## 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 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). This figure comes up from the remaining life expectancy of the recipients of the intervention. 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 is denoted with . It can be seen as the expected value of the random variable , also called "Curtate Future Lifetime", which is defined as , where maps to the amount of additional time that an individual of age is projected to live. For our purposes, we can use the discrete random variable instead of directly . Thus, with being the probability of surviving between age and age :

If is the probability of dying between year and year , then:

When the whole population benefits from LEV, the risk of death will fall for everyone. By definition, it will fall at a rate such that the expected future lifetime of any given individual will remain constant until aging gets eradicated completely. So, in order to make the most conservative estimate about life expectancy after LEV, we need to find the minimum rate of decrease of such that this condition holds. The answer to this doesn't seem easy, so I'll find this lower bound in another post.

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 , 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,

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 whic