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.