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

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 x 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 p(x) 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 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, 14 of the pop­u­la­tion reaches LEV; in the sec­ond year, 12; in the third, 45; and in the fourth, 55. 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 = 14 of the deaths of ag­ing oc­cur­ring dur­ing that year. In the sec­ond year, we pre­vent 1/​2-1/​4 = 14 of the deaths by ag­ing that oc­cur dur­ing that year. In the third year, we pre­vent 4512 = 310 of the deaths by ag­ing oc­cur­ring dur­ing that year. In the fourth year, we pre­vent 5545 = 15 of the deaths by ag­ing oc­cur­ring dur­ing that year. So, in to­tal, by shift­ing the date of LEV by one year, we pre­vented: 14 + 14 + 310 + 15 = 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:

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

the year in which the ther­a­pies lead­ing to LEV be­gin spread­ing.

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

ex­presses how many deaths from ag­ing are pre­vented in a given year dur­ing the time that ther­a­pies are spread­ing. How ex­actly is defined de­pends on how the ther­a­pies spread (e.g. ex­po­nen­tially or lin­early), but we know that and that .

If LEV spreads to the whole pop­u­la­tion all at once, then and . In this case if the date of LEV is moved closer by year, then the re­sult­ing new func­tion , has as the only mem­ber of its do­main, also map­ping to . So the deaths pre­vented on the mar­gin by mak­ing the date of LEV closer by one year are ex­actly .

We want to prove for all val­ues of and 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 .

Let be the func­tion that ex­presses deaths by ag­ing pre­vented each year af­ter mak­ing LEV come closer by one year and the (already defined) func­tion that ex­presses deaths by ag­ing pre­vented each year with­out LEV be­ing moved closer. There­fore has the fol­low­ing prop­er­ties:

, this holds un­der the very solid as­sump­tion that mak­ing the date of LEV closer only shifts : it doesn’t change how it is defined, but only sub­tracts 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:

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 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 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 is . The num­ber of deaths averted on the mar­gin if we make the date of LEV come closer by the time in­ter­val is:

Let’s di­vide the in­ter­val in n smaller pe­ri­ods of time of length (the pe­riod of time LEV is moved closer by). Let’s call those subin­ter­vals . Then the above in­te­gral can be rewrit­ten as a sum of in­te­grals over the smaller in­ter­vals.

But since it’s true that:

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

No­tice that if hap­pens one unit of time be­fore LEV be­gins spread­ing and is the time at which LEV has reached the whole pop­u­la­tion, then and is ex­actly the num­ber of deaths by ag­ing that would have oc­curred in the time in­ter­val ; this is ex­actly the num­ber of deaths by ag­ing pre­vented if LEV was moved closer by 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 is always equal to the num­ber of deaths by ag­ing oc­cur­ring dur­ing , 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.


This is a cross­post from my post in the Effec­tive Altru­ism Fo­rum.

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