at a single life or rather lifespan, it is hard. We have to ask at each age, what are the costs and benefits to society? What about the individual? When is a life worth living? (We are even touching on the freedom of medically assisted suicide here and the question of happiness; are people alive happy to be alive and thus life years gained are per definition a boon?)

Remember, given lifespan extension you will spend more years being 80 years old, while being biologically younger than 80 years; you will have less mid-life diseases (e.g. hair graying, hair loss, wrinkling, obesity, etc.); maybe you will be even healthier in your 30s (hello joint diseases!); you will spend more years suffering; more years loving, enjoying, dancing, drinking and carousing. You will be able to spend more time with your loved ones, your parents, your spouse, your children and siblings -- and you will attend fewer funerals every year!

Philosophically we may agree that the freedom to live longer and healthier is close to an absolute good (7); but this is not the question we want to address here, although this freedom too should contribute when we tally the quasi-monetary benefits and disadvantages of lifespan extension.

To gauge the benefits of lifespan extension we could look at the biologic models we have. We can draw some lines across those beautiful survival graphs (of mice being dose with lifespan extending drugs) and estimate how long they might spend in good health, but it does not tell us the whole story. Do mice translate to men, translate to women? Many people pre-retirement are unhappy and a net-burden to society, whereas many 70-year-olds are productive, working part-time jobs, enjoying their hobbies, caring for their grandchildren or some such.

What is more, strictly speaking the experiment has never been conducted. We do not know if we will be able to extend human lifespan without trying it. An alternative to running the experiments is to use standard epidemiologic and actuarian arguments; extrapolating known trends, which we will also do later in this blog post.

It is difficult, nevertheless, people have tried to pinpoint the benefits of lifespan extension and I will point out a couple papers that made such an effort. Apart from this, we will develop a general intuition for this issue using naive toy examples and arguments 'from first principles'.


The dependency ratio
A society with extended lifespan would undergo a shift towards an improved dependency ratio. This can be easily visualized in an extreme example, but the math should scale proportionally (albeit with some diminishing returns). So, if we magically add 10% adults and 10% sick elderly to a population symmetrically - thus the elderly people are "consuming" the economic output of the adults - we as a society still gain, because we have 1 more adult that is not dead at this stage; and thus does not "have" to be replaced with a child that will first study for 15-25 years before they can give back to society! (8)

Figure. Developing a rough intuition for changes in the dependency ratio based on the German age pyramid. The intuition here is that healthy lifespan is increased by a fixed factor and so is the lifespan spent in frailty. This makes at least some sense since in many animal experiments both mean (mostly healthy) lifespan and maximum lifespan are extended by 10-30%. In contrast if we assume that lifespan and healthspan is increased by a constant then the DR increases and converges to 1, but even this conservative scenario can be beneficial because population aging is delayed into the very far future (9).

We can also look at a different toy example. Imagine a dystopian society with a life expectancy of 20 years (maybe the HIV/AIDS pandemic got out of hand in this parallel universe?). In this society people study for 15 years, work five years, then die relatively quickly. If we could double lifespan, did we not gain anything because we just delayed their death? No, years worked went from 5 to 25, i.e. increased five-fold because the person did not have to be replaced by a child! Humans are beautiful and precious.

With the world getting ever more complex and education being more important than ever, every human is becoming more precious and harder to replace, further favouring long lives instead of human turnover. (This is more as a side note since I doubt the effect is huge.)


Is there symmetry in lifespan - "disease-span" extension?
This is crucial and where I would concede several points to the critics. Most of the benefits of lifespan extension can only be realized if, at worst, the extension of healthy lifespan and diseased lifespan is more or less balanced. Unfortunately, we do not know for sure whether this is the case and we cannot possibly know without running the experiment. However, we can develop a good intuition based on the biology of aging.

First of all, it is impossible to live much longer without also extending healthspan. A minor increase in lifespan may be possible** at the cost of healthspan but still very unlikely. A major increase is basically impossible. It is the age-related diseases that cause both death and morbidity after all!

(** To give a real-world example: I recall the notion that women live longer than men but often at poorer health. See note 12.)

So what does our knowledge of the biology of aging tell us? We already have elite survivors with a 10-20% extended lifespan, mostly due to genetics. These can serve as a model to study to question whether healthspan or disease-span is disproportionately affected. Research on long-lived people reaching 100 years of age and older, termed centenarians, has generally shown that they are also much healthier than average. While this could be some sort of statistical quirk (some form of survivorship bias), this seems unlikely because even centenarian offspring tend to be healthier on average than normal people.

Figure. from Ref 2. showing percentage of life with disease; Andersen et al. 2012. Cent=centenarian (100+), Nonag=nonagenerian (90+), semi=semi supercentenarians (105+), Super=supercentenarians (110+).  Caveat emptor, be aware. I am not an expert in this field, but at first glance other work tends to support this study. Centenarians often suffer from poor health, however, at the same age as "normal" people they have exceptionally good health.

Apparently I am not the only person who thinks this way (Sebastini et al. 2017):

...substantial progress has been made in the epidemiology of extreme human longevity, particularly regarding evidence supporting Fries’s “compression of morbidity” hypothesis in oldest centenarians (Andersen et al., 2012, Fries, 1980, Sebastiani et al., 2013a, Ismail et al., 2016) 

From mouse experiments, we know that most treatments extend mean lifespan, while failing to extend maximum lifespan. This is considered an extension of healthspan, aka, "squaring the curve" or compression of morbidity -- and would be extremely cost-effective. However, bona fide life extension treatments could behave differently. I thought it would be cool to check if our intuition as aging researcher is correct with a little experiment. The intuition is that median lifespan is more amenable to extension than maximum lifespan (3), hence the time spent in bad health should decrease.

Looking back at the seminal publications on rapamycin lifespan extension in UM-HET3 mice (e.g. Miller et al. 2010) we can see the following pattern. If we define "morbidity" as area under the curve after the cohort/treatment specific median lifespan. Females spent around 7% in this morbid state, with or without rapamycin. In this study, male mice responded less robustly to rapamycin and spent around 8.5% of their lifespan in the morbid state and around 11.4% after rapamycin treatment. This finding is consistent with "eye-balling" the lifespan curves. Of course surviving above the median lifespan does not necessarily mean morbidity, as we have seen with the centenarian studies above.

I will have to say, and I also found this the last time I did research on the issue, there is not enough data on this topic. At least not as much as I would like to have, in order to fully address the claims of the critics. For our little experiment, I went down the rabbit hole of measuring lifespan curves to guesstimate time-spent-morbid so you do not have to. As expected, the data suggests that the rapamycin result in males is an outlier and not the norm. Usually even the better treatments / interventions, i.e. those that actually do extend maximum lifespan, tend to improve the healthspan, as defined above.

Showing how long mice treated with various interventions spent "frail" (using an arbitrary cutoff at median lifespan) (11). Importantly, this favours the skeptics because, in my brief analysis, I only included interventions that extend maximum lifespan, excluding "weak" interventions that solely extend mean lifespan and thus healthspan; since from a biogerontologist's point of view they are not truly anti-aging and less likely to work in humans. Please also refer to the publication in note (11), Fig. 2C, D for a more rigorous but similar analysis with α-ketoglutarate treatment.

Compression of morbidity - the taxpayer's magic potion?
Further elaborating the above point, compression of morbidity is the demographically (although not necessarily biogerontologically) optimistic assumption of an extension in healthspan >> disease-span.

healthspan << disease-span (physically / biologically impossible)
healthspan < disease-span (rarely possible, esp. at small lifespan increments)
healthspan = disease-span (underlying the symmetry assumption)
healthspan > disease-span (compression of morbidity)
healthspan >> disease-span (extremely unlikely given already compressed morbidity)

What makes the symmetry assumption erroneous is not the claim that healthspan and disease-span might be balanced, but ignoring second order effects (see dependency ratio, bereavement quotient, compound interest) and failing to put biogerontology in context and failure to compare it with other disciplines (see Täuber's paradox). 

Perhaps even more importantly healthspan and lifespan extension are not balanced. All in all, the evidence suggests that compression of morbidity is real (4) and to continue our tongue-in-cheek analogies, it yields said "magic potion that simply makes older people just disappear" which people inquired about on twitter.

The bereavement quotient
Let us stick to our thought experiments. Imagine that each death causes one year of lost life to others (in terms of QUALY or some QUALY-like concept). You can easily imagine that a person's siblings, spouse, parent(s) and closest friends would suffer for >1year, might develop depression, be unable to focus on work, etc. Ok, so what, we all must die, right? But when? And does it matter when?

Let us keep constant the number of years lived, thus population size and economic output would be roughly equal. Let us look at a span of 100 years. We can roughly fit one or five "complete" lives into this period so that it is still consistent with basic biology. If the symmetry assumption holds, it should make no difference because the benefits and disadvantages are about equal. But can you already see where this is going wrong?

If the life expectancy is 20 years - now, for example, imagine a dystopian world where everyone contracts HIV/AIDS at birth - within a span of 100 years there will be five different bereavement events that will affect the same or different people and their effects will be additive. Under the above assumption we will lose 5 additional life years to bereavement whereas if we manage to extend human lifespan to 80 by controlling HIV and other diseases and then by around 20% through biogerontology - not utopian as it is routinely achieved in mice - we end up with only 1 year of life lost to bereavement per 100 years lived. We can call this effect the bereavement quotient.

Taeuber's paradox does apply
Täuber's paradox could be described as the cornerstone of all biogerontology. It is one of the main reasons why biogerontology is so important to society. Täuber, Keyfitz and many others confirmed an interesting fact (1). Namely, that curing one age-related condition, like heart disease, would only entail very small benefits for lifespan extension because one disease can substitute for another. This makes sense if you visualize it a bit: the very old are also very sick, they do not just have cardiovascular disease; they have many issues, problems.

This an entirely correct way of thinking about it because aging is the common root cause for many diseases that increase at the same time and often quickly, even exponentially. Multi-morbidity. If cardiovascular disease does not kill you, your failing kidney will and if you survive that, soon, you will succumb to the once dormant prostate tumour.

I have a hard time imagining how Täuber's could not apply to morbidity. It almost seems like the critics - and those who think the symmetry assumption is not erroneous - should prove why it does not apply, rather than the other way round (5). Let us start with this graph.

Figure. A schematic illustration that helps to understand Taeuber's paradox

Axiomatically we can state that mortality is preceded by (peak) morbidity. If one disease can substitute for another, in regard to mortality, the same shift should be evident for the peak morbidity (i.e. the period of suffering and disability preceding death with some diseases and conditions). If we can construct a toy example, again, this may be helpful. Imagine an elderly person that is bed-ridden due to frailty. What if this same person was bed-ridden due to a stroke or a hip fracture? What if one happened instead of the other or both happened at the same time? If both happen at the same time, the additive effects should be lower because the person already needs 24hr medical care. However, the substitution effect becomes evident if you look at the morbidity-lifespan trajectory and ask what happens if one of the diseases is averted.

Person A suffered from frailty and was bed-ridden in early 2021, died in mid-2021 from respiratory disease (lack of muscle mass was a contributing factor), however, they were bound to fall in late summer and suffer a hip fracture leading to a similar outcome, if severe frailty had been averted (a fall was possible e.g. because balance issues persist despite reduced frailty). If they had not fallen in late summer, the cerebral arteries were not looking good and an ischemic stroke would have happened in winter.

As you can see, because frailty was magically cured, by our silver-bullet-single-disease-focused-muscle-researchers, death from respiratory disease was exchanged for a period of frailty due to a fall which again was due to a combination of osteoporosis and balance issues. Only if we had genuinely slowed aging we might have slowed osteporosis, reduced frailty, balance issues and rejuvenated the cerebral arteries thus leading to a larger than expected gain in healthspan (vs our standard modalities). We have proof of principle in a dozen of animal models that it is possible to delay aging in toto and strong epidemiologic rationale that it makes sense in humans to do so.

If Täuber's paradox applies to morbidity as well, it does not suggest that lifespan extension is beneficial. Much more interesting than that, it only suggests that lifespan extension (slowing aging) is more beneficial than treating heart disease or cancer in isolation. It could still be that none of this is efficient, that none of it makes sense. In a way there is some logic to it. This would imply that to increase total human well-being and decrease suffering we have to focus on entirely different conditions, e.g. find a means to alleviate the limitations imposed by the hedonic treadmill. Treatments for depression would be a perfect example of this modality. If we extend lifespan we extend both suffering and pleasure symmetrically; during each timepoint nothing is gained or lost, no matter the treatment, due to the hedonic adaptation.

Täuber's paradox does, however, strongly suggest that biogerontology is the king of the health sciences; one-eyed king, or not.

Extending the QUALY concept to aging
If we can apply the Quality-Adjusted Life Year (QUALY) concept to certain age-related diseases, there is no reason why we cannot apply it to the composite of all age-related diseases, which is aging itself and have it bear on the question of lifespan extension.

In a pretty classical paper by Goldman et al. 2013 the authors use "the Future Elderly Model (FEM), a microsimulation that tracks older cohorts of people and projects their health and economic outcomes." in order to evaluate the benefits of lifespan extension. The underlying model assumes Taeuber's paradox to be true for both mortality and morbidity leading to a delay and compression of morbidity: "the delayed-aging scenario assumed that all fatal and disabling diseases were influenced simultaneously"

The results of their simulation suggest no 'regression' or symmetry effect for at least 50 years, i.e. the benefits to the population structure and overall disability rates are maintained for very, very long times:

"the delayed aging scenario yielded a larger share of nondisabled seniors in every year between 2010 and 2026, compared to the status quo scenario. Although the size of the difference declined from 2030 to 2060, during that thirty-year period an additional 5 percent of elderly people were nondisabled in the delayed aging scenario."

The key finding is that even if there is a symmetry (healthspan extension first, disease-span extension afterwards), i.e. if the savings eventually diminish, this effect takes a long time to manifest. This means the savings come first and can be used to fund further research into aging that leads to more savings, or, at worst, can be reinvested at market rate to yield much higher savings in the future due to compound interest. Note that compound interest (and related phenomena) take on more importance than one thinks at first, since we are dealing with net savings and decisions spread out over a period of at least 50 years!

One way to think about the future gains is to look at the present discounted value of all the additional quality-adjusted life-years that would arise from delayed aging relative to the status quo. These life-years can then be valued using a conservative metric, such as $100,000 per life-year [often lower, however]. Doing so yields a social benefit of approximately $7.1 trillion—without even considering the cognitive benefits to individuals that could arise from these interventions [that is 7000 billion or around one third of the US GDP].

At first I was not so sure if these assumptions are water-tight. For one, is a QUALY really worth that much to society and is there no other way to achieve these gains? (14) Somehow my intuition first jumped to the toy models I employed in the paragraphs above: if we keep life years lived constant, does it matter how we distribute them and could we not come up with a distribution that is more utilitarian? Then I quickly realized that in this model, starting from the status quo, there are only two ways to improve net human wellbeing. We can either hasten death (with, say, a bullet) or delay morbidity. I can imagine that the first possibility of increasing net human wellbeing will not be very popular (6).

Now hot off the presses, another article in this vein (Scott, Ellison & Sinclair 2021) which we will briefly discuss. The study is based on willingness to pay (WTP) calculations (similar concept to estimating QUALYs) and demographic characteristics of the US population. We may take issue with some of the numbers specifically, but overall it looks like a solid piece of demographic research (hence not my field of expertise). First the authors show a couple of trivial things, e.g. that 1y of healthspan is preferable to 1y of lifespan extension in their model. More interestingly, they also find that the difference between one time rejuvenation (think e.g. senolytics) vs slowing aging (think e.g. caloric restriction) is less clear in their model.

Later on it gets interesting when the authors play the 'what if metformin slows down aging' game with their underlying data based on another published study.

The authors do caution that "the efficacy of metformin awaits confirmation from large sample trial data such as from the Targeting Aging with Metformin (TAME) trial." which David Sinclair did not do when he tweeted about the study and he was rightly criticized for it. However, it does not change the argument that IF metformin works, as expected from the cited reference and others, THEN the data does hold up. The reference they cite which they use to estimate the benefits of metformin is an interesting article by Wang et al. 2017 published in the Journal of Diabetes and its Complications. Those following the field may be more familiar with the Campbell et al. meta-analysis that suggested reduced mortality from metformin (even compared with non-diabetic controls!) At least I was not familiar with the Wang paper.

We can see certain similarities and obvious problems when we take a very brief look at the data. The work by Wang et al. is a single cohort study whereas Campbell was a meta-analysis of trials and observational studies, however, the key findings were based on only a few observational studies. Importantly, and this applies to both studies, it is impossible to control for all confounding factors in epidemiology. In general we want to see a randomized controlled trial (RCT) with your drug and endpoint as a primary outcome, with the following ranking of evidence: RCT (primary outcome) > RCT (secondary outcome) > good cohort studies. We have to be careful! Aspirin, for example, had a good signal for cancer prevention in RCTs with cancer as a secondary outcome and totally floundered as time went on and more RCTs were published (16).

On the positive side, Scott, Ellison & Sinclair 2021 generally report much higher monetary benefits to society from slowed aging than did Goldman et al. 2013, and I do like it that they try to model additional effects as well, although they are obviously missing some (13):

"Focusing on the aggregate WTP reveals a powerful additional dynamic at work. Slowing down aging leads to a population that is on average older and larger (as more people live for longer), both of which increase the aggregate WTP for further improvements. This creates a virtuous circle around delaying aging; the better that society ages, the more valuable any further improvements."

Compound interest and opportunity cost
If you could invert your life-morbidity trajectory, would you, and would this benefit society? If you could now suffer the brunt of age-related diseases, then be healthy until at some point you die at the pre-destined age-of-death, would you like to?

What if I rephrase it a bit. If I asked this question in 2010, would you prefer to suffer from advanced melanoma** back then or ten years later, i.e. today, when checkpoint inhibitors have more than doubled five-year survival rates? Would you have preferred to contract HIV/AIDS before the advent of HAART or afterwards? What about heart disease and the invention of statins? Parkinson's disease before or after modern symptomatic treatments that reduce motor symptoms? All treatments that came about in the late 80s or early 90s, if I am not mistaken, so not that long ago!

** you could substitute any other disease that had a breakthrough treatment at some point; melanoma is not known to be strongly age-related but this is irrelevant as this argument refers to scientific progress in general.

Ignoring scientific progress, you still have to pay for your medical treatment or at least someone else has to. At a conservative annual return rate of <5% for the Dow Jones, 100$ today buys you around 160$ of medical expenses in 10 years, or a little less in real, inflation-adjusted dollars, but still more than when you started out. Would you rather pay today or tomorrow?

As a sidenote, the most extreme version of this argument is known as longevity escape velocity as coined by Aubrey de Grey and to our argument it is irrelevant whether this is a sound concept as long as partial escape velocity exists. As we have shown, partial escape velocity is known to occur. For example, a treatment that extends your lifespan by 5 years, given today's medical treatments, will end up extending your lifespan by >5 years.

There are various reasons why extending human lifespan is beneficial to society as a whole and these range from moral to purely cynical ones, like money. This is obvious to me as an aging-researcher but probably less obvious to others. Some of these ideas may be wrong, to some extent, and I invite debate; but overall the concept is sound, as far as I can tell. The main reasons why the push towards radically extending human lifespan would benefit taxpayers and the world are:

  • it is easier to extend healthspan than lifespan (compression of morbidity)
  • extended lifespan improves the demographic structure of society (dependency ratio) and decreases overall suffering (bereavement quotient)
  • trying to extend lifespan is the most efficient way to extend healthspan (Taeuber's paradox)
  • being alive in the future is generally preferable to being alive in the past or present for the same period of time (due to compound interest and research progress)

Key References & Notes
Epistemic status:
I'm still stealing the idea from the lesswrong forums, because it allows me to actually write instead of trying to produce the perfect article. The notes also serve to provide additional discussion, explanations and critical remarks so I do not feel like I am being unfairly one-sided. With that being said, most of the statements in this article would be echoed by other biogerontologists, although specifics are hotly debated and the field is not known for strong group consensus (yet?) Several of the toy models and napkin math may be weak.

1. Keyfitz, Nathan. "What difference would it make if cancer were eradicated? An examination of the Taeuber paradox." Demography 14.4 (1977): 411-418.

2. Andersen, Stacy L., et al. "Health span approximates life span among many supercentenarians: compression of morbidity at the approximate limit of life span." Journals of Gerontology Series A: Biomedical Sciences and Medical Sciences 67.4 (2012): 395-405.

3. Is this a (mouse) researcher's intuition, consensus or both? Gems 2015:
"Based on animal model studies a plausible outcome of geroprotection is a compression of lifetime morbidity in relative terms (i.e., as a percentage of time alive), but not in absolute terms (i.e., years of morbidity; Blagosklonny, 2012); this is described using a standard representation in Figure 1"

4. In contrast, there is now some evidence that existing therapies and modalities (and I think we all can agree that these do not affect the aging-rate) failed or will fail to further compress morbidity and extend healthy lifespan (Nikolich-Žugich et al. 2016):

Unfortunately, increased disability rates and rates of multimorbidity are now accompanying increases in life expectancy in the United States, and likely all over the world—leaving healthy life span (healthspan) either declining or unchanged.

[However, aging research comes to the rescue!] It is clear that competing health risks limit the impact of major clinical breakthroughs for specific diseases—that is, making progress in one disease means another one will eventually emerge in its place. This universal problem of competing risks in aging populations makes research and investment to delay or slow aging highly valuable, given the evidence that delayed aging would yield notable reductions in most if not all fatal and disabling disease simultaneously.

5.  The notion that Taeuber's paradox applies both to mortality and morbidity is generally shared by almost everyone in the field, including serious, rather conservative demographers like Jay Olshansky:

The sixth inconvenient truth is that combating diseases of aging as if they are independent of each other is likely to lead to a rising prevalence and severity of aging related diseases. The solution is to challenge the conventional approach to disease and instead of attacking one disease at a time, enhance the effort to combat the processes of aging that give rise to these diseases

From: Olshansky, S. Jay, and Bruce A. Carnes. "Inconvenient truths about human longevity." The Journals of Gerontology: Series A 74.Supplement_1 (2019): S7-S12. 

6. The cynical idea of the "bullet to the head" metaphor is popular with certain people of certain political affiliations I know (can you guess which?) However, rest assured, that no, smoking and drug abuse is not equivalent to a clean, utilitarian bullet to the head. Even if it may save the taxpayer money in rare circumstances, this is not equivalent to a net benefit for society. Still, in principle any condition that shortens lifespan more than it extends morbidity, would fit the bill. Also something worth noting here is that we are constructing an "intuitive" argument against hard utilitarianism (interesting because I consider myself a harder utilitarian than the average person.)

Regarding "We can either hasten death (with, say, a bullet) or delay morbidity." Remember that we cannot delay morbidity without extending lifespan and we cannot shorten lifespan without resorting to unconstitutional means or extending morbidity (e.g. by incentivizing obesity).

7.  We may agree on this point, but this "we" does not include all of humanity, of course. The bioluddites, primitivists, theocrats, extreme conservatives, the emotionally cold and blind, the mistaken, the cynical, the misanthropes, the enemies of reason do not agree. However we call them, whatever their reasons, and I have in general no kind words for these people, but they do exist. The desire to see others limited by a short lifespan, the desire to see them die is often termed "deathism" in lifespan extension circles. While I am always open to sound arguments against lifespan extension and discussing its shortcomings (see the notes on the hedonic treadmill, for example) I am genuinely afraid of people like Leon Kass whose arguments are as dangerous as they are vacuous.

8. Yes, an improvement in the dependency ratio generally relies on the assumption that health and disease-span are extended at least symmetrically (see also note 9). Apart from that, I wish I could find a rigorous treatment of this topic that considers plausible outcomes based on different forms lifespan extension / different treatments. For now, our little intuition will have to do.

Also note: "if we magically add 10% adults and 10% sick elderly to a population symmetrically" would probably better be phrased as "if we magically add N% adults and M% elderly, at their current ratios, corresponding to the currently observed dependency ratio" then society should still benefit because there are fewer children at any one point in time.

9. It was on my mind to develop a slightly less naive model based on a simple simulation (although this would be just a worse version of what Goldman et al. 2013 did). For now, some napkin math to show the delayed changes in population aging is attached:

9a. A bit more on the standard assumption and why it is reasonable to assume that healthspan and disease-span would be extended by the same percentage and not by a constant, additive factor (as e.g. in [9]). A typical lifespan curve for a good intervention looks as below. Methionine restriction is used as an example of a lifespan extending intervention:

NB: To be fair to the skeptics, I selected a better lifespan curve here, as for methionine restriction some cohorts do show early life mortality due to the severity of the protocol. Presumably moderate methionine restriction and protocol improvements alleviate the issue, but I have not kept up with the field to tell for sure.

10. Goldman, Dana P., et al. "Substantial health and economic returns from delayed aging may warrant a new focus for medical research." Health affairs 32.10 (2013): 1698-1705. 

11. We assume that a mouse with extended mean lifespan, is as healthy at the new mean lifespan as was the mouse with no extended lifespan at its respective lifespan. Obviously, this calculation will be very sensitive to this assumption. In general we do have data that long-lived mice are healthier at the same age compared to short-lived mice, but we do not know the details. Put another way, old mean= 900d, new mean after treatment= 1000d, are the 1000d old, treated mice as healthy as 850, 900 or 950d old regular mice? The first attempt to quantify this, or at least the first attempt that came to my mind, was made by the Brian Kennedy group in Shahmirzadi et al. 2020. 

Shahmirzadi, Azar Asadi, et al. "Alpha-ketoglutarate, an endogenous metabolite, extends lifespan and compresses morbidity in aging mice." Cell Metabolism 32.3 (2020): 447-456.

12. I think this was based on the work of Austad, see for example:
Austad, Steven N., and Andrzej Bartke. "Sex differences in longevity and in responses to anti-aging interventions: a mini-review." Gerontology 62.1 (2016): 40-46.
The below also is consistent with my intuition at first glance with the healthspan advantage of women being smaller than their lifespan advantage: 

13. If the average person lives 20 years longer they might well support more and better policies that aim to reduce gun violence, environmental pollution, CO2 emissions or the likelihood of armed interstate conflict. Besides, this paper does not e.g. model anything resembling the bereavement quotient. It is possible we may also have to ask "How much would you pay for one additional year of productive life, not for yourself, but for your dear father; or Neil deGrasse Tyson, or Albert Einstein, or Peter Scholze?" But of course we then get into another (symmetry?) argument because the somewhat less desirable lives of dictators and unrepentant criminals might also be extended.

14. Sure there may be a willingness to pay more than the per-capita-GDP for a QUALY, but does this really mean that the benefit of a QUALY to society is this number? How could the benefit be larger than GDP? Sure, in the long term due to virtuous loops maybe it can be marginally higher, but overall it does not make sense. Either I am misunderstanding the concept or it is used somewhat inappropriately to calculate the "benefit" of anti-aging and other treatments? I think there are a lot of interesting subtleties in the demographic research we discussed here that are beyond the understanding of a mere mouse researcher (with some knowledge of classic epidemiology); but what matters is that all models always arrive at the same conclusion.

A couple of quick glance notes from an interesting paper on QUALY. Yes, QUALYs can be higher than GDP:
"When WTP [willingness to pay] values were compared to GDP per capita of each country for specific study years, the ratios of WTP per QALY and the country’s GDP per capita ranged from 0.05 [21] to 5.40 [20]. "
This is counter to the skeptics assumption and some other findings that suggested people value healthspan much more than lifespan. (IMHO, in most cases both are important but of course that is model and question dependent):
"The average ratio of WTP per QALY and GDP per capita for extending life or saving life (2.03) was significantly higher than the average for improving quality of life (0.59) with the mean difference of 1.43 (95% CI, 1.81 to 1.06)."
Is this the "I will pay to have my family and beloved ones live longer" effect we discussed in (14)?
It was also found that, on average, the estimates from a societal perspective (2.16) were clearly higher than those from an individual perspective (0.63) (p-value <0.01).

Are we able to pay more than GDP for a QUALY because we can "save up for it" since the increase in QUALY is considered a one-time often end-of-life event? (since we are dealing with the avoidance of age-related diseases in many such calculations). In that case it would make sense that the willingness to pay should decrease in the long term since we cannot pay more than GDP ad infinitum, where does the money come from?

Duration of scenario was significantly associated with the ratio between WTP per QALY and GDP per capita (p-value<0.01). The shorter duration (1 month to 1 year) scenario seemed to have higher WTP per QALY (p-value<0.01).

15. I am just now noticing that many of these tweets were in response to some recent rather controversial claims by Sinclair and included snide and not so snide remarks by Charles Brenner, who managed to really piss me off and I am also thankful for this as it motivated me to write. Apologies for being so cross in my tweets, though!

16. The fact that most of the aspirin RCTs were initially designed to detect CVD and not cancer was often criticized in prior reviews but it is not entirely clear to me if newer studies were negative, because they were better designed with cancer as a primary endpoint (or at least with attention paid to avoid potential sources of bias that could affect apparent cancer mortality and incidence), or because they were better or due to regression to the mean, etc. Whatever the reasons, ARRIVE, ASCEND and ASPREE all looked pretty bad.

Wu, Qibiao, et al. "Long-term aspirin use for primary cancer prevention: An updated systematic review and subgroup meta-analysis of 29 randomized clinical trials." Journal of Cancer 11.21 (2020): 6460.