A general framework for evaluating aging research. Part 1: reasoning with Longevity Escape Velocity

[Emanuele_Ascani]

Summary

To this day there is a lack of systematic research to evaluate a cause area with immense potential: aging research. This is the first of a series of posts in which I’ll try to begin research to address this gap. The points made in this post are about how to evaluate impact using the concept of Longevity Escape Velocity. Bringing the date of Longevity Escape velocity closer by one year would save 36,500,000 lives of 1000 QALYs, using a conservative estimate. Other sources of impact that arise from the same concept include: increasing the probability of Longevity Escape Velocity, making Longevity Escape Velocity spread faster, and making a new future portion of the population reach Longevity Escape Velocity by increasing its life expectancy. Aging research could also positively impact the cost-effectiveness of other interventions by increasing the probability that Longevity Escape Velocity will be attained in the recipients’ lifetimes. I will also discuss why the probability of Longevity Escape Velocity is substantial and why QALYs should be the measure of impact, and I’ll give mathematical proofs that the adoption speed of the technologies that arise from research doesn’t impact cost-effectiveness analyses.

The need of a theoretical foundation to evaluate aging research

I think one important approach to research in Effective Altruism is to try to lay theoretical foundations and put together tools for helping to evaluate a specific cause area that can be generalised to any intervention inside that cause area. Such work is often not possible because of lack of time and expertise, making it preferable, sometimes, to scout specific promising interventions or refine existing research.

One cause area that absolutely needs this kind of more systematic groundwork is aging research. The current EA research about aging is lacking in number and in what I think are crucial considerations, even though informal discussion with members of the community reveals that many people regard it as potentially promising. The expertise required to make such an analysis possible is rare to find. It requires people with a strong quantitative background who are also interested not only in biology but in the biology of aging in particular, and they must be accustomed to predicting the future of scientific research and making cost-effectiveness evaluations. I observed that the Effective Altruism community seems to have plenty of people with a background in philosophy, economics, social sciences or computer science, but people with a strong background in biology, or at least a strong interest in it, are scarce. This makes it even harder to find people willing to do the work of evaluating the cause area of aging research.

For these reasons, and since I’m very familiar with the topic and I think I have important things to say about it, I am willing to try to lay as much groundwork as possible, at least until I think I’m needed.

My long-term hope is that the groundwork I will lay will be good enough for a more formal discussion about this topic within Effective Altruism, both for evaluating specific interventions inside this cause area and for evaluating the cause area as a whole. I will write about what I think are original points and put together all the existing tools that could help both Effective Altruism organisations and organisations within the cause area of aging to make better decisions.

I have chosen to split the analysis into multiple posts so that I can receive and incorporate feedback during the process and thereby modify my work and its planning along the way. Organising the work in this way will also make the whole thing easier to read.

I’m doing this alone and in my free time, between university and other activities, so the posts will probably come out a few weeks or even months apart.

Although I hope that the bottom line of my arguments is strong, there will probably be many mistakes and many corrections to make. I encourage you to comment, give feedback and to contribute new ideas, especially if you have a consideration about something that I didn’t address that would substantially impact the result of a potential cost-effectiveness analysis. Along the way I will probably need to collaborate with other people and coauthor some posts, since my knowledge probably has gaps and needs to be complemented. Nonetheless I will try to learn what I currently don’t know along the way.

What will this series of posts be about?

This is the first of a series of posts in which I’ll explore different ways of reasoning about the potential cost-effectiveness of aging research. Each post will focus on one or more considerations. In the last post I would like to wrap everything up with a comprehensive framework useful for evaluating the cost-effectiveness of any given avenue of scientific research into the aging processes and how to treat their various facets. The points made will also provide an idea of the potential of the cause area as a whole.

An initial major focus will be on the scope of the problem and on moral considerations that could affect it. Neglectedness and tractability will be given space in later posts, in which I will try to lay out useful methods and heuristics to evaluate them in this cause area.

After this work, I would like to discover the best funding opportunities within this area and compare my conclusions with other past efforts within Effective Altruism that have been made to evaluate aging research.

Points made in this first post:

• Longevity Escape Velocity (LEV) is the minimum rate of medical progress such that individual life expectancy is raised by at least one year per year if medical interventions are used.

• Reasoning with Longevity Escape Velocity substantially changes cost-effectiveness analyses.

• A conservative estimate for life expectancy after Longevity Escape Velocity is 1000 years, although it’s still not a lower bound.

• In order to account for making Longevity Escape Velocity arrive more quickly in cost-effectiveness analyses (CEAs) the relevant variables are deaths by aging per year, life expectancy after LEV and Expected number of years LEV is made closer by. This without accounting for moral weights and other possible discounts.

• The probability of Longevity Escape Velocity is substantial.

• Another factor potentially greatly influencing impact is the life expectancy increase resulting from research projects or health interventions. If the project is not likely to be funded in the future or subsumed by other research, the recipients of the intervention who would have died near LEV get saved.

• QALYs should be the measure of impact, as one life saved counts more than 30-80 QALYs in this cause area.

• Mathematical proofs that cost-effectiveness analyses aren’t influenced by how Longevity Escape Velocity, or any technology that arises from a given financed research project, spreads to the whole population

• Making LEV spread faster is another impact consideration that is pertinent to projects potentially leading to policy change or public awareness.

• Certain research projects could also have the effect of increasing the probability of Longevity Escape Velocity, potentially influencing cost-effectiveness analyses substantially.

• Aging research can boost the impact of other altruistic interventions by increasing the probability of LEV happening in the recipients’ lifetimes.

The next posts in the series will probably be about:

• A better lower bound for the life expectancy after Longevity Escape Velocity, and how this affects the probability of LEV.

• The longevity dividend.

• The value of information (depending on if I need to include considerations specific enough to aging research).

• Moral weights.

• If old people are replaceable in a utilitarian moral framework.

• What is neglected and what is tractable in the cause area of aging research.

• Putting the framework together.

Longevity Escape Velocity: what it is

Longevity Escape Velocity (LEV) is the minimum rate of medical progress such that individual life expectancy is raised by at least one year per year if medical interventions are used. This does not refer to life expectancy at birth; it refers to life expectancy calculated from a person’s statistical risk of dying at any given time. This is equivalent to saying that a person’s expected future lifetime remains at least constant despite the passing years.

It’s possible, given sufficient ongoing improvement of medicine and its democratisation, that nearly everyone on the planet, at a certain date in the future, will benefit from therapies that allow Longevity Escape Velocity to be attained, at least until aging is eradicated completely. Then, other factors will influence risk of death, and expected future lifetime could start falling again each passing year if risk of death flattens or doesn’t continue to fall fast enough.

How likely that Longevity Escape Velocity is to become a reality in the future depends on a number of factors, which will be explored later in this post.

Reasoning with Longevity Escape Velocity substantially changes cost-effectiveness analyses

If a given intervention “saves a life”, this usually means that it averts 30 to 80 Disability-Adjusted Life Years (DALYs). In order to evaluate the impact of aging research, one could be tempted to try to estimate how many end-of-life DALYs that a possible intervention resulting from the research could save and adjust the number using the probability of success of the research.

This is the line of reasoning that OpenPhilanthropy’s medium investigation on aging uses, although without making any explicitly quantitative argument. This is part of the impact, and it has to be factored in, but it doesn’t consider where the largest impact of aging research is: making the date of Longevity Escape Velocity come closer. This would have the effect of saving many lives from death due to age-related decline and disease, but here, “a life” means, more or less, 1000 Quality-Adjusted Life Years (QALYs). This figure is derived as follows:

Life expectancy after LEV:

In actuarial science, the expected future lifetime of an individual at age $x$ is denoted with $e_x$. It can be seen as the expected value of the random variable $K\left(x\right)$, also called “Curtate Future Lifetime”, which is defined as $K\left(x\right):=\lfloor T\left(x\right)\rfloor$ , where $T\left(x\right)$ maps to the amount of additional time that an individual of age $x$ is projected to live. For our purposes, we can use the discrete random variable $K\left(x\right)$ instead of directly $T\left(x\right)$. Thus, with ${}_k{p}_x$ being the probability of surviving between age $x$ and age $x+k$:

$e_x=E\left[K\right(x\left)\right]={\sum }_{k=0}^{\infty }k\cdot P\left(K\right(x)=k)={\sum }_{k=0}^{\infty }k\cdot ({}_k{p}_x-{}_{k+1}{p}_x)=={\sum }_{k=0}^{\infty }k\cdot {}_k{p}_x-{\sum }_{k=0}^{\infty }k\cdot {}_{k+1}{p}_x={\sum }_{k=1}^{\infty }{}_k{p}_x$

If $p\left(x\right)$ is the probability of dying between year $x$ and year $x+1$, then:

$e_x={\sum }_{k=1}^{\infty }{}_k{p}_x={\sum }_{k=1}^{\infty }{\prod }_{i=1}^k(1-p(x+i-1\left)\right)$

For now, I’ll use a constant risk of death to calculate the life expectancy of individuals after aging is eradicated completely and risk of death has presumably stopped falling. While this method doesn’t yield a lower bound, since it leaves out from the calculation the risk of death when it’s decreasing, it can be made conservative using a relatively high risk of death. I’ll use $p\left(x\right)=1/1000$, which is more or less the current risk of death of someone between 20 and 30 years old. It is conservative because it doesn’t account for future improvements in medicine and general safety outside of aging research. I also don’t expect the lower bound to be much smaller. Therefore,

$e_x={\sum }_{k=1}^{\infty }{}_k{p}_x={\sum }_{k=1}^{\infty }(1-1/1000{)}^k=999\approx 1000$

Since we are talking about life expectancy in a world without aging, 1000 years of life expectancy should amount more or less to 1000 QALYs.

Accounting for making LEV come closer in CEAs

Any given aging research project, if successful, could have the effect of making the date at which most people will reach Longevity Escape Velocity come closer by a certain amount of time. We can estimate the expected QALYs gained because of such an effect. We have established that the average lifespan of a person who reached LEV will be around 1000 years, mostly without disability, and somewhat less if we use a lower bound. The number of QALYs saved are then calculated by multiplying 1000 by the number of people who would otherwise have died of aging if LEV wasn’t moved closer. Currently, around 100,000 people per day (36,500,000 people per year) die due to age-related decline and diseases, although this figure will be larger when LEV arrives due to population growth.

So, in order to calculate an almost lower bound for how many expected QALYs that a certain research project would save by making LEV come closer, you simply multiply these values:

• 1000 QALYs

• 36,500,000 deaths/​year

• Expected number of years LEV is made closer by

This is true for a crude estimate, without accounting for moral weights and potential discount rates.

It is important to stress the fact that none of these variables depend on how soon LEV will arrive, so we can totally ignore this kind of discussion, even if it is a highly debated topic outside the setting of cost-effectiveness evaluations.

The first two variables have been already discussed. Then, we need to examine the third one, which depends on many factors, such as:

• How promising the project being examined is, for different meanings of the word “promising”. For example, it may have direct translational value into effective therapies targeting aging processes or hallmarks, or it could have an effect of speeding up the field, such as by providing new tools, by enabling political entities to aid in achieving LEV sooner, or by enabling a new line of research to start sooner or become widespread more rapidly.

• The neglectedness of the project would make the figure larger.

• If there are other projects that could subsume the effect of the examined project, some of which would universally subsume all potential projects. These include technologies outside the field of aging research that are potentially very disrupting and sudden, such as artificial general intelligence.

• The number of years necessary for another group to step in and do the same project.

• The probability of catastrophic events: existential risks or events catastrophic enough to make the information acquired by the project lost or useless.

• Lastly, the probability that LEV will happen in the first place also has a role in estimating this variable. This is because we can model the number of years that LEV is brought closer as the expected value of the random variable that maps to various numbers of years, among which is zero. The probability that the years LEV is brought closer by is zero, in turn, depends not only on the specifically examined project but also on the probability that LEV will not happen. That’s why it’s useful to outline how to reason about the probability of LEV.

Probability of LEV

If we had the minimum rate of decrease of risk of death such that LEV would happen, then the probability of LEV happening is the probability that the risk of death would fall at that rate or faster, and so the probability largely depends on that rate and on how fast medical research will be.

For now, we can reason about the problem by dividing the situations in which LEV will not happen in at least two scenarios:

• Very slow research scenario: In this scenario, each new therapy is developed in the span of an entire generation and contributes only a few more years of healthy life. This slow rate of progress is maintained more or less constantly within the span of a few centuries. Example: every 30 years or so, only one new therapy grants 5 more years of healthy life for the general population. If progress is this slow, LEV will never be reached. Negligible senescence will eventually be met after a few centuries, and generations will have progressively longer lifespans without anyone suddenly making very large jumps in life expectancy. New therapies may rely on previous ones for having substantial effects, forcing new treatments to come sequentially and not in parallel. It’s also possible that they could theoretically be developed in parallel, but an incredibly inefficient research community develops them sequentially. This scenario seems somewhat unlikely. This tells us that reaching the minimum rate of decrease of risk of death shouldn’t be too difficult.

• Dire roadblocks scenario: This is the scenario in which there are roadblocks so dire that aging research is stalled for enough time that the recipients of previous interventions die. This doesn’t necessary prevent LEV all the time; these kind of roadblocks must be enough in number to effectively make the average decrease of risk of death the same as the one of the very slow scenario until aging is cured completely.

The scenarios in which LEV will happen, instead, are the ones in which the risk of death falls fast enough, which means that new therapies would be developed sufficiently close together. This would be brought about through steady progress in medicine or relatively large jumps in life expectancy that enable previous recipients of therapies to extend their lives by another large amount of time. We can imagine how such scenarios could unfold:

• Today’s therapies or future therapies appear to be somewhat effective on humans or very effective on mice. This increases public focus on translational aging research, which, in turn, results in a multiplication of resources dedicated to it. It’s argued that that this first “proof of concept” required to convince the world is Robust Mouse Rejuvenation, which would double the remaining life expectancy of elderly mice, as demonstrated and then replicated in rigorous laboratory studies. A multiplication of resources for the field should result in therapies following the first proofs of concept. After this, the rate of therapy development and improvement will increase exponentially following the initial success of therapies. The history of technology is full of examples of this feedback loop, in which successive improvements are faster than the development of the proof of concept, a prominent one being flight.

• Without invoking a large public interest, LEV could also be caused by combinations of different treatments coming in waves and by the improvement of treatments over time. This would mean sudden jumps in life expectancy that would buy enough time for other treatments to be developed. A sudden future enlightenment about the nature of aging could be also possible, or the first therapies could also have the effect of slowing down the accumulation of other damages, other than doing the job of addressing their specific targets. This would happen by breaking negative feedback loops of damages or processes. LEV could also happen in a sudden way if effective delivery methods are developed after many proof-of-concept therapies have been demonstrated, for example, in vitro.

• The two scenarios above sound somewhat optimistic, but they might not be needed at all. The research could unfold silently but surely and the risk of death could still fall fast enough to ensure LEV. This would happen if the current situation of very slow improvement is overcome and there isn’t a large number of new dire roadblocks ahead.

Given these scenarios, can we have a preliminary idea, without knowing how fast the risk of death needs to fall, of how likely LEV is? There are, at least, probably some relevant points to make regarding the current best guesses about aging and the present state of research.

It’s difficult to predict major future roadblocks, but at least it seems that the “very slow research” scenario is proving less and less likely. This doesn’t mean that we already have effective therapies against aging, or that the pace of science is optimal. But how research is distributed and the theories about what aging is make believable the possibility of therapies being developed closer together, thereby enabling a high-enough rate of decrease of overall risk of death.

The current best guess about how to tackle aging rests on a milestone paper from 2013: The Hallmarks of Aging. The paper has citations in the thousands and counting, and researchers are using it as a framework to orient and justify their own research. It proposes various categories of dysfunction. Every category, or almost every category, should be addressed periodically in order to maintain a youthful state of health. Reversing one hallmark would mean restoring an internal state of the body that is typical of a youthful body. It could also prove true that it will not be necessary to address every hallmark, due to the possible cause-effect relationships between each of them.

What does this say about how close together therapies will come? It says a lot: a paper like The Hallmarks of Aging means that the field already has an idea of what combination of foreseeable therapies will bring major gains in health and, in turn, life expectancy. This is because this theoretical categorisation constitutes what needs to be addressed.

It also implies that it enables thinking about rejuvenation, not only “slowing down” aging. This is because the dysfunctions described are exactly what is “wrong” with an old body, and not how those dysfunctions arise, so getting rid of those kind of dysfunctions means rejuvenation.

It’s a “downstream” view of aging that decomposes the problem and leaves out what is unnecessary to know in order to intervene, increasing the tractability of the problem. We don’t need to know how the Hallmarks arise in order to develop therapies that address them. One added benefit is that the hallmarks influence each other in negative feedback loops; reversing one slows down the progress of many others.

Theoretically, interventions aiming at reversing all of the hallmarks of aging could be developed in parallel, and, in fact, they currently are (although not optimally so). Interventions to ameliorate each one of the Hallmarks, at least in specific parts of the body, are underway. You can follow the progress of each research targeting each hallmark by using the Rejuvenation Roadmap made by the Life Extension Advocacy Foundation. This map tracks the progress of research projects that ameliorate each hallmark and provides links with explanations of each project; it also contains citations to the relevant papers.

As you can see, there are some hallmarks, such as mitochondrial dysfunction and loss of proteostasis, which are in the very early stages of research: the furthest they have reached, so far, is the preclinical stage. Research on how to ameliorate mitochondrial dysfunction, in particular, is in such an early stage of research that it is only pursued by nonprofits and academia, but it needs to be addressed in the wider scheme of therapies that will be needed in order to address all of the dysfunction arising from aging.

There are other hallmarks, such as cellular senescence and stem cell exhaustion, which are in fairly advanced stages of research (phase 1 and phase 2 trials), and research on them is pursued by well-funded, for-profit companies, such as Unity Biotechnology.

The fact that all of these lines of research are pursued in parallel is important. It means that at an unspecified time in the future, near or far, lines of research could come together in a relatively short period of time. The fact that right now, many interventions are being researched on specific diseases (e.g. Unity Biotechnology’s trial is for arthritis) does not negate the previous point: treatments that are being researched using the Hallmarks framework, even though they are being tested for specific conditions, are relevant for therapies that treat a wide range of diseases. Parallel development makes it more likely that therapies will come in waves, with each therapy being released shortly after another.

There are also other approaches in aging research, such as targeting aging in a more upstream fashion, with less ambitious interventions that target metabolic pathways. One example is metformin, although I don’t think that, right now, science is advanced enough for research on specific medical interventions using this approach to substantially make the date of LEV come closer or substantially impact its probability. These kinds of research projects, nonetheless, could have the effect of buying some time for an additional slice of the population to reach LEV. This brings us to another way of accounting impact in this cause area.

Accounting for making an additional slice of the population reach LEV

Another factor potentially greatly influencing impact is the life expectancy increase resulting from research projects or health interventions. If the project is not likely to be funded in the future or subsumed by other research, the recipients of the intervention who would have died near LEV get saved. I think the health interventions or projects for which this factor is relevant are very few or maybe even non-existent. This consideration influenced the impact measure I used in my previous analysis on the TAME trial, but in retrospect I think I overestimated the probability that the health benefit of metformin will not be subsumed by other research.

In order to account for this, the relevant factors to multiply are:

• Life expectancy after LEV.

• Recipients of the interventions who would have died just before LEV if their life expectancy wasn’t extended by the intervention.

• Probability that the project will not be funded by someone else, or is subsumed by other research.

QALYs should be the measure of impact

Due to the possibility of LEV, expected QALYs should be the measure of impact of aging research. Lives saved lose their original meaning, unless 1 life of 1000 QALYs is counted as multiple lives of 30-80QALYs. Exactly how many also depends on how moral weights are chosen. In my previous analysis about the cost-effectiveness of the TAME trial, I made the mistake of measuring impact in lives saved instead of directly in QALYs, without considering the fact that a life saved in that context amounted to 1000 or more QALYs and actually counted as multiple lives saved. In that analysis, I also didn’t account for DALYs averted at the end of life and every other factor that influences impact, which I will discuss in future posts.

How LEV spreads will have no impact on CEAs

A concern sometimes comes up when I present LEV-based reasoning: how do we account for the fact that LEV will probably spread to the whole population over a large period of time (e.g. following the sigmoid technology adoption curve)? This consideration has no effect on the final estimate of cost-effectiveness, and making the date of LEV closer by any given period of time prevents exactly the number of deaths by aging occurring during that period of time, regardless of how LEV spreads. Let’s first see a simple example where this holds and then prove it mathematically in the general case. I came up with two proofs, each one of which is sufficient alone.

These same arguments and proofs work for any other outcome of a given technology. How a certain technology (health-related or not) will spread doesn’t influence the cost-effectiveness of financing the research leading to it. I may include the generalised version, which trivially follows from this one, in a separate post.

Keep in in mind that this does not mean that making LEV spread faster doesn’t impact CEAs. In fact, this is a potential impact factor that I will discuss. This result means that the impact of making the date of LEV come closer isn’t influenced by how LEV spreads.

I will use deaths prevented in the example and in the proofs, but a generic measure of impact yields the same result. Using QALYs is not necessary in this case.

Example

Let’s consider two specific scenarios as an example: in the first scenario, LEV spreads to the whole population instantly, and in the second, it spreads over four years.

First scenario: A particular piece of research makes LEV come closer by one year. Since LEV spreads instantly over the whole population, it’s easy to see that the resulting deaths prevented are exactly the deaths by aging occurring during one year: more or less 100k.

Second scenario: A particular piece of research makes LEV come closer by one year, but LEV spreads over the world during a period of four years. In the first year, ¹⁄₄ of the population reaches LEV; in the second year, ¹⁄₂; in the third, ⁴⁄₅; and in the fourth, ⁵⁄₅. If we shift this gradual transition by one year, then in the first year, we prevent, on the margin (deaths that would have occurred if we didn’t move the date), 1/​4-0 = ¹⁄₄ of the deaths of aging occurring during that year. In the second year, we prevent 1/​2-1/​4 = ¹⁄₄ of the deaths by aging that occur during that year. In the third year, we prevent ⁴⁄₅ − ¹⁄₂ = ³⁄₁₀ of the deaths by aging occurring during that year. In the fourth year, we prevent ⁵⁄₅ − ⁴⁄₅ = ¹⁄₅ of the deaths by aging occurring during that year. So, in total, by shifting the date of LEV by one year, we prevented: ¹⁄₄ + ¹⁄₄ + ³⁄₁₀ + ¹⁄₅ = 1. That is, we prevented the deaths by aging occurring during one year: more or less 100k.

As you can see, the number of deaths prevented in the two scenarios is the same: the number of deaths by aging occurring during one year. LEV is moved closer by one year in both scenarios, but it spreads differently.

Now, I’ll prove, more generally, that making LEV closer by any given period of time prevents exactly the number of deaths by aging occurring during that period of time, regardless of how LEV spreads.

Proof 1:

$n=$ the number of years needed for therapies to spread to the whole population.

$y=$ the year in which the therapies leading to LEV begin spreading.

$d=$ number of deaths caused by aging each year ($d$ could be the number of deaths by aging occurring in any arbitrary unit of time; the proof remains the same).

$f:\{y,...,y+(n-1\left)\right\}\to [0,d]$ expresses how many deaths from aging are prevented in a given year during the time that therapies are spreading. How exactly $f$ is defined depends on how the therapies spread (e.g. exponentially or linearly), but we know that $f(y+n-1)=d$ and that $f\left(y\right)=0$.

If LEV spreads to the whole population all at once, then $n=1$ and $f:\left\{y\right\}\to \left\{d\right\}$. In this case if the date of LEV is moved closer by $1$ year, then the resulting new function $f^{\left(1\right)},$ has $y-1$ as the only member of its domain, also mapping to $d$. So the deaths prevented on the margin by making the date of LEV closer by one year are exactly $d$.

We want to prove for all values of $n$ and $y$ that if the date of LEV is moved closer by one year but the therapies do not spread to the whole population all at once, the number of deaths prevented on the margin still amounts to $d$.

Let $f^{\left(1\right)}$ be the function that expresses deaths by aging prevented each year after making LEV come closer by one year and $f$ the (already defined) function that expresses deaths by aging prevented each year without LEV being moved closer. Therefore $f^{\left(1\right)}$ has the following properties:

$f^{\left(1\right)}:\{y-1,...,y+n-2\}\to [0,d]$

$f^{\left(1\right)}(y-1)=f\left(y\right),f^{\left(1\right)}\left(y\right)=f(y+1),...,f^{\left(1\right)}(y+n-2)=f(y+n-1)$, this holds under the very solid assumption that making the date of LEV closer only shifts $f$: it doesn’t change how it is defined, but only subtracts $1$ to all the members of its domain.

Then, the deaths by aging prevented each year on the margin if we make LEV come closer by one year are:

$f^{\left(1\right)}(y-1)+\left[f^{\left(1\right)}\right(y)-f^{\left(1\right)}(y-1\left)\right]+...+f^{\left(1\right)}(y+n-3)+\left[f^{\left(1\right)}\right(y+n-2)-f^{\left(1\right)}(y+n-3\left)\right]=$

$=\left[f^{\left(1\right)}\right(y-1)-f^{\left(1\right)}(y-1\left)\right]+\left[f^{\left(1\right)}\right(y)-f^{\left(1\right)}(y\left)\right]+...+\left[f^{\left(1\right)}\right(y+n-3)-f^{\left(1\right)}(y+n-3\left)\right]+f^{\left(1\right)}(y+n-2)=$

$=f^{\left(1\right)}(y+n-2)=f(y+n-1)=d$

$■$

Note that the same exact proof works if the date of LEV is moved closer by more or less than one year: It is sufficient to let $d$ be the deaths by aging prevented in an arbitrary unit of time. Another proof, with $f$ having a continuous domain, involves manipulating integrals. Here it is:

Proof 2:

Let $f\left(t\right):R\to R$ be the function that associates time with deaths by aging prevented at that time. Then, the total number of deaths prevented in a given time interval $[t_0,t_1]$ is ${\int }_{t_0}^{t_1}f\left(t\right)dt$ . The number of deaths averted on the margin if we make the date of LEV come closer by the time interval $\Delta t$ is:

${\int }_{t_0}^{t_1}f(t+\Delta t)dt-{\int }_{t_0}^{t_1}f\left(t\right)dt$

Let’s divide the interval $[t_1,t_{n+1}]$ in $n$ smaller periods of time of length $\Delta t$ (the period of time LEV is moved closer by). Let’s call those subintervals $\Delta t_i=[t_i,t_{i+1}]$. Then the above integral can be rewritten as a sum of integrals over the smaller intervals.

${\sum }_{i=1}^n\left({\int }_{t_i}^{t_{i+1}}f\right(t+\Delta t)dt-{\int }_{t_i}^{t_{i+1}}f(t\left)dt\right)$

But since it’s true that:

${\int }_{t_i}^{t_{i+1}}f(t+\Delta t)dt={\int }_{t_{i+1}}^{t_{i+2}}f\left(t\right)dt$

Then, the terms of the sum simplify with each other and we have:

${\sum }_{i=1}^n\left({\int }_{t_i}^{t_{i+1}}f\right(t+\Delta t)dt-{\int }_{t_i}^{t_{i+1}}f(t\left)dt\right)={\int }_{t_n}^{t_{n+1}}f(t+\Delta t)dt-{\int }_{t_1}^{t_2}f\left(t\right)dt$

Notice that if $t_1$ happens one unit of time before LEV begins spreading and $t_{n+1}$is the time at which LEV has reached the whole population, then ${\int }_{t_1}^{t_2}f\left(t\right)dt=0$ and ${\int }_{t_n}^{t_{n+1}}f(t+\Delta t)dt$ is exactly the number of deaths by aging that would have occurred in the time interval $\Delta t$; this is exactly the number of deaths by aging prevented if LEV was moved closer by $\Delta t$ and the therapies spread instantly. This proves that the number of deaths by aging prevented on the margin by moving the date of LEV closer by $\Delta t$ is always equal to the number of deaths by aging occurring during $\Delta t$, regardless of how the therapies spread over the world.

$■$

Accounting for making LEV spread faster

As anticipated, another potential source of impact to consider is if a certain project, for example an advocacy-related or policy change, can change how fast people get access to treatments. This would make LEV spread faster, and, in turn, save the people who otherwise wouldn’t reach it.

In order to evaluate this, we need to come up with an estimate of how the future adoption curve will look like. This could possibly be achieved by looking at the way that current health treatments spread, and then evaluate how many people, and, in turn, QALYs, get saved by a change in the curve resulting from the project.

This consideration will probably be given more space in a separate post investigating current adoption curves for health-related technologies and the impact of advocacy and inducing policy change in this area.

Accounting for increasing the probability of LEV

Another consideration that may be taken into account to evaluate impact is how much a given research project increases the probability of LEV. This doesn’t mean increasing the probability of aging getting eradicated completely; it means increasing the probability of research being fast enough to ensure LEV and not a scenario in which research is so slow, or roadblocks so dire, that aging eventually gets eradicated but no one experiences LEV in the meantime.

This probably depends much on the project in question, but it is also possible that, in general, the impact of this consideration could be small, unless we assume a really inefficient research community, or we are analysing a specific research project that is highly neglected and has the potential effect of removing a major roadblock or unlocking further progress, thus speeding up the general pace of research and making the risk of death for future recipients of interventions fall faster. This could be true for research on new scientific tools or research done in a particularly original way that shows a new approach to problems that wasn’t seen before.

In case this consideration has to be taken into account and we need to calculate how many QALYs that increasing this probability would save, we should come up with a distribution of probabilities (with the sum of the probabilities = 1 - the probability of LEV not happening) about how fast the risk of death would fall after LEV. Each outcome yields a different number of QALYs saved by LEV. Then, we should calculate the expected value in QALYs of the distribution with an increased total probability of LEV and the expected value in QALYs of the distribution without an increased total probability of LEV, then determine the difference between the two results.

Aging research boosts the impact of other altruistic interventions

It should be noted that another effect of aging research is to increase the chance for people saved by other interventions to reach LEV. If a life in Africa is saved thanks to insecticidal nets, then the expected QALYs saved will be more or less the person’s expected remaining life plus his/​her life expectancy after LEV in QALYs (more or less 1000 as we have seen) multiplied by the probability that person has to achieve LEV during the rest of his/​her life.

The probability of an individual reaching LEV depends on:

• The probability of dying of causes not related to aging.

• The probability of LEV arriving in the lifetime of the recipient of the intervention.

The first depends on the recipients of the intervention, but even in the worst cases, it should be a pretty high number, considering that even in Africa, the lowest average life expectancy for children born in 2018 is 57 years. The second probability depends on how likely LEV is to appear in any given year. In order to determine this, a very thorough and detailed analysis is needed, and so I will probably tackle this problem in another post.

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Crossposted to LessWrong after the publication here.

[CarlShulman]

One issue I would add to your theoretical analysis: with assigning 1000+ QALYs to letting someone reach LEV is that people commonly don’t claim linear utility with lifespan, i.e. they would often prefer to live to 80 with certainty rather than die at 20 with 90% probability and live to 10,000 with 10% probability.

I agree it’s worth keeping the chance that people will be able to live much longer in the future in mind when assessing benefits to existing people (I would also add the possibility of drastic increases in quality of life through technology). I’d guess most of this comes from broader technological improvements (e.g. via AI) rather than reaching LEV through biomedical approaches), but not with extreme confidence.

However, I don’t think it has very radical implications for cause prioritization since, as you note, deaths for any reason (include malaria and global catastrophes) deny those people a chance at LEV. LEV-related issues are also mainly a concern for existing humans, so to the extent one gives a boost for enormous impacts on nonhuman animals and the existence of future generations, LEV speedup won’t reap much of those boosts.

Within the field of biomedical research, aging looks relatively promising, and I think on average the best-targeted biomedical research does well for current people compared to linear charity in support of deployment (e.g. gene drives vs bednets). But it’s not a slam dunk because the problems are so hard (including ones receiving massive investment). I don’t see it as strongly moving most people who prefer to support bednets over malaria gene drives, farmed animal welfare over gene drives, or GCR reduction over gene drives.

[Emanuele_Ascani]

I just answered your other comment, but I saw this one only now. Apparently both notifications didn’t arrive. Thanks a lot for taking the time to read and answer both.

Some of my replies in the other comment apply here too. I’ll go in order.

Regarding your first paragraph: Yes, I’m preparing a post about potential age discounting that could be applied. I included it among the moral considerations that would correct impact. But you made a good point, and I may need to modify it in the light of it.

Regarding AI and other technology: For the very specific case of AI potentially automating R&D I think the timeline is longer than for LEV achieved through biomedical research (I’m taking the view that arises from the probability distribution given by AI researchers), but, as you said, it’s not the only technology that would make some of the efforts made now less useful.

Regarding your third paragraph: Yes, probably the only non-human animals benefitting from LEV would be pets, although I don’t know how many. I should try to do an estimate.

Regarding comparisons with other cause areas: I think there are some interventions in aging research that could reap massive benefits which are neglected and somewhat tractable. Copying from the other comment: The foundational research is not very neglected, while there are wide areas of translational research that could use much more funding and that are necessary to reach the final goal. From the lifespan.io’s Rejuvenation Roadmap you should get a preliminary idea.

Your example using the SENS approach is correct: areas like stem cell research and cancer research don’t seem to be underfunded. But they are only two pieces of the puzzle. Some others are being much more neglected. That’s why SENS itself gives higher priority to the most neglected areas, like mitochondrial dysfunction and crosslinks, which should be also more tractable (an interesting fact is that Aubrey de Grey often emphasises neglectedness, tractability and scope in his conferences, but I haven’t heard anyone within EA pointing this out). If stem cells research, cancer and other difficult and highly funded areas were all there is to aging research, it wouldn’t look like a very good candidate EA cause. In fact, not only de Grey but many researchers in the area are pursuing projects they believe are very much funding constrained (example: Steve Horvath).

About the comparison with x-risk reduction: Yes, I broadly agree that x-risk reduction looks overall more promising as a cause area. However I think that many x-risk focused interventions have a higher level of uncertainty. It also seems that within Effective Altruism little to no effort has been made to evaluate aging research, while, to me, it looks highly competitive with many of the other focuses of EAs (some specific interventions inside aging research should be very recognisably better). So it should be analysed further, especially because we may be missing out on especially important opportunities.

[MichaelPlant]

Thanks for writing this.

Can you explain in a bit more detail, and without complicated formalisation, why life expectancy after LEV is 1000. I note life expectancy is 1000 and the chance of death in 1 year is 1/​1000. Is that a coincidence, or is life expectancy post-LEV just 1/​annual chance of death?

I know you’ve said you’re going to cover this later, but I want to flag how sensitive this is to population ethics. On totalism (the value of the outcome is the sum total of well-being of everyone who will ever life), it’s good to create lives, so it’s not necessarily a problem that there’s a higher ‘turnover’ of lives, i.e. people die and other people replace them. Totalists will want to know how longevity affects the long run for everyone, not just those that get to live longer. By contrast, if you’re a person-affecting deprivationism (there is no value creating new lives, but for those lives that count, the badness of death is the amount of well-being they would have had had they lived), life extension looks super important!

[Emanuele_Ascani]

Hey, I just published the second post of the framework, which answers your comment pretty well. I even mentioned you inside it. Here it is: https://​​forum.effectivealtruism.org/​​posts/​​uR4mEzMR7fiQzb2c7/​​aging-research-and-population-ethics

[Emanuele_Ascani]

Yes, if the chance of death each year is constant it turns out that remaining life expectancy is around 1/​chance of death. In fact in a previous draft of the post I just used this fact and called it a day. I had to use more formalism though, because chance of death is not constant. After LEV hits there will be a period in which it will fall down, and that needs to be taken into account in order to find a true lower bound for life expectancy. The question that is still open is what is the minimum initial decrease of risk of death that ensures LEV.

Regarding the point about population ethics: Yes, impact depends on population ethics, in the sense that it is for sure as large as it can be under person-affecting deprivationism. Even on totalism though (which seems a more reasonable view of ethics to me), I expect the considerations made to really change the view on the impact of this cause area. This because, for example, a Malthusian outcome in which the disposable resources are always all employed is not necessarily the default outcome, and also not necessarily the most desirable one if well being is took into consideration. It’s also not clear if, under a non Malthusian condition, old people would take resources that would be also useful for young people. There could be vast amount of not used resources. Then added years to life expectancy could be “for free”, without negating the new younger people that would be born anyway. I think you could argue both ways, so the impact evaluation needs a downward correction but it is not invalidated. Another important thing to consider on totalism are moral weights: in general I don’t think that it would be better ethically to have generations and generations of people with a 5 years life span. At least if we don’t only account for how much time a person lives in our ethics, but how valuable that time is. The same argument could apply for much longer lifespans. Maybe a 1000 years life span is much more preferable than a 100 year one. Or maybe not, and time discounting is needed. Again, I think you could argue both ways, because the answer largely depends on informations we currently don’t have: how a 1000 years old mind looks like and how it is different from the one of a current adult.

[MichaelPlant]

Yes, if the chance of death each year is constant it turns out that remaining life expectancy is around 1/​chance of death

Can you explain this is the case? Sorry if this is obvious, but I’m not getting it and can’t think offhand how to do the maths.

On population ethics, for totalists it then seems the dominating concern will be how valuable it is to have a population with longer lives, which puts the emphasis in a difference place from the value of keeping particular individuals alive longer.

[Emanuele_Ascani]

It’s not necessarily obvious that this is the case.

Premise: In probability theory the chance of two independent events (which are events that don’t affect each other) happening together, like six coming up after you toss a dice and head coming up after you toss a coin, is calculated by multiplying the probability of the two events. In the case of the dice and the coin $1/6\cdot 1/2=1/12$.

In the case of calculating expected future lifetime you need to sum all the additional number of years you could possibly live, each multiplied by their probability. This is how an expected value is calculated, and if you think about it it’s basically a weighted average: you want to know the “average” year you will live to, but in making the average each year can weight more or less depending on its probability.

It turns out, though, that in this case you can simplify the expected value formula, by only adding the probabilities of being alive at any given future year. This works, intuitively, because you are basically adding up all expected values that are made like this: $1MoreYear\cdot probabilityOfSurvivingToThatYear$. But what is the probability of surviving one more year? It is the probability of not dying all of the previous years! And so to find the probability you need to multiply all the independent events of not dying in a particular year between your current age and the year you are measuring the probability of arriving to. If the chance of dying any given year is constant at $1/1000$ then the probability of not dying is $1-1/1000$, and the multiplication is like this $(1-1/1000)(1-1/1000)(1-1/1000)\dots$ the number of factors is the number of years between now and the year you are calculating the probability to arrive to. Let’s call this number $k$. The the multiplication becomes $(1-1/1000{)}^k$

So you are basically adding up probabilities made like this: $(1-1/1000{)}^k$ but with k growing till infinite, since you want to account the probability of surviving to any arbitrary future year when calculating the expected value.

Why those probabilities add up exactly to 1/​chance of death? I would think about it this way: when $k$ is small, the term $(1-1/1000{)}^k$ is large, but still smaller than $1$. The subsequent terms of the addition will be subsequently each time a little smaller. So you are basically adding up terms a little smaller than $1$ but each time smaller and smaller. So what happens when you will have added $1000$ terms? You will not quite reach $1000$ in your sum. But this is compensated by all the subsequent super small terms you add till the infinite addition is complete.

Regarding population ethics: I finished to write the first draft of the second post in the series, and it is exactly about this topic. Can I send the Google Doc to you so you can comment in advance on it? It’s around 2k words. I know you are a moral philosopher (I remember you writing so in your post about Hippo), so it would be great to have feedback.

[Ben Millwood🔸]

If you want to look up the maths elsewhere, it may be helpful to know that a constant, independent chance of death (or survival) per year is modelled by a negative binomial distribution.

[Emanuele_Ascani]

Yes, looking back at this, I should have just said that on average, if someone dies with a probability of 1/​1000, then he will live 999 years and die in the 1000th. And then I should have linked him the “Expectation” section of the Wikipedia page of the negative binomial distribution.

[agdfoster]

I work with donors and feel I don’t have enough to say when ageing comes up. Fancy giving me a quick primer?

A few things I’m clearly confused on:

• why aging isn’t always discussed under the restriction of global population capacity, seems like we should have reached it by then (assuming no AGI). I realise this is everyone’s first intuitive response but seems like it should still be a key factor in any analysis.

• seems like under a full capacity assumption the impact either comes from an improved distribution of where people are at in life (less teenage depression and end of life suffering or something like that) which seems uncertain. Or from increased career length which also seems not certainly net positive. Maybe I missed it but couldn’t see any of this in your calc discussion.

• I know there are plenty of arguments for aging being neglected and so worth it from the medium term also but it seems like if you’re talking about escape velocity then pop cap needs to factor in.

If you’d be up for that primer I’m On my username (Agdfoster) and @gmail.com

[Emanuele_Ascani]

Population capacity gets larger as technology improves, so it’s not obvious we’ll reach maximum capacity in the near future (next centuries). Regardless of this, even if we reached it, the impact of aging research wouldn’t be impacted, because impact comes from making LEV closer, not from guaranteeing LEV’s existence. You will find answers in the second post of the framework: https://​​forum.effectivealtruism.org/​​posts/​​uR4mEzMR7fiQzb2c7/​​aging-research-and-population-ethics

Notice that the post you are commenting under is just the first in a series. I already published four of them! Here the second, third and fourth. There are more to come, and I also plan to do some interviews with organizations. I suggest you read what I wrote so far and get back if you have more doubts and still want more pieces of information or a primer on the field. It will be probably useful for you to subscribe to my posts through the “Subscribe to this user’s posts” option in my profile.

[gavintaylor]

Interesting post.

One extra point I thought of: the analysis calculates the value of LEV based on it eventually spreading to the entire population. But if LEV tech is very expensive and/​or restricted/​proprietary, then it may only ever be adopted by a small elite. This consideration should reduce the value of research that achieves LEV but has limited adoption. I don’t know enough about population ethics to know how this would be considered, could creating more inequality be considered negative? Or just a small positive for the population overall.

In terms of probability of reaching LEV, I think that it is also worthwhile considering that even if all of the hallmarks of ageing are addressed rapidly and people start living longer, people might not make it out to 1000 year average life spans. My intuitive feel as a biologist is that these hallmarks may just be the first signs of ageing, and that treating them might then allow other hallmarks to arise that tend to lead to deaths at say, 200 or 300 years. We obviously don’t know what these are yet and it might be that they can be more easily addressed than the original hallmarks—or maybe not.

[Emanuele_Ascani]

Thanks for the points made, it’s nice to hear from a biologist :)

I think your first point is a possibility, but almost only theoretical. Most medical technology drops in price over time. The possibility that some technology won’t ever drop in price has a place in the analysis, as people may want to correct their measure of impact if they think a situation of such extreme inequality has a non negligible probability of happening. I think, though, that it’s very improbable. Aging is such a burden on a state’s economy that it would make sense very soon to distribute therapies for free. I think this is similar to why basic education gets distributed for free. This may seem very utopian given the current state of healthcare accessibility in the US, but not so much for the rest of the world. I would also be very surprised if such inequality existed and policies against it wouldn’t been made. I think it’s safe to say that the population would be extremely outraged about it, and politicians proposing policies to make treatments accessible for everyone would be voted immediately.

Regarding the second observation: You make a good point. In the analysis this is probably not clear, but I’m also pretty sure that putting all the hallmarks described in “The Hallmarks of Aging” under medical control will not eradicate aging. Even for some parts of the hallmarks there is not complete consensus if they are dangerous in a normal human lifespan. This is mostly fine but it influences the probability. Here how I reason about this: since LEV is about how fast medical technologies and treatments are invented, If “post-hallmarks” therapies get on the market fast enough, then the people who benefitted from the first ones could further increase their lifespan, and so on. At that point I would expect that funding for aging research would have skyrocketed, due to the fact that society will be well aware of what’s happening, and the problems making my analysis necessary will not exist. So I think there’s at least a decent probability that the subsequent therapies will come fast enough. Regarding if the next problems will be more difficult or not: this is difficult to predict, but at least we know that we will probably benefit from better technology, so even if they will be somewhat more difficult we could be able to solve them faster.

[Mati_Roy]

Thanks for writing this!

Looking forward to a review of charities in that area.

I invite people interested in this topic to join the Effective Altruism & Life Extension Facebook group.

I suggest you add a summary at the top of the post.

Here’s a summary of LEV leverage points: Bringing the date we solve aging forward by one year could extend the life of 36,500,000 by 1000 years (under conservative assumptions^1). But if Longevity Escape Velocity (LEV) is reached before that (and maintained until we solve aging), then it’s bringing the LEV forward by 1 day that will be the crucial point. Note that solving other causes of death (than aging) near the LEV point would also bring the LEV point forward. Other leverage points would be increasing the probability that LEV is maintained until we solve aging, and increasing the speed of distribution of LEV technology (note that this doesn’t impact the value of the other leverage points).

1. a) Probably more than 36,500,000 actually given that—actually in the short term—population will increase, and the fraction of death from aging will also increase.

1. b) probably more than a 1000 years in expectation given a 1000 years might be enough to solve the other death causes, and radically increase that number

Musing: I wonder if it would be technically more accurate to call it Death Escape Velocity. And while solving aging is the crucial point in the model, solving other death causes near LEV could also expedite when LEV is achieve. And once we solve aging, the LEV model stays relevant: we could (realistically) still increase life expectancy by more than a year per year by reducing the rate of the other causes of death, such as accidents, until we stop adding a year every year, and eventually reach a maximum lifespan (or we get complete immortality).

Edit: previous version was mistakenly saying 36,500,000 lives per day instead of year

[Aaron Gertler 🔸]

I second the suggestion to add a summary at the top of the post.

The Forum has a feature that it took me a while to notice: On pages that show lists of posts, each post has an estimated reading time. The time for this post, for example, was “20m”. If someone is thinking of investing 2o minutes in a post (and that number is likely conservative if they need to pause, think, go back, etc.), giving them a summary can be really valuable in helping them make that decision.

[Emanuele_Ascani]

Thanks Mati_Roy and aarongertler for the suggestion of adding a summary. Now there is one!

Maty_Roy, thank you for the points made! I would like to correct what I think are a couple of misunderstandings and I would like to elaborate on your idea about using Death Escape Velocity, instead of Longevity Escape Velocity:

Misunderstandings:

1) 36,500,000 are the people dying of aging in a year, so bringing LEV closer by one year (and not by one day) would save this number of lives.

2) If Longevity Escape Velocity doesn’t happen, bringing the date in which aging is cured completely closer could simply do nothing. This because people living at that time could have already a really low risk of death, that can’t go much further down with an additional improvement on treatments for aging. This because if Longevity Escape Velocity doesn’t happen, then I would expect the “very slow scenario” or the “dire roadblocks” scenario to be true, and aging would be eradicated really slowly, possibly in centuries.

The points about why my estimate is conservative are summarised well, thanks for doing that :)

Regarding the idea of using “death escape velocity”: I didn’t use it because technologies that would decrease the risk of death by other causes other than aging are substantially different from the ones brought about by aging research. So it would be another cause area completely! I also would expect them to become more relevant in the future. I think there is not much use of thinking about them now and they wouldn’t make potential EA interventions to fund, since our ideas will be probably be made useless by potentially much better technology existing after aging gets eradicated (that is the first step). “Death escape velocity”could be brought about, for example, by friendly AGI, if that ever comes about. I think this input is valuable though, since it’s an existing related concept that is not talked about much.

[Arepo]

Can I suggest keying the maths in the post, so that those of us wanting to try and parse it but without a mathematical background can feasibly do so?

[Emanuele_Ascani]

I’m thinking about writing a post just for the proofs, so I can generalise to every technology. I could try to explain the maths in there for who has less background. It should be feasible making pictures of examples of graphs.