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.
- 's comment on Immortality: A Practical Guide by (26 Jan 2015 22:47 UTC; 11 points)
- Expansion on A Previous Cost-Benefit Analysis of Vaccinating Healthy Adults Against Flu by (12 Nov 2014 4:36 UTC; 6 points)
- 's comment on Expansion on A Previous Cost-Benefit Analysis of Vaccinating Healthy Adults Against Flu by (12 Nov 2014 15:07 UTC; 0 points)
Omitting death seems like a big deal. Very crudely, it looks like p=10^-4. It’s said that society values each life at $5M, so that’s E=-$500 already, but each individual likely values their own life a bit higher.
This is a very good point.
I have redone the analysis with this concern in mind. I also removed the outcomes involving hospitalization from the decision tree, as they were barely making any contribution to the expected values of the outcomes in which an individual either received or did not receive a flu shot.
The contribution of E(death) to E(getting a flu shot) ended up being around - $30-90 for healthy adults of ages 19-64, rather than - $500, mainly because around 90% of deaths from flu are in people of ages 65+.
Not with respect to their revealed preferences for working in high risk jobs I understand. There are a bunch of economic papers on this but it was a surprisingly low number.
That, and a little pondering why, is all you ever needed to know.
Actually estimating the utility of a vaccine is very difficult for individuals who are not complete shut-ins interacting with nobody (but then those people won’t get sick in the first place), or individuals who aren’t complete psychopaths without a job or with a job unusually resistant to damage from absence of coworkers (because even a psychopath would generally not want to get the co-workers sick). This is because a vaccine massively affects the ability of the virus to spread to other people, and in the beginning phase of the epidemic one person infects more than other person. It matters a great deal to an insurance company (or a government), so they can invest a lot of man-hours into modelling of the spread of the virus.
It is fortunate that the cost of the vaccine is so low and the illness is so common you arrive at the correct decision regardless.
Yeah, it would be a pity if it diseases were less common.
(While I’m obviously overreading your use of the word “fortunate” for the sake of humor, I do wonder if there is a bias where one would prefer an objectively worse territory if one’s map would be clearer for it. And if it affects, say, decisions of doctors, or of patients.)
It was meant to be humorous. As in, with that sort of thinking, he’s lucky the flu is common enough that he’ll get a vaccine and won’t get the flu. Though I was thinking of things like measles and other anti-vaxxer fodder where precisely because of the use of the vaccine, disease risk seems very low, and it might even be in some instances the case that an agent that’s considering a very narrow scope of consequences wouldn’t vaccinate.
Another problem is that vaccines are most advantageous when everyone who can be vaccinated is vaccinated, but at that point it is selfishly better for everyone individually not to vaccinate. Since we don’t have identical or even similar source code, you can’t solve this by playing with the notion of consequence and pretending that most people’s decision will track yours, you have to group together and implement a policy applying to everyone.
Also by the way some governments seem to under-vaccinate (possibly for the same selfishness reasons) and it’s best to follow WHO recommendations. E.g. in my country they don’t vaccinate little kids for rotavirus, which is a condition that not only hurts the child but is so annoying for the parents that vaccinations got great pay-off—while on an individual level the pay at job may not be lower, at the country level nobody’s going to compensate for the productivity decrease from dealing with a sick child. And almost everyone gets rotavirus. More than once. And, generally if you earn more than average wage you’re probably interested in more vaccinations.
I don’t think I’ve ever had flu—certainly I have never been diagnosed with it—but when I’ve had an incapacitating heavy cold, palliative care consists of staying in bed and surviving on half a can of soup a day, and maybe some over-the-counter symptomatic treatment. This agrees with the recommendations for actual flu here and produces a saving of money, not a cost.
The analysis presented in this post has been updated to reflect this concern. I’ve completely removed the figure representing costs of palliative care from the analysis.
I guess that I tend to purchase things like anefrin (a nasal decongestant), cough drops, extra tissues, Benadryl, and cough expectorant/cough suppressant medicine when sufficiently sick, in addition to spending the time to get checked out at a clinic or doctor’s office. I can see that this sort of behavior, and these sorts of costs, might not be common, especially among usually healthy young adults.
In case it was not obvious, the correct takeaway from this article is that you should go and get a flu shot, if you haven’t gotten one already this year. If you have already gotten a flu shot this year, and you reply to this comment with a message that states that you have done so, I would be more than happy to upvote you.
I got one and took my young son to get one as well. Convincing a child of the benefit of getting a shot or nasal spray makes for an excellent lesson in rationality since you must convince the kid to accept immediate and certain pain in return for a moderately reduced chance of experiencing a larger amount of future pain.
I got the shot (for free via my insurance), and it was completely painless. I looked away from my arm to prevent tensing up, and I literally did not feel the needle go in. There was a little soreness later that day, but not much. Worth keeping in mind—getting the shot is not unpleasant.
Shots, including the flu shot, always cause me pain. I usually tell the person about to give me the shot not to stop if it looks like I’m in extreme pain.
I don’t think most effective way to convince a child of getting a child is through rational argument. Appearing really confident is important for convincing but being really confident for the sake of convincing others is not a good habit to have when you seek for the truth.
You don’t use rational argument because it’s the most effective way to convince a child, you use rational argument because it’s the most effective way to teach a child the use of rational argument. (which as a side benefit, eventually makes rational argument the most effective way to convince the child)
Kids notice these things! And not just the ‘smart’ ones.
In general you are probably right but for LW parents this might be different as rationality-related traits are probably heritable that about the same level (0.6) than e.g. IQ. Judging from my sons (8, 10) I’d guess that they’d be able to follow the reasoning and likely given the choice decide pro-innoculation. But then they are not very squeamish to begin with and wouldn’t value a shot that bad.
I got one this year! I didn’t get one last year, and someone else ended up getting very sick as a direct consequence… :(
Sorry, I’m not good at following instructions :-P
Haven’t gotten a flu shot, this year or ever. I have a functioning immune system and some exercise is good for it. I’ll re-evaluate when I’m 65 :-)
Let us assume that your “functioning immune system” gives you a 95% chance of avoiding the flu, as opposed to the population’s average 90% chance (such that your immune system is significantly stronger than average).
The immunisation still has a 60% efficiency; your odds of not getting the flu with the immunisation are thus 98%. Assuming the ration of hospitilasation/non-hospitalisation is as given in the article:
The expected cost of the flu shot is thus $30+(0.02*1000)+(0.0001*7000) = $50.7
The expected cost of not getting the flu shot is then $0+(0.05*1000)+(0.00025*7000) = $51.75
So, with every assumption made in favour of reducing the expected cost of not getting the shot, even more so than in the article, it is still more expensive, on average, than getting the shot.
By a dollar and five cents, according to your calculation. That doesn’t seem even worth the time talking about it.
If that many assumptions are slanted in the direction of conclusion A, and the data is still in favour of conclusion B, even by such a minor amount, then that suggests that conclusion B is (significantly) liklier to be the correct course of action than A.
In other words, once we start factoring in the potential cost of death; the cost to society of your spreading the flu further; assuming an immune system suitable to a human and not to Hercules; then that dollar and five cents is likely to grow to a respectable sum.
Sounds like motivated cognition to me...
Then let me demonstrate the point by leaning all the assumptions in the opposite direction.
Assumption: The vaccine has an efficacy of 60%. This will be altered to 90%, which it can reach for a healthy adult.
Assumption: There is a 0.5% chance of a hospital stay if you get sick. This will be put up to 1%.
Assumption: There is a 0% chance of death, given that you are sick enough to require a hospital stay. This will be put up to 50%.
Assumption: Your immune system gives you a natural 95% chance of avoiding the flu. This will be reduced to 92%. (That may still be too high).
Result:
Flu shot: $30+(0.008*1000)+(0.00004*7000) = $38.28, plus 0.00002% chance of death
No flu shot: $0+(0.08*1000)+(0.0004*7000) = $82.80, plus 0.0002% chance of death
So, around $50 is all it comes down to, even if you “lean” the assumptions? :-D
Meh.
$50 plus a 0.00018% chance of death, in pretty much pure benefit.
Unless he has an above-average income to go with his above-average immune system.
Wasn’t the time to take it included in the costs analysis?
Yes, but not the time to read the discussion we’re all having. In personal finances, $1.05 is below noise level for anyone not in grinding poverty. I can save that by skipping a coffee.
Well, if we’re doing the calculation specifically for me, we can put in more precise numbers. If I stay at home sick for week, my income will drop by $0. So, replace $1000 with $0. I also have health insurance which will pay for the hospital visit, but I’m sure there will be some co-pays, let’s say $200. So...
flu shot: $30+(0.02*0)+(0.0001*200) = $30.02
no flu shot: $0+(0.05*0)+(0.00025*200) = $0.05
Ooops :-D
Well, if you don’t value your health at all, then this seems valid.
OP’s analysis has a term for quality of life issues stemming from the illness; it just happens to be a fourth of the magnitude of lost productivity ($200 vs. $800). The latter ends up dominating the calculation. There’s also a term for the costs of palliative care, estimated at $100, but that looks a little sketchy to me; a package of Theraflu and some tissues and cough drops would run maybe $20.
On the other hand, Lumifer’s health insurance would probably cover the flu shot. Mine would.
Virtually all health insurance will also pay for the flu shot (since paying for a flu shot for all their members is less expensive than paying for their hospital stays). So:
flu shot: $0+(0.02*0)+(0.0001*200) = $0.02
no flu shot: $0+(0.05*0)+(0.00025*200) = $0.05
...percentage-wise, that’s huge.
Evidently, socialized medicine (in the UK) does not.
LOL.
Huh. Well, that’s unexpected.
Only some of the $1000 cost was lost income. You are, of course, welcome to substitute your own numbers for the expected cost of self-care and your subjective disutility of being sick for a week, but setting those to zero seems implausible: that is, if there were an instant flu-curing pill, I strongly doubt you would be unwilling to buy it at any price.
Judging by some of the attitudes I have heard from my friends about getting a flu jab (similar to Lumifer’s comment), I have found that it is actually more effective to encourage people to get flu jabs for the benefit to others via herd immunity, rather than by emphasising the benefit to them.
I don’t know if this is maybe some kind of ego-bias in that healthy people underestimate their chances of getting sick, or that doing something for you doesn’t get you fuzzies, whereas doing it to help sick people and babies does.
Of course I am in a country that won’t pay for healthy people to get the flu jab, but will pay for their hospital stay if they get sick enough to be hospitalised. The NHS does, however, pay for elderly people and people with most long-term health conditions (including asthma and diabetes) to get the jab.
I imagine that the NHS has done a cost-benefit analysis of the costs to itself to pay for healthy peoples’ flu jabs versus their hospital stays if they do get sick, but I don’t know if they have.
I’d like to see more analyses like this. Does anyone want to do blood donation?
Would that be altruistic value? If I’m not mistaken, the cost of blood donation is generally just time, and the benefit is to other people. I have heard infrequent blood donation might be a health benefit, but I don’t know much about that.
Sure, why not altruistic value? If you consider hospitalisation cost even for users with insurance you can consider altruistic value in blood donation too.
Of course, any topic is fine. I didn’t even know I wanted to know this before I read this post.
I think the calculation somewhat under values the cost of being sick. If it’s been a while since the last turn you were serriously sick it’s easy to forget just how deeply unpleasant it is. I was really sick with food poisoning recently and would have happily paid >500 USD to avoid that. It’s been a while since I had the flu, but I think putting the misery and suffering at less than 300 USD is not optimal modeling.
I would agree that 200 USD is a low estimate for the cost of the experience of being sick. The reason I chose that figure was because I was trying to show that getting flu shots was still an activity with positive expected value for healthy adults, even given uncharitable assumptions. If you value not getting sick with the flu as being worth more than 200 USD, then the expected value that you would derive from receiving yearly flu vaccinations would be even higher than the figure cited in the report.
Also, note that the reason I did the calculation for healthy adults, rather than for, say, an average person living in a first-world country, is because healthy adults don’t benefit quite as much from getting the vaccine as other demographics do. So, if getting a flu shot is preferable to not getting a flu shot for healthy adults, then getting a flu shot is even more preferable to not getting a flu shot for other demographics.
Huh, I’ll look into this. At 33yo it never really occurred to me healthy people got flu shots. I have never had a shot or the flu, and the only people I know who have had other contributing weaknesses. I’m not saying I will necessarily get one, but this definitely opens the question for me. Thanks!
That was a very nice article, well-researched and thorough; However, I do think I need to point out that you have made an error in your maths. (Interestingly, the effect of the error was to increase the cost of getting a flu shot).
Specifically, take a look at figure one, at the probabilities. You have stated, earlier, that the flu injection has an efficacy of 60%; that is to say, 60% of people who get the flu shot, who would otherwise have got the flu, don’t get the flu.
Given that 90% of people don’t get the flu, whether they have the shot or not, this means that the odds of not getting the flu after getting the shot should be 96%, not 94%.
Similarly, the odds of being hospitalised should be 0.0002, not 0.0003; and the odds of getting the flu but not being hospitalised should be 0.398, not 0.597.
In short, your calculations presumed an efficacy of only 40%. (The fact that it was still shown to be worthwhile, with such a low efficacy, is quite telling).
This reduces the expected cost of getting the injection to $71.40.
That minor point aside, thank you very much for doing the research for this article.
This error has been corrected; thank you for pointing this out!
I actually did a bit more research, and it really seems like flu vaccine efficacy in healthy adults is more like 70% (and sometimes as high as 90%), despite the fact that the average efficacy of the vaccine throughout the population is around 60%. The reason that efficacy in healthy adults is so high, relative to the average efficacy, is that efficacy in the elderly is around 30-40%.
Also, note that about 42% of the US population gets flu shots on any given year. So, if 10% of people on average get the flu, and the vaccine is 60% efficacious throughout the population, then we can write the following equations, defining sick1 as the event in which a person who was vaccinated gets the flu, and sick2 as the event in which a person who was not vaccinated gets the flu:
p(sick1) x 0.42 + p(sick2) x 0.58 = 1 x 0.10
p(sick1) = p(sick2) x 0.60
Solving this system of equations, we get:
p(sick1) = 0.0721
p(sick2) = 0.120 (previous typo: had been written as 0.0120)
The practical implication of this is that the conservative analysis conducted in this report, and shown in Figure 1, assumes that around 5.7% (rather than a more realistic 10 or 12%) of the population will catch the flu in any given year.
...I’m sorry, but I’m rather pedantic when it comes to maths.
I believe that should be p(sick1) = 0.072 and p(sick2) = 0.12, not 0.012.
Which I’m pretty sure is just a typo, and not an actual math error...
So the equations should be (definition of vaccine efficacy from wikipedia)
.6 * p(sick2) = p(sick2) - p(sick1)
p(sick1) - .4 p(sick2) = 0 . i.e. efficacy is the difference be the unvaccinated and vacinated rates of infection divided by the unvaccinated rate. You have to assume there is no selective pressure in terms of who gets the vaccine (they have the same risk pool as the normal population for flu which is surely untrue) to get your assumtion that
.42 p(sick1) + .58p(sick2) = .1 p(sick1) + 1.38p(sick2) = .238
or 1.78 p(sick2) = .238
p(sick2)=.13 (weird I getting a different result) p(sick1) = .05
Did I solve wrong or did you. I do math so I can’t actually manipulate numbers very well but I not seeing the mistake.
This confusion is due to the fact that the system of two equations I wrote in my comment above was originally crammed onto one line, rather than being separated onto two lines. Sorry! This formatting error made the comment hard to read, and has since been corrected. The correct system of equations to solve is:
p(sick1) x 0.42 + p(sick2) x 0.58 = 1 x 0.10
p(sick1) = p(sick2) x 0.60
Instead of:
.42 p(sick1) + .58p(sick2) = .238
.1 p(sick1) + 1.38p(sick2) = .238.
Getting complications (allergy, …) from the flu shot should be included somewhere in the graph—it can’t be totally screened away, and while it’s unlikely to happen, it’s not much more unlikely than dying from the flu.
But most importantly (and this time, arguing for the shot), the “herd immunity” effects should be considered. Even if just half of the people take the shot, those who because of the shot didn’t get the disease won’t be carriers and won’t spread the disease to even those who did get the shot.
The Coleman paper provides some stats on how likely e.g. muscle pain is to result from receiving a flu shot (5-30%, authors are not sure how significant this effect is, though a couple RCTs report this effect), as well as on fever (which 3.2% of those who got a flu shot, and 1.6% of those who received a placebo experienced, according to one RCT cited by Coleman).
I never saw anything about the probability of experiencing an allergic reaction to the vaccine, but I haven’t specifically looked for this information.
Yes, they could be. The reason I didn’t consider herd immunity effects is because I was calculating the benefit which a (possibly un-altruistic) individual would receive from vaccination.
I’m not seeing where the probabilities in the decision tree come from. Does 10% of the unvaccinated population catch flu every year, and 6% of the vaccinated? Those seem extraordinarily high figures, and I don’t see them in the text. The two figures together imply an efficacy of 40%, not the 60% cited. The connection of the other probabilities to the data is also not clear.
You’re still paying for the medical care you receive on insurance. You’re just paying in advance, at a rate that the insurance company calculates to cover the expected costs, plus their own profits. If the entire population suddenly goes out and gets flu shots this year, that will show up in everyone’s premiums down the road. If your employer pays your insurance, you’re still paying, in the form of a lower salary. The only people who don’t pay medical costs are those on public benefits, whose costs are paid by those not on benefits.
ETA: This applies to nationalised health systems as well. Flu jabs are there paid for by taxes. All these different ways of paying for it may distribute the cost in different ways, but that cost is always paid. If it were not paid, there would be no vaccinations.
ETA2: Likewise sick pay. If your employer guarantees your salary while you’re sick, it’s at the cost of your salary when you’re well. The cost is spread over the whole company, but it is paid. The cost is always paid.
I’d also like to see some sensitivity analysis, given that the $14 benefit derived from the model is a difference between much larger figures, $104 and $90.
I have already gotten a flu shot this year, primarily because the cost of getting one is approximately 10 minutes and 0 USD (They’re covered by cost of attendance at my university and in a very convenient location for me).
This is this bit that stands out the most to me as warranting some analysis. Maybe in the US things are very different, but in Australia we have sick leave for the full time employed—which is most people on 20USD/hour (or local equivalent). Being sick for 4-5 would not cost you a penny. Mind you, this may then translate to an argument for employers to provide free flu inoculations as has been advocated elsewhere: http://www.abc.net.au/news/2014-05-05/employers-encouraged-to-provide-flu-vaccinations-for-staff/5431698
I think the analysis changes a lot if you have insurance/live in a country with a public health care system.
Also where did 200 USD for diminished quality of life come from? That phrase has a particular legal meaning—is that intentional, or do you just mean “what I would pay to not have the flu, other economic considerations aside”?
I think there’s a pretty big mistake here—the value of not getting flu is a lot more than $200.
At a $5M value of life, each day is worth about $200, so 7 days of almost complete incapacitation is -$1400.
I would certainly pay $1400 upfront to make a bad flu just instantly stop.
What about the cost of pain from the flu shot? Based on my past experiences (all from childhood, so maybe not that accurate for me now), I would be willing to pay $20-$50 to avoid the pain from a shot. I also didn’t find the flu that unpleasant, so I might only be willing to pay $120-150 to avoid it assuming no risk of death. It seems like the expected value of a flu shot is small enough for these sorts of subjective preferences to tip the balance in many cases.
I think you’re quite miscalibrated… only 4x worse to get the flu than the shot ? The shot pain lasts a few seconds, while the flu means headache, nose pain and muscle pain for at least a day, usually more. It usually knocks you out for a day or two, where you can’t do much.
Or maybe you’re confusing the flu with the common cold ? Flu is similar, but usually much stronger than common cold.
Agree with kilobug. eric3′s numbers seem way off.
The pain from the needle during the injection lasts just a few seconds, but the muscle pain at the injection site is noticeable for hours. That said, I’d rate it as much lower than eric3 rated it. For me, this is one of those situations where having the explanation for a sensation in hand, and knowing that it is self-limiting and harmless, makes a large difference. I’d be quite concerned if I had a pain of identical magnitude but with no explanation for what caused it.
I’d like to know how elastic the result is for changing cost values. Did you plug in different values and what were the results?
Am I being particularly dense or are there no numbers in the form of “expected value of not getting the shot: $Y”, “expected value of getting the short: $X” and “difference $(X-Y), therefore ….”
EV (Shot) = -$90 EV (No Shot) = -$104
Difference (Getting the shot minus not getting it) = -$90 - (-$104) = $14
Therefore, get the shot.
The first two values are in the tree. The difference can be figured out by mental arithmetic.
The costs in your calculations, they are costs for whom?
To make an obvious observation, medical insurance exists for a reason and a lot of people are employed in such a way that missing a week of work does not cost them $1000. Another lot of people isn’t employed at all.
Since you wrote this comment, I’ve updated the calculations in such a way that it is now the case that:
Nice sharing thanks
What about the non-serious responses? How much would you pay to avoid a mild fever/etc, how often does it happen?
I haven’t seen all the comments on this post nor kept up with the different versions, but: have you considered doing an analysis with added information as how long into the flu season the person is? That is, the likelihood of my getting the flu this year goes down as time goes on, while the costs of getting the shot remain constant: at which point would the costs outweigh the gains?
If it’s possible to have a life-threatening allergic reaction to the flu shot, and that doesn’t count as “serious adverse responses”, what would have counted?
Is this actually true? And you mean this is a routine part of the procedure? How is that done?
What is meant here is that flu shots cannot give patients cancer, autism, Alzheimer’s, etc. There are actually misguided groups which identify themselves with the “anti-vaccine movement”, all of which make lots of false claims regarding the safety of vaccines in general.
In the US, at least, doctor’s offices often have sheets like this which are given to patients who come in to receive a flu shot.
Oh, I see, okay. Why not actually say what you mean, then? To claim “no serious adverse responses” after you listed the possibility of one, and indeed when the sheet you link to above explicitely includes advice on “What if there is a serious reaction”, makes me wonder how much I should trust the literal meaning of other statements in the article.
Huh? That sheet seems to basically tell patients “if you’re deathly allergic to flu shots, let the doctor know”. So “A healthcare professional will be able to tell you whether or not it is safe for you” (such a reassuring, comprehensive statement!) actually means “a healthcare professional may advise you not to take the flu shot if you already know and tell them that you shouldn’t”?
Added 3/25/15: I happened to reread this comment several months after writing this post, and gosh, I have to say that I wish I had worded this comment more kindly. I’ll leave the text of the original comment below. While I still stand by all of the factual claims I’ve made in this thread, I apologize if the tone of this comment hurt anypony’s feelings.
Arguments that getting flu shots can cause certain serious adverse responses like autism, Alzheimer’s, etc. tend to be comparable in quality to arguments that that the earth is 5,000 years old. Such arguments do not specifically deserve a reply.
In the same way that e.g. Dawkins has declined to debate creationists, a sensible person might refuse to debate about whether or not flu shots make people autistic. Since the hypothesis that “flu shots give people autism” is so ridiculously improbable, I didn’t even want to bring it up directly in the article. The bit about “None of the meta-reviews examined in this report found any evidence that receiving an influenza vaccine can cause serious adverse responses in patients” was supposed to be a general refutation/dismissal of the “flu shots give people autism” brand of argument.
The best source I can give you on how flu shots don’t cause people to have serious adverse responses would be the Demicheli paper cited in the references section. The Coleman paper also discusses this topic.
As noted in the paper, people with GBS, allergies to gluten, allergies to eggs, etc. can have serious adverse responses to flu shots, but I would expect people to know whether or not they had these sorts of problems before they went in to get a flu shot.
That’s fine and mostly reasonable, and you don’t need to convince me that flu shots don’t cause autism or cancer. What I’m saying is that I wasn’t able to glean what exactly you meant from the article as you worded it.
You could have addressed those autism/Alzheimer claims clearly, or refused to address them, but you somehow tried to do both. Maybe that wasn’t a good idea.
Maybe, but in a cost analysis I’d expect to see not what seems reasonable to you, but what the numbers say about what happens in reality. How many people actually get severe allergic reactions after a flu shot? Have there been deaths, and if so, what is the risk?
Well, apparently it’s less than 1 in a million for that first one, and nothing definite about the second if we exclude paranoia sites, so I guess that’s that.
It’s behind the paywall, you don’t happen to have a copy handy?
Also, it’s interesting to look at the Demicheli abstract. It says:
An interesting question is what are the “yearly” vaccines which have such low effectiveness?
This might be the paper you’re looking for, although OP cites a 2014 version with an additional author; perhaps an update?
(ETA: Here’s the 2014 version. And here’s what appears to be the Coleman paper, just for giggles.)
Aha, thanks. As usual, the paper is more interesting and nuanced than its rendering designed to drive home a single point...
While flu shots very likely cause no serious adverse responses it’s a quite different case then the earth being 5,000 (or 6,000) years old.
There no good reason to assume that everybody has an allergy to gluten knows about it. If there are known conditions under which flu shots can have serious adverse reaction we can’t be as confident that we don’t miss an additional case as we are confident that the earth is older than 6000 years.
Claiming that’s the same order of confidence seems to me quite a stretch.
I don’t think that being a cost-benefit analysis is sufficient for something to be relevant to this site.
Knowing that getting a flu shot is a good idea might encourage individuals to optimize their lives by getting a flu shot every year, which would make them less likely to become sick on any given year. If I can encourage other people to act in sane ways which benefit themselves, then I am going to try to do just that.
I don’t think this website is about object level ways to improve people’s lives. There are far too many topics which fall into this category.
I’d generally say that in any intellectual activity, Examples Are Good.
Also, “Replies to downvoted comments are discouraged. Pay 5 Karma points to proceed anyway”? −4 is enough to shut down a conversation? What a terrible idea. How do we get rid of this mechanism?
I don’t like it either, but Eliezer seems convinced that long conversations descending from posts by trolls (or, more often, sincere but badly mindkilled people) are destructive enough to site culture that they’re worth going to great lengths to punish.
So, if you want the feature gone, he’s the guy to talk to. Ideally in person.
In practice it doesn’t happen all that often and there is a trivial workaround—start a new (sub)thread quoting the downvoted post and indicate you want to continue talking...
Avoiding the karma toll is a recipe for being downvoted, and doing it enough to attract moderator attention is unwise.
What’s the problem with there being too many topics? We don’t have to discuss them all. I find it refreshing to read a well-written consideration of something (i.e. “object level ways to improve people’s lives”). If nothing else, it’s good practice!