Willpower Thermodynamics
Content warning: a couple LWers apparently think that the concept of ego depletion—also known as willpower depletion—is a memetic hazard, though I find it helpful. Also, the material presented here won't fit everyone's experiences.
What happens if we assume that the idea of ego depletion is basically correct, and try to draw an analogy between thermodynamics and willpower?
Figure 1. Thermodynamics Picture
You probably remember seeing something like the above diagram in a chemistry class. The diagram shows how unstable, or how high in energy, the states that a material can pass through in a chemical reaction are. Here's what the abbreviations mean:
- SM is the starting material.
- TS1 and TS2 are the two transition states, which must be passed through to go from SM to EM1 or EM2.
- EM1 and EM2 are the two possible end materials.
The valleys of both curves represent configurations a material may occupy at the start or end of a chemical reaction. Lower energy valleys are more stable. However, higher peaks can only be reliably crossed if energy is available from e.g. the temperature being sufficiently high.
The main takeaway from Figure 1 is that reactions which produce the most stable end materials, like ending material 2, from a given set of starting materials aren't always the reactions which are easiest to make happen.
Figure 2. Willpower Picture
We can draw a similar diagram to illustrate how much stress we lose while completing a relaxing activity. Here's what the abbreviations used in Figure 2 mean:
- SM is your starting mood.
- TS is your state of topmost stress, which depends on which activity you choose.
- EM1 and EM2 are your two possible ending moods.
Above, the valley on the left represents how stressed you are before starting one of two possible relaxing activities. The peak in the middle represents how stressed you'll be when attempting to get the activity underway, and the valley on the right represents how stressed you'll be once you're done.
For the sake of simplification, let's say that stress is the opposite of willpower, such that losing stress means you gain willpower, and vice versa. For many people, there's a point at which it's very hard to take on additional stress or use more willpower, such that getting started on an activity that would normally get you to ending mood 2 from an already stressed starting mood is very hard.
In chemistry, if you want to make end material 2 instead of end material 1, you have to make sure that you have some way of getting over the big peak at transition state 2—such as by making sure the temperature is high enough. In real life, it's also good to have a plan for getting over the big peak at the point of topmost stress. Spending time or attention figuring what your ending mood 2-producing activities are may also be worthwhile.
Some leisure activities, like browsing the front page of reddit, are ending mood 1-producing activities; they're easy to start, but not very rewarding. Examples of what qualifies as an ending mood 2-producing activity vary between people—but reading books, writing, hiking, meditating, or making games or art qualify as ending mood 2-producing activities for some.
At a minimum, making sure that you end up in a high willpower, low stress ending mood requires paying attention to your ability to handle stress and conserve willpower. Sometimes this implies that taking a break before you really need to means that you'll get more out of your break. Sometimes it means that you should monitor how many spoons and forks you have. In general, though, preferring ending mood 2-producing activities over ending mood 1-producing activities will give you the best results in the long run.
The best-case scenario is that you find a way to automatically turn impulses to do ending mood 1-producing activities into impulses to do ending mood 2-producing activities, such as with the trigger action plan [open Reddit -> move hands into position to do a 5-minute meditation].
Dry Ice Cryonics- Preliminary Thoughts
Edited nearly a year later to clarify: dry ice cryonics probably won't work, for reasons hinted at in the post, and stated by Gav in the comments, regarding nanoscale ice crystals. It seems like there may be less of a tradeoff between fracturing and having ice crystals now than there used to be, especially if newer approaches involving e.g. cryonics with persufflation end up working well in humans.
This post is a spot-check of Alcor's claim that cryonics can't be carried out at dry ice temperatures, and a follow-up to this comment. This article isn't up to my standards, yet I'm posting it now, rather than polishing it more first, because I strongly fear that I might never get around to doing so later if I put it off. Despite my expertise in chemistry, I don't like chemistry, so writing this took a lot of willpower. Thanks to Hugh Hixon from Alcor for writing "How Cold is Cold Enough?".
Summary
More research (such as potentially hiring someone to find the energies of activation for lots of different degradative reactions which happen after death) is needed to determine if long-term cryopreservation at the temperature of dry ice is reasonable, or even preferable to storage in liquid nitrogen.
On the outside view, I'm not very confident that dry ice cryonics will end up being superior to liquid nitrogen cryonics. Still, it's very hard to say one way or the other a priori. There are certain factors that I can't easily quantify that suggest that cryopreservation with dry ice might be preferable to cryopreservation with liquid nitrogen (specifically, fracturing, as well as the fact that the Arrhenius equation doesn't account for poor stirring), and other such factors that suggest preservation in liquid nitrogen to be preferable (specifically, that being below the glass transition temperature prevents movement/chemical reactions, and that nanoscale ice crystals, which can grow during rewarming, can form around the glass transition temperature).
(I wonder if cryoprotectant solutions with different glass transition temperatures might avoid either of the two problems mentioned in the last sentence for dry ice cryonics? I just heard about the issue of nanoscale ice crystals earlier today, so my discussion of them is an afterthought.)
Motivation
Using dry ice to cryopreserve people for future revival could be cheaper than using liquid nitrogen for the same purpose (how much would using dry ice cost?). Additionally, lowering the cost of cryonics could increase the number of people who sign up for cryonics-- which would, in turn, give us a better chance at e.g. legalizing the initiation of the first phases of cryonics for terminal patients just before legal death.
This document by Alcor suggests that, for neuro and whole-body patients, an initial deposit of 6,600 or 85,438 USD into the patient's trust fund is, respectively, more than enough to generate enough interest to safely cover a patient's annual storage cost indefinitely. Since around 36% of this amount is spent on liquid nitrogen, this means that completely eliminating the cost of replenishing the liquid nitrogen in the dewars would reduce the up-front cost that neuro and whole-body patients with Alcor would pay by around 2,350 or 31,850 USD, respectively. This puts a firm upper bound on the amount that could be saved by Alcor patients by switching to cryopreservation with dry ice, since some amount would need to be spent each year on purchasing additional dry ice to maintain the temperature at which patients are stored. (A small amount could probably be saved on the cost which comes from cooling patients down immediately after death, as well).
This LW discussion is also relevant to storage costs in cryonics. I'm not sure how much CI spends on storage.
Relevant Equations and Their Limitations
Alcor's "How Cold is Cold Enough?" is the only article which I've found that takes an in-depth look at whether storage of cryonics patients at temperatures above the boiling point of liquid nitrogen would be feasible. It's a generally well-written article, though it makes an assumption regarding activation energy that I'll be forced to examine later on.
The article starts off by introducing the Arrhenius equation, which is used to determine the rate constant of a chemical reaction at a given temperature. The equation is written:
k = A * e^(-Ea/RT) (1)
Where:
- k is the rate constant you solve for (the units vary between reactions)
- A is a constant you know (same units as k)
- Ea is the activation energy (kJ/mol)
- R is the ideal gas constant (kJ/K*mol)
- T is the temperature (K)
- v is the rate of the reaction (mol/(L*s))
- k is the rate constant, from the Arrhenius equation above
- [A] and [B] are the concentrations of reactants-- there might be more or less than two (mol/L)
- m and n are constants that you know
Effects of Castration on the Life Expectancy of Contemporary Men
Follow-up to: Lifestyle Interventions to Increase Longevity
Abstract
A recent review article by David Gems discusses possible mechanisms by which testosterone and dihydrotestosterone could shorten the life expectancies of human males, and examines previous research on the effects of castration on male survival. However, Gems does not examine how age at castration affects how much castration extends one's life by, which this post does. In general, castration after puberty in males prolongs life to a lesser extent than castration before the onset of puberty.
Additionally, Gems' review does not estimate how long modern-day eunuchs might live relative to intact human males. Two of the other three known studies on the effects of castration on human life expectancies found that, historically, castration prolonged life by more than a decade in the median case. However, some of the life expectancy gains from castration are due to the increased ability of eunuchs to fight off infections. The fact that fewer men die from infections in the 21st century than was the case in previous centuries means that modern-day eunuchs gain fewer years of life from castration than eunuchs gained from castration in the past. As seen from comparing Figure 3b and Figure 4, eunuchs castrated just before the onset of puberty extended their (mean) life expectancies by 11 years in Hamilton & Mestler's study, though modern eunuchs castrated at similar ages might expect to extend their life expectancies by 7 years.
Introduction
A few relevant studies, such as the study of institutionalized eunuchs by Hamilton & Mestler, the study of Korean eunuchs by Min, Lee, and Park, and the review article by Gems are particularly worth reading or skimming for those interested in this topic. The excel file showing the work behind this post is also available. These documents are supplementary; reading them is not a prerequisite for reading this post.
This post will examine the proposition that castration of human males (specifically, orchiectomy, the surgical removal of both testicles, but not the penis) either before or after the onset of puberty will extend both their life expectancy, and their lifespan. In light of antagonistic pleiotropy, it a priori makes sense that castration might extend one's life expectancy.
A number of papers have mentioned that the effects of castration on the life expectancy of different types of nonhuman animals don't provide a good model for the effects of castration on the life expectancy of human males. Specifically, "the relationship of gonadal functions to survival seems to involve many variables... individuals, strains, and species may vary in their response to gonadectomy". This leaves only a small number of studies that have much bearing on the question of whether or not orchiectomy extends human life expectancy. While there are some studies on the health effects of chemical and physical castration of (often elderly) modern men with prostate cancer, it seems like having prostate cancer would correlate with having other pathologies. Further, as will be examined later, it seems that orchiectomies performed at early ages have many positive effects on health, whereas orchiectomies performed later in life have fewer positive effects, and may even negatively affect some aspects of health.
After setting aside animal studies and studies of men with prostate cancer, only four papers directly relevant to whether orchiectomy increases the life expectancy of men remain. This is worth stating explicitly, since citing only a fraction of the available research on a given topic can be a fallacy. First, the study by Min, Lee, and Park found that, historically, Korean eunuchs lived 14-19 years longer than intact males from similar social classes in the median case. Secondly, Hamilton and Mestler's study of the effects of orchiectomy on the life expectancies of mentally retarded individuals found that males castrated before puberty lived about 13 years longer than intact men in the median case, and that males castrated after puberty experienced smaller lifespan gains. Thirdly, a letter to Nature by Nieschlag et. al which compared the lifespans of famous castrato singers to the lifespans of other singers from the same era found that orchiectomized male singers lived about as long as intact male singers. Lastly, page four of the review article by David Gems examined all three of these studies, and, after finding methodological issues with the letter to Nature, concluded that the results in these papers were "consistent with the idea that testes are a determinant of the gender gap in human lifespan".
Evidence Regarding Whether or Not Orchiectomy After Puberty Increases Life Expectancy
The only study that examined the effect which age at orchiectomy had on the life expectancy gains from castration in humans was Hamilton and Mestler's study of mentally retarded, institutionalized individuals. Note that the participants in Hamilton & Mestler's study lived shorter lives than non-institutionalized Americans of the same era lived, which could likely be explained by the mentally retarded status of the participants, and the plausibly poor conditions under which participants might have lived. In Figure 4 and Table 10 from Hamilton and Mestler's paper, it is shown that males castrated between 15 and 40 years of age live longer than intact males, but that within this range, earlier castrations added more years to the life expectancy of eunuchs than later castrations did.
It is worth reproducing Figure 4 from Hamilton & Mestler's article, which shows the survival curves (starting at 40 years of age) of intact males and males castrated at various ages:

One thing about this figure that stands out is that the portion of the survival curve for institutionalized non-castrates shown in this figure is nearly linear. In the present day, intellectually disabled populations have survival curves which look quite different from the one for non-castrates shown in the figure above. For reference, the survival curve for castrated females in Figure 5 of this post has a shape which is comparable to the shape of survival curves for modern first-world populations. It is also remarkable that the tail end of the survival curve for non-castrates in the above figure is fatter than the tails of the survival curves for men castrated after 14 years of age-- it isn't obvious whether or not this difference reflects a real phenomenon. Further, the 3.7 % centenarian rate for Korean eunuchs in the study by Min, Lee, and Park suggests that eunuchs should have a longer (maximum) lifespan than non-castrates, which isn't borne out in Figure 4 from Hamilton & Mestler. This having been said, Figure 4 and Table 10 from Hamilton & Mestler's study show that castration at earlier ages prolongs life more than castration at later ages does.
Below, in Figure 1, the attempted linear fit between median life expectancy versus age at castration given on p. 403 of Hamilton and Mestler's paper is shown. The authors used data from Table 10 of their paper to determine this fit, but did not graph the data or determine an R2 value for this linear fit. The estimated median life expectancy of the non-castrates was 64.7 years-- a reasonable value, given their status as institutionalized mentally retarded men in the early 20th century. Thus, Figure 1 can be used to visualize the fact that even men who were castrated at 30-39 years of age lived longer than non-castrates in the study (p = 0.002). Since the data shown in Figure 1 did not follow a linear trend, additional fits were tried below.
Figure 1. Hamilton & Mestler's Regression of Median Life Expectancy v. Age at Castration
Figure 2. Polynomial Fit for Median Life Expectancy v. Age at Castration
Figure 3. Raw Data and Fits For Interpolation of Mean Life Expectancy v. Age at Castration
Data and fits for the median and mean life expectancies of eunuchs are given in Figures 2 and 3, respectively. The data plotted in sections a and b of Figure 3 could not be reasonably fitted to a curve directly, so sections c and d of Figure 3 show the same data as sections a and b, but plotted on an inverted x axis and successfully fitted to a curve. The polynomial data fits given in all Figures are only intended for use in interpolation.
Effects of Orchiectomy on Mortality from Infectious Diseases and Cardiovascular Mortality
Literature has suggested that castration in human males may promote longer lifespans and higher life expectancies by protecting against infections and cardiovascular events. Much of the evidence for the proposition that castration protects against cardiovascular disease (CVD) comes from basic biology rather than from studies of eunuchs, since Hamilton & Mestler's paper is the only study on eunuchs which attempted to collect data on causes of death in castrated men, and only did so from clinical diagnoses of the primary causes of deaths of eunuchs and intact men between 1940-1964. Still, modern men die of cardiovascular events more often than modern women do, so investigating whether or not castration protects against cardiovascular events is worthwhile.
The authors of the study on Korean eunuchs cite this review as evidence that "male sex hormones reduce the lifespan of men because of their antagonistic role in immune function". Gems' review article also suggests that male sex hormones may act as an immune suppressant. Moreover, in Hamilton & Mestler's study, 27% of eunuchs died of infections, compared to 44% of intact men (p = 0.02), and the mean age of eunuchs dying of infections was 44, compared to 35 for intact men (p = 0.03). However, Table 14 of Hamilton & Mestler's study suggests that castration protects more against deaths from certain kinds of infections, such as tuberculosis, than others. In general, it seems like the claim that castration protects against deaths from infections is true.
On the other hand, the data relevant to whether or not eunuchs die more from CVD than intact men do is muddled at best, and it isn't obvious that castration protects males from CVD by much, if at all. One mostly irrelevant data point is men who have undergone chemical or physical castration after being diagnosed with prostate cancer, as well as hypogonadic men in general; many meta-analyses on the relationship between hypogonadism and frequency of adverse cardiovascular events (and on the effects of hormone replacement therapy on the frequency of adverse cardiovascular events) in men have been done. Men castrated after being diagnosed with prostate cancer tend to have more adverse cardiovascular events than other similarly aged men, but this could be because hypogonadism correlates with being unhealthy, rather than because castration at advanced ages decreases life expectancy.
One poorly done study on Danish eunuchs who were predominantly drawn from the lower class found that these eunuchs did not live as long as men in Denmark did on average, and also found that the standardized mortality ratio for cardiovascular disease-related deaths was higher than the all-cause standardized mortality ratio in eunuchs. However, men in this study were often castrated later in life-- all but one man were castrated after the age of 18, and the average age at castration was 35. As suggested by Figure 2 and Figure 3 above, this means that most of the Danish eunuchs gained appreciably fewer years of life from being castrated than they would have gained if the castrations had been carried out much earlier in their lives. These concerns suggest that this study should not change one's credence in the proposition that castration protects against CVD mortality by much.
Lastly, Hamilton & Mestler's study found that eunuchs dying of cardiovascular disease during or after 1940 lived an average of 51.6 years, while intact males dying of that cause lived an average of 51.1 years. This difference was not found to be significant. However, since not all eunuchs included in the study had died by the time of publication, it is still possible that castration early in life protects against late-life cardiovascular mortality, but not early and mid-life cardiovascular mortality.
Effects of Orchiectomy on Modern Lifespans and Life Expectancy
Some common causes of death in both Hamilton & Mestler's study and the study of Korean eunuchs, such as tuberculosis, are no longer common causes of death. Thus, data from Table 14 in Hamilton & Mestler were used alongside modern actuarial data to crudely predict how long eunuchs castrated in the 21st century might live. The details of the analysis are given in this excel file. The results of this analysis are given below.

Figure 4. Life Expectancy Gains for Modern Eunuchs
Table 1. Life Expectancy Gains for Modern Eunuchs

For the most part, the data in Figure 4 and Table 1 are consistent with my holistic understanding of the effects of castration in men. It is hard to say how castration after age 35 would affect life expectancy, as very few eunuchs in Hamilton & Mestler's study were castrated after 35. It's also a shame that about 27% of the eunuchs and intact males who died during 1940-1964 were not listed as having a primary cause of death-- this may have led to an overestimation of the extent to which castration is expected to extend modern eunuch's life expectancies. On the other hand, Min, Lee, and Park found that 3.7% of Korean eunuchs who died between the late 14th to early 20th century were centenarians, "a rate at least 130 times higher than that of present-day developed countries", which suggests that modern eunuchs would likely benefit from increased lifespans.
Effects of Orchiectomy on Health and Physiology
Gems' review article, this article on historical eunuchs, the wikipedia page on castration, and Hamilton & Mestler's study all note certain effects that castration can have on human males.
All castrated males have an increased risk of developing sarcopenia, and becoming overweight. Wilson and Roehrborn note that eunuchs have historically suffered from skeletal problems such as osteoporosis and kyphosis; this is especially true of elderly eunuchs, and eunuchs castrated at earlier ages. Hormone replacement therapy can prevent or deter sarcopenia, osteoporosis and kyphosis. Castration also decreases sex drive, prevents baldness if done early enough in life, and may result in enlarged pituitaries and enlarged breasts. Castration causes the prostate to shrink over time, and if done early enough in life, effectively prevents the development of prostate cancer. Castration also prevents the development of prostatic hyperplasia and testicular cancer.
Men castrated before puberty will develop higher voices, little or no sex drive, and smaller penises.
Effects of Gonadectomy on Human Females
There is very little data relevant to whether or not oophorectomy (castration) of women extends life expectancy or lifespan. Hamilton & Mestler have a small section dedicated to estimating the life expectancy of castrated females based on only 11 female castrates of known fate. They also find the median lifespans of castrated and intact females known to be dead by the end of the study to be equal. Lastly, Hamilton & Mestler find the mean lifespan of institutionalized castrated females known to be dead by the end of the study, 56.2 years, to be significantly greater than the mean lifespan of institutionalized intact females known to be dead by the end of the study, 33.9 years (p < 0.001). The estimated survival curves for all castrated females and all intact females-- not just those known to be dead by the end of the study-- are given in Figure 5.

Figure 5. Survival Curve for Intact and Castrated MR Females
Conclusion and Motivation
Orchiectomy should prolong the lifespans of modern males, especially if done before puberty. While the estimates of life expectancy gains from castration given in Figure 4 and Table 1 aren't perfect, they are my best guesses, and should be interpreted with the correspondingly appropriate level of credence.
My original motivation for writing this post was that I was interested in learning about the different ways in which humans could extend their lifespans and life expectancies. So, while being castrated is one way for males to live longer, quitting smoking and improving one's diet and exercise regimen are better uses of time and energy for people who are just beginning to think about changing their lifestyles in order to live longer.
Thanks to Vaniver, who caught several errors in an earlier draft of this post, and thanks to btrettel for pointing me to a few papers early on. All remaining errors in this post are solely my own.
References
1. Castration. http://en.wikipedia.org/wiki/Castration
2. Antagonistic Peliotrophy Hypothesis. http://en.wikipedia.org/wiki/Antagonistic_pleiotropy_hypothesis
3. Bittles, A. H.; Petterson, B. A.; Sullivan, S. G.; Hussain, R.; Glasson, E. J.; Montgomery, P. D. The influence of intellectual disability on life expectancy. J. Gerontol. A Biol. Sci. Med. Sci. 2002, 57, M470-2.
4. Corona, G.; Maseroli, E.; Rastrelli, G.; Isidori, A. M.; Sforza, A.; Mannucci, E.; Maggi, M. Cardiovascular risk associated with testosterone-boosting medications: a systematic review and meta-analysis. Expert opinion on drug safety 2014, 13, 1327-1351.
5. Corona, G.; Rastrelli, G.; Monami, M.; Guay, A.; Buvat, J.; Sforza, A.; Forti, G.; Mannucci, E.; Maggi, M. Hypogonadism as a risk factor for cardiovascular mortality in men: a meta-analytic study. Eur. J. Endocrinol. 2011, 165, 687-701.
6. Gems, D. Evolution of sexually dimorphic longevity in humans. Aging (Albany NY) 2014, 6, 84-91.
7. Hamilton, J. In Duration of Life in Lewis Strain of Rats After Gonadectomy at Birth and at Older Ages; Reproduction & Aging; 1974; pp 116-122.
8. HAMILTON, J. B. Relationship of Castration, Spaying, and Sex to Survival and Duration of Life in Domestic Cats. J. Gerontol. 1965, 20, 96-104.
9. Hamilton, J. B.; Mestler, G. E. Mortality and survival: comparison of eunuchs with intact men and women in a mentally retarded population. J. Gerontol. 1969, 24, 395-411.
10. Jones, C. M.; Boelaert, K. The Endocrinology of Ageing: A Mini-Review. Gerontology 2015, 61, 291-300.
11. Mestler, H. In The Role of Testicular Secretions as Indicated by the Effects of Castration in Man and Studies of Pathological Conditions and the Short Lifespan Associated with Maleness; Pincus, G., Ed.; Recent Progress in Hormone Research; Laurentian Hormone Conference: 1948; pp 257.
12. Min, K.; Lee, C.; Park, H. The lifespan of Korean eunuchs. Current Biology 2012, 22, R792-R793.
13. Nieschlag, E.; Nieschlag, S.; Behre, H. M. Lifespan and testosterone. Nature 1993, 366, 215-215.
14. Roberts, M. L.; Buchanan, K. L.; Evans, M. Testing the immunocompetence handicap hypothesis: a review of the evidence. Anim. Behav. 2004, 68, 227-239.
15. Talbert, G. B.; Hamilton, J. B. Duration of life in Lewis strain of rats after gonadectomy at birth and at older ages. Reproduction & Aging 1974, 116.
16. Wilson, J. D.; Roehrborn, C. Long-term consequences of castration in men: lessons from the Skoptzy and the eunuchs of the Chinese and Ottoman courts. The Journal of Clinical Endocrinology & Metabolism 1999, 84, 4324-4331.
Efficient Food
Yudkowsky's 2014 April Fools Day's confession notes that food production could be more efficient:
Food in dath ilan was made by people who were very good at making a particular variety of food, and they’d pick a few dishes and make a huge amount of it on any given day. There’d be many places like that within 2 miles of you, and a small courier-carlike-thing would attach itself to another car and arrive with the food you liked within 2 minutes.
A quick Google search suggests that restaurants tend to spend around a third of their revenue on ingredients (more quick estimates of restaurant operational costs on page five of this slideshow). Of course, fast food and fast casual restaurants spend a higher percentage of revenue on ingredients than other types of restaurants, but spending 30-35% of revenue on ingredients seems standard. So, it should be possible to reduce the cost of food by producing food more efficiently, that is, by making huge batches of one or two types of food at a given restaurant.
I've only been able to find one example of an establishment that actually does this. Ugi's, an Argentinian pizza chain, sells 12-inch (?) cheese pizzas for about 4.91 USD in Buenos Aires. Ugi's has a couple of locations in the US, too-- this one in Boston sells 12-inch cheese pizzas for 6.55, but also sells items other than cheese pizzas. For comparison, a 12-inch cheese pizza from Domino's pizza costs around 11 USD to order via carryout in Boston.
I, for one, am fascinated by the idea of restaurants that only serve one item, and would definitely purchase food from such establishments if they were more common in the US.
Also relevant:
Tentative Thoughts on the Cost Effectiveness of the SENS Foundation
It should be emphasized that back-of-the-envelope calculations, such as the one given in this post, ought to be adjusted to account for the fact that interventions can look much more cost-effective than they are, especially when the interventions were only shallowly investigated.
Previously, Givewell has looked into the cost-effectiveness of life sciences funding, as well as publishing a simple estimate of the impact of the average dollar spent on cancer research, which suggested that, in the past, each $2790 spent on cancer-relevant biomedical research in the US added one year of life lived (YLL) to the life of a US resident. Givewell has also interviewed Aubrey de Grey of the SENS foundation. Owencb has previously estimated the cost-effectiveness of funding SENS/ anti-aging research as being around $50 per QALY. Aubrey de Grey has previously been averse to giving explicit cost-effectiveness estimates regarding how many QALYs would be gained per unit of funding supplied to SENS, though he has been clear that SENS's funding needs are "$100 million per year for each of the next ten years".
This part of the post will consist of me using lots of best guesses to produce something vaguely resembling a cost-effectiveness estimate for SENS. You should not take this cost-effectiveness estimate literally.
If SENS needs one billion dollars to ensure that rejuvenation technologies that give individuals 30 extra years of healthy life are available to the public in 30 years, we might (completely arbitrarily) assume that someone else will come along and fund SENS in ten years if we don't contribute to funding SENS today. This means that if we fund SENS today instead waiting for it to be hypothetically funded in ten years from now, about ten times the number of people who die each year would live 30 years of healthy life that they wouldn't have lived otherwise. Given that there are about 57 million deaths per year worldwide, this translates to about 17 billion YLLs lost by waiting ten years to fund SENS; since SENS ostensibly requires only 1 billion of philanthropic funding, this implies that $0.059 of funding for SENS produces a YLL.
Of course, regenerative medicine won't be free to the people receiving it, and I have no idea how to account for this, given that I don't have a good idea of how much regenerative therapies will initially cost. The above estimate hasn't been adjusted to account for the fact that there is a time-delay between when funding is provided, and when the benefits of regenerative therapies are available to the public. Perhaps Aubrey isn't well-calibrated, and the "$100 million per year for ten years" figure is entirely wrong. It may be the case that starting work on SENS's research agenda earlier rather than later would allow certain people who would have otherwise died to live until aging escape velocity is reached, which would have lots of utility. There are plenty of other issues with this cost-effectiveness estimate which I am sure that readers could point out.
The point I wanted to make, though, was that maybe, possibly, SENS is competitive with GiveWell's top charities-- I'm legitimately not sure whether I would fund SENS or GiveWell if I were making a charitable donation today. Does anyone have any further thoughts on this topic?
Expansion on A Previous Cost-Benefit Analysis of Vaccinating Healthy Adults Against Flu
This post is an expansion on my post in main, A Cost- Benefit Analysis of Immunizing Healthy Adults Against Influenza (see http://lesswrong.com/lw/l81/a_cost_benefit_analysis_of_immunizing_healthy/). The purpose of this post is to examine different approaches to conducting the cost-benefit analysis given there, as well as to serve as an archive for a previous version of that post.
Conservative Cost-Benefit Analysis of Receiving the Flu Vaccine (for Healthy Adults)
The cost-benefit analysis of receiving yearly flu shots in the main article was conducted with conservative estimates. The decision tree from this analysis is reprinted below:
The utility which each possible outcome contributes to either receiving a flu shot, or to not receiving a flu shot, is given in the following table:
Optimistic Cost-Benefit Analysis of Receiving the Flu Vaccine (for Healthy Adults)
The optimistic model was not discussed or referenced in the post on Main, and is only shown here. The assumptions which the optimistic model makes which differ from those made by the conservative model are:
1. In the optimistic model, it is assumed that one's insurance completely covers the cost of the flu shot.
2. In the optimistic model, a vaccine efficacy of 80% (rather than 70%) is used.
3. In the optimistic model, the expected percent of the population infected with influenza is taken to be 10%, rather than 5.7%, as in the conservative model.
4. In the optimistic model, it is assumed that one does not receive sick pay for time missed from work.
Assumption 2 was made on the basis of the NCIRD source (see http://www.cdc.gov/vaccines/pubs/pinkbook/flu.html), which suggested that the efficacy of flu shots in healthy adults was 70-90%. Assumption 3 was made on the basis of the CDC Q&A source (see http://www.cdc.gov/flu/about/qa/disease.htm), which estimated that 5-20% of US citizens get the flu during the average flu season.
The utility which each possible outcome contributes to either receiving a flu shot, or to not receiving a flu shot, is given in the following table:
Drastically Conservative Cost-Benefit Analyses of Receiving the Flu Vaccine (for Healthy Adults)
After I started doing cost-benefit analyses which included factors that accounted for how much individuals valued not dying, I wasn't easily able to make the expected value of not receiving a flu shot higher than the expected value of receiving a flu shot, given literature values for all parameters. However, I will note that it is possible to construe the expected value of receiving a flu vaccine as being higher than the expected value of not receiving a flu vaccine by making the changes in (1) below to the conservative estimate given in the first section of this post:
1. Valuing your own life at 1,250,000 USD yields the following results from cost-benefit analysis:
2. Using different values for the average number of deaths of people aged 19-64 in the US, such as those given in Table 1 of the [Thompson article](http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5933a1.htm), yields the following results from cost-benefit analysis:
This having been said, Thompson et. al advised that "if only one category is used to summarize the mortality effects of influenza, the respiratory and circulatory data likely provide the most accurate estimates". That is to say that the authors of the Thompson paper suggested that the data on average yearly number of deaths of people aged 19-64 in the US due to influenza used to produce the above table weren't quite as likely to be correct as the data used in both the conservative and optimistic cost-benefit analyses above.
Revised Text
All text below this point in this post is the text first-draft version of my "Cost- Benefit Analysis of Immunizing Healthy Adults Against Influenza" article. I wanted to archive this somewhere, for the sake of transparency, so here you are.
Overview
The purpose of this post is to provide adult readers of LessWrong with a summary of the what the literature has to say about the efficacy and safety of influenza vaccinations, as well as to weigh the costs of receiving yearly flu vaccinations against the benefits which healthy adults gain from vaccination. As illustrated in the "Cost-Benefit Analyses" section of this report, the expected value of receiving flu vaccinations is highly positive for healthy adults; therefore, a further motivation for authoring this post is that writing this post may encourage LessWrong readers who have not yet been vaccinated this flu season to receive immediate vaccination.
Introduction and Review of Literature
Several meta-analyses on the efficacy and safety of live-attenuated influenza vaccines (LAIV), trivalent inactivated influenza vaccines (IIV3), and tetravalent inactivated influenza vaccines have been published within the last two years (see Coleman et. al, Demicheli et. al, Osterholm et. al). These meta- analyses reached broadly similar conclusions regarding the efficacy of flu vaccines, which groups were most at risk for being infected with influenza, the safety of being vaccinated, and the magnitude of social harm caused yearly by influenza. However, there was disagreement between some articles regarding whether or not vaccination of healthy adults against influenza should be pursued as a public health policy. Specifically, the Demicheli paper (wrongly) found "no evidence for the utilization of vaccination against influenza in healthy adults as a routine public health measure". The issue of whether or not healthy adults should receive flu shots will be examined in the "Cost-Benefit Analyses" section of this report.
While the severity of flu seasons varies greatly year-to-year, an average of 24,000 deaths from the flu occur yearly in the US (NCIRD); at least 90% of these deaths are in people of at least 65 years of age (NCIRD, CDC Key Facts). An average of 200,000 people are hospitalized yearly for flu and flu-related complications (NCIRD, CDC Q&A). Since infants and the elderly are disproportionately likely to be hospitalized for the flu, only about 0.04% of healthy people in the 5-65 age range are hospitalized yearly in the US (footnote 1). The approximate cost of hospitalization for a flu-related illness in 2004 was 6,900 USD (Milenkovic, footnote 2), and the average duration of a flu-related hospital stay was 4 to 5 days (Milenkovic, Aetna). Between 5 and 20 percent of the US population becomes infected with flu virus each flu season (CDC Q&A).
The *efficacy* of a vaccine is a measure of how effective a vaccine is; if half of a population of 2,000,000 people were given a vaccine with 60% efficacy, and 100,000 of the 1,000,000 total unvaccinated people got sick, then 40,000 of the 1,000,000 vaccinated people would get sick, as well. Many sources report the average efficacy of the flu vaccine throughout the US population to be 60% (Demicheli et. al, ) or 59% (Osterholm et. al, Coleman et. al). The CDC reports that the flu vaccine is more efficacious in young adults (70-90% efficacy, depending on how closely active viruses match the ones included in the vaccines manufactured during a given season), and less efficacious in those over 65 years of age (NCIRD). This has led to increased efforts at targeting healthcare workers, nursing home attendants, and others who are in frequent contact with elderly persons for yearly vaccination.
While some health agencies only recommend that elderly, infants, healthcare workers, pregnant women, and adults with certain medical complications, such as respiratory diseases, receive flu shots, the CDC recommends that all people 6 months and older get a flu shot every year (CDC Key Facts). The value which such at-risk individuals gain from being immunized against the flu is higher than the value which healthy adults gain from receiving flu shots. Certain individuals with extremely rare conditions, such as Guillain-Barré Syndrome (GBS), or people who may experience life-threating allergic reactions to components of the flu shot, should not receive flu shot. A healthcare professional will be able to tell you whether or not it is safe for you to receive a flu shot prior to you receiving the immunization.
None of the meta-reviews examined in this report found any evidence that receiving an influenza vaccine can cause serious adverse responses in patients (Coleman et. al, Osterholm et. al, Demicheli et. al). Receiving the influenza vaccine is safe, and it is not at all possible to catch the flu from receiving an influenza vaccine (CDC). Flu shots can cause arm pain or soreness, and can cause headache, mild fever, and muscle pain (Coleman et. al, Demicheli et. al).
Cost-Benefit Analyses
Estimates of the expected monetary values of possible flu-related outcomes were calculated relative to the value of not getting sick despite not receiving a flu shot, which was defined as having a utility of 0 USD. Probabilities were assigned to each outcome, as shown in Figure 1, and a calculation of the expected value of receiving or not receiving a flu shot in a given year was carried out. The motivation for simplifying the calculation of the expected value of receiving a flu shot by restricting the outcome space as shown in Figure 1 was to demonstrate that, despite using conservative estimates and ignoring certain benefits of vaccination in the model, the expected value of vaccination is still positive, even for healthy adults. Since other demographics are expected to benefit even more from receiving flu vaccinations than healthy adults benefit from receiving flu vaccinations, the fact that healthy adults would benefit from receiving yearly flu vaccinations strongly suggests that all individuals above 6 months of age would benefit from receiving flu shots, excepting e.g. patients with GBS or allergies to components of the flu shot.
The cost of getting a flu shot was calculated as being 30 USD, given that it costs around 20 USD to receive a flu shot out of pocket, and given that it takes around 30 minutes to get a flu shot at a clinic. I have estimated the value of one's time as being 20 USD/hour, though changes in this estimate would not appreciably affect the outcome of this analysis, since lost time is assumed to be the largest component of the utility lost from being sick, as described below.
The cost of catching the flu despite not receiving a flu shot was estimated as being 1000 USD for a healthy adult, given the cost of losing 4-5 days of productivity if one's time is valued at 20 USD/hour, plus the costs of providing palliative care to oneself, estimated at 100 USD, and the cost equivalent to the negative monetary value of experiencing a lower quality of life than usual while sick, estimated at 200 USD. The outcome in which one catches the flu despite receiving a flu shot was given a cost of 1030 USD, which was calculated by adding the cost of being vaccinated against the flu to the cost of catching the flu calculated above.
The cost of catching the flu and being admitted to the hospital was calculated as being 8000 USD. This cost was determined by adding the expected hospital bill, 7000 USD, to the additional costs of becoming infected with influenza, previously estimated as being 1000 USD. For the outcome in which one is admitted to the hospital despite having received a flu vaccine, an estimated cost of 8030 USD was used.
Figure 1. Decision Tree for Assessing the Impact of Immunization in Healthy Adults
Although the costs of the possible outcomes shown in Figure 1 were calculated under the assumption that the individual receiving the flu shout was uninsured, having an insurance policy greatly increases the expected value of receiving a flu shot, as many insurance companies will completely cover the cost of receiving a flu shot.
There are several positive benefits of receiving flu shots which have not been included in the above model. In particular, being vaccinated against the flu protects others in your community from becoming sick; this effect is known as the [herd immunity](http://en.wikipedia.org/wiki/Herd_immunity) effect. Also, the risk of death from flu was not considered in the above analysis, despite the fact that healthy adults may die from flu in strongly pandemic flu seasons. Lastly, receiving the flu vaccine provides one with a small degree of protection against influenza-like infections (Coleman et. al, Demicheli et. al); this positive effect of the flu vaccine was not considered in the construction of the model used to assess the costs and benefits associated with healthy adults receiving the flu vaccine.
Again, the above analysis of the expected utility of receiving the flu vaccine each year was conducted with conservative estimates and a simple model which did not take into account all of the benefits of receiving the flu vaccine; this was done to show that the expected gain from receiving a flu shot is positive in the general case, given uncharitable assumptions.
Error Analysis and Author's Reflections
This section will note some things that I could have done better in writing this report.
I only read the "Methods", "Findings", and "Interpretation" sections of the Lancet article, as I did not have access to the full text of this paper.
Before writing this article and conducting the research which necessarily had to be conducted before writing it, I would have estimated the prior probability of elderly people, infants, pregnant woman, and asthmatics receiving a net benefit from vaccination as being very high, and the prior probability of healthy adults receiving a net benefit from influenza vaccination as moderately high.
The NCIRD book chapter cites the efficacy of flu immunizations as being 70-90% in people who are younger than 65 years old. If I was to rewrite this report with realistic, rather than conservative estimates, I might use an efficacy value of 70% in Figure 1, rather than an efficacy value of 60%, which is what I actually used.
I was raised in a family which, in general, valued being healthy, and, in particular, valued the practice of keeping up to date on one's vaccinations. However, I do not believe that the conclusions of this report would have been different if I had not come from such a culture.
Further Considerations
While I feel that this report is fairly complete, I could have been more thorough. Part of why I am publishing this post now, rather than conducting more research before doing so, is that I expect that conducting additional research would be very unlikely to cause me to change any of the major conclusions of this report. To say the same thing from a decision-theoretic standpoint, information which has a very low chance of making one change their mind about something has little value, and I think that reading more papers on this topic would have a very low chance of changing any of my opinions on this topic.
Footnotes
1. Since I knew that 0.1% of infants (ages 0-4), and 0.21% of elderly (65+) have been hospitalized for flu each year in the US on average (see NCIRD), and that the total number of hospitalizations per year in the US due to flu was 200,000, it was possible to calculate that an average person of age 5-65 had a 0.04% chance of being hospitalized for flu in a given year, given statistics on the age distribution of the US population from Wikipedia. I recognize that, within this broad age bracket, 5-year olds and 65-year olds are more likely than 25-year olds to be hospitalized for flu. However, per Figure 1, the costs of a hospital stay weighted against the probability of that event is in no case more than 4% of the cost of becoming infected with flu and not staying in the hospital weighted against the probability of that event, so I do not think that this approximation is too worrying. Especially virulent strains of flu, such as the pandemic H1N1 which surfaced in 2009, are more likely to infect healthy adults than non-pandemic strains.
2. I wanted to have a source for the average cost and length of flu-related hospital stays, which is why I cited the Milenkovic paper. From comparison with non-academic sources (i.e. http://www.aetnabetterhealth.com/pakids/members/what-health-care-really-costs/), it seems like the cost of being hospitalized for the flu really is around $8,000, which is close enough to the figure given in the Milenkovic paper, especially considering that the Milenkovic paper is eight years old. The cost of being hospitalized for influenza is around 80-90 % of the cost of the average hospital stay in the US. However, even though I am only citing the Milenkovic paper so that I have an estimate on the cost of the average flu-induced hospital stay, I want to note that there is one large problem which negatively impacted my ability to cite other results from the Milenkovic paper. This problem is that much of the data from the Milenkovic paper is for the 2004 flu season; since the number of cases of flu in the US vary greatly from year to year, I would not feel at all comfortable taking data on e.g. the number of hospitalizations due to flu in one year in the US from the Milenkovic paper, and presenting this data as representative of the yearly average.
A Cost- Benefit Analysis of Immunizing Healthy Adults Against Influenza
As of 11:30CST, 11/11/14, this cost-benefit analysis has been revised, in order to address concerns raised in the comments. See http://lesswrong.com/r/discussion/lw/l8k/expansion_on_a_previous_costbenefit_analysis_of/ for more on how the cost-benefit analysis was carried out, and on how varying certain parameters affected the determined expected value of receiving a flu shot.
Overview
The purpose of this post is to provide readers of LessWrong with a summary of what the literature has to say about the efficacy and safety of influenza vaccinations, as well as to weigh the costs of receiving yearly flu vaccinations against the benefits which healthy adults gain from vaccination. As illustrated in the "Cost-Benefit Analyses" section of this report, the expected value of receiving flu vaccinations is positive for healthy adults. Therefore, a further motivation for authoring this post is that writing this post may encourage LessWrong readers who have not yet been vaccinated this flu season to receive immediate vaccination.
Introduction and Review of Literature
Several meta-analyses on the efficacy and safety of live-attenuated influenza vaccines, trivalent inactivated influenza vaccines, and tetravalent inactivated influenza vaccines have been published within the last two years (see Coleman et. al, Demicheli et. al, Osterholm et. al). These meta- analyses reached broadly similar conclusions regarding the efficacy of flu vaccines, which groups were most at risk for being infected with influenza, the safety of being vaccinated, and the magnitude of social harm caused yearly by influenza. However, there was disagreement between some articles regarding whether or not vaccination of healthy adults against influenza should be pursued as a public health policy. Specifically, the Demicheli paper (wrongly) found "no evidence for the utilization of vaccination against influenza in healthy adults as a routine public health measure". The issue of whether or not healthy adults should receive flu shots will be examined in the "Cost-Benefit Analyses" section of this report.
While the severity of flu seasons varies greatly year-to-year, an average of 24,000 deaths from the flu occur yearly in the US (NCIRD); approximately 90% of these deaths are in people of at least 65 years of age (NCIRD, CDC Key Facts). For all flu seasons between 1976 and 2007, an average of 2,385 adults of ages 19-64 died each year from flu and flu-related causes in the US (Thompson). Between 5 and 20 percent of the US population becomes infected with flu virus each flu season (CDC Q&A).
The *efficacy* of a vaccine is a measure of how effective a vaccine is; if half of a population of 2,000,000 people were given a vaccine with 60% efficacy, and 100,000 of the 1,000,000 total unvaccinated people got sick, then 40,000 of the 1,000,000 vaccinated people would get sick, as well. Many sources report the average efficacy of the flu vaccine throughout the US population to be 60% (Demicheli et. al) or 59% (Osterholm et. al, Coleman et. al). The CDC reports that the flu vaccine is more efficacious in young adults (70-90% efficacy, depending on how closely active viruses match the ones included in the vaccines manufactured during a given season), and less efficacious in those over 65 years of age (NCIRD). This has led to increased efforts at targeting healthcare workers, nursing home attendants, and others who are in frequent contact with elderly persons for yearly vaccination.
While some health agencies only recommend that elderly, infants, healthcare workers, pregnant women, and adults with certain medical complications, such as respiratory diseases, receive flu shots, the CDC recommends that all people 6 months and older get a flu shot every year (CDC Key Facts). The value which such at-risk individuals gain from being immunized against the flu is higher than the value which healthy adults gain from receiving flu shots. Certain individuals with extremely rare conditions, such as Guillain-Barré Syndrome (GBS), or people who may experience life-threating allergic reactions to components of the flu shot, should not receive flu shot. A healthcare professional will be able to tell you whether or not it is safe for you to receive a flu shot prior to you receiving the immunization.
None of the meta-reviews examined in this report found any evidence that receiving an influenza vaccine can cause serious adverse responses in patients (Coleman et. al, Osterholm et. al, Demicheli et. al). Receiving the influenza vaccine is safe, and it is not at all possible to catch the flu from receiving an influenza vaccine (CDC). Flu shots can cause arm pain or soreness, and can cause headache, mild fever, and muscle pain (Coleman et. al, Demicheli et. al).
Cost-Benefit Analyses
Estimates of the expected monetary values of possible flu-related outcomes were calculated relative to the value of not getting sick despite not receiving a flu shot, which was defined as having a utility of 0 USD. All payoffs shown are the payoffs which an average individual would derive from experiencing particular outcomes, rather than the value which either society, employers, or other parties would gain from a given individual either getting sick or not. Probabilities were assigned to each outcome, as shown in Figure 1, and a calculation of the expected value of receiving or not receiving a flu shot in a given year was carried out. The motivation for simplifying the calculation of the expected value of receiving a flu shot by restricting the outcome space as shown in Figure 1 was to demonstrate that, despite using conservative estimates and ignoring certain benefits of vaccination in the model, the expected value of vaccination is still positive for healthy adults. Since other demographics are expected to benefit even more from receiving flu vaccinations than healthy adults benefit from receiving flu vaccinations, the fact that healthy adults would benefit from receiving yearly flu vaccinations strongly suggests that all individuals above 6 months of age would benefit from receiving flu shots, excepting e.g. patients with GBS or allergies to components of the flu shot.
The cost of getting a flu shot was calculated as being 30 USD, given that it costs around 20 USD to receive a flu shot out of pocket, and given that it takes around 30 minutes to get a flu shot at a clinic. I have estimated the value of one's time as being 20 USD/hour for this calculation.
The value of not feeling sick for 3-10 days was subjectively estimated as being 200 USD for those who caught the flu, yet did not receive a flu shot. The outcome in which one catches the flu despite receiving a flu shot was given a payoff of - 230 USD, which was calculated by adding the cost of being vaccinated against the flu to the cost of feeling sick from getting the flu, calculated above.
The value a given individual would gain from not dying was estimated as being 5,000,000 USD.
Figure 1. Decision Tree for Assessing the Impact of Immunization in Healthy Adults
Although the costs of the possible outcomes shown in Figure 1 were calculated under the assumption that the individual receiving the flu shout was uninsured, having an insurance policy increases the expected value of receiving a flu shot, as many insurance companies will completely cover the cost of receiving a flu shot. Some governmental health insurance programs do not cover the cost of flu vaccinations. If one has insurance which covers the cost of the flu vaccine, the expected value of being vaccinated against the flu rises by 20 USD.
There are several positive benefits of receiving flu shots which have not been included in the above model. In particular, being vaccinated against the flu protects others in your community from becoming sick; this effect is known as the herd immunity effect. Also, the above analysis assumed that an individual would not lose income from missing work due to being sick from the flu; the effect which making this assumption had on the cost-benefit analysis presented here is examined in the link given at in the first paragraph of this post. Lastly, receiving the flu vaccine provides one with a small degree of protection against influenza-like infections (Coleman et. al, Demicheli et. al); this positive effect of the flu vaccine was not considered in the above assessment of the costs and benefits associated with healthy adults receiving the flu vaccine.
Again, the above analysis of the expected utility of receiving the flu vaccine each year was conducted with conservative estimates and a simple model which did not take into account all of the benefits of receiving the flu vaccine; this was done to show that the expected gain from receiving a flu shot is positive in the general case, given uncharitable assumptions.
Author's Reflections
I only read the "Methods", "Findings", and "Interpretation" sections of the Lancet article, as I did not have access to the full text of this paper.
Before writing this article and conducting the research which necessarily had to be conducted before writing it, I would have estimated the prior probability of elderly people, infants, pregnant woman, and asthmatics receiving a net benefit from vaccination as being very high, and the prior probability of healthy adults receiving a net benefit from influenza vaccination as moderately high.
I was raised in a family which, in general, valued being healthy, and, in particular, valued the practice of keeping up to date on one's vaccinations. However, I do not believe that the conclusions of this report would have been different if I had not come from such a culture.
Further Considerations
While this report is complete, I could have been more thorough. Part of why I am publishing this post now, rather than conducting more research before doing so, is that I expect that conducting additional research would be very unlikely to cause me to change any of the major conclusions of this report. To say the same thing from a decision-theoretic standpoint, information which has a very low chance of making one change their mind about something has little value, and I think that reading more papers on this topic would have a very low chance of changing any of my opinions on this topic.
References
1. Centers for Disease Control and Prevention. Key Facts About Seasonal Flu Vaccine. http://www.cdc.gov/flu/protect/keyfacts.htm (accessed 11/9, 2014).
2. Centers for Disease Control and Prevention. Seasonal Influenza Q&A. http://www.cdc.gov/flu/about/qa/disease.htm (accessed 11/9, 2014).
3. Coleman, B.; Cochrane, L.; Colas, L. Literature Review on Quadrivalent Influenza Vaccines. Public Health Agency of Canada 2014.
4. Demicheli, V.; Jefferson, T.; Al-Ansary, L.; Ferroni, E. Vaccines for preventing influenza in healthy adults. Cochrane Library 2014.
5. Milenkovic, M.; Russo, A.; Elixhauser, A. Hospital Stays for Influenza, 2004. Agency for Healthcare Research and Quality 2006.
6. National Center for Immunization and Respiratory Diseases. Epidemiology and Prevention of Vaccine-Preventable Diseases. http://www.cdc.gov/vaccines/pubs/pinkbook/flu.html (accessed 11/9, 2014).
7. Osterholm, M. T.; Kelley, N. S.; Sommer, A.; Belongia, E. A. Efficacy and effectiveness of influenza vaccines: a systematic review and meta-analysis. The Lancet infectious diseases 2012, 12, 36-44.
8. Thompson, M.; Shay, D.; Zhou, H.; Bridges, C. Estimates of Deaths Associated with Seasonal Influenza --- United States, 1976--2007. 2010.





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