Ohio started the ball rolling with a recurring $1 million dollar prize for people to get vaccinated. More states are rolling out lotteries and other incentives as well to get more people vaccinated. So let’s think about cost-effectiveness of this program.
We know that vaccines save lives. They save lives directly in that they dramatically lower the probability of someone becoming infected and conditional on infection with vaccination, a vaccinated person has massively lower death rates than a non vaccinated person. They save lives indirectly as the evidence is growing that vaccinated individuals are unlikely to infect non-vaccinated individuals. Vaccination stops some (not all) chains of transmission.
So the question is how many vaccines need to be administered due to the lottery than would have happened otherwise for this intervention to be cost effective?
We need to figure out how many life-years will be saved and how much suffering is avoided. We can do this with the concept of a Quality Adjusted Life Year (QALY). A QALY is a statistical measure of the quality of an extra year of life. It is a product of time of extra living and quality of that time. Someone who is in a permanent vegetative state who is treated with a new drug that gives them an extra year of life will have a lower QALY than a person who, after taking that same drug gets a year of perfect health. QALYs in the United States are typically valued somewhere between $50,000 and $150,000.
If we take a midpoint, we need the lottery to “buy” about 10 QALYs to pay for the prize and then some more QALY to pay for the vaccines needed to be administered to avoid a case of COVID and a death of COVID. If we think that the all-up cost of administrating a vaccine dose if $100 (the vaccine itself and the cost of shooting it into your arm combined), then every 10,000 people vaccinated due to the lottery increases the break-even point by about another QALY.
An important number to remember is the Number Needed to Treat (NNT). The NNT is the number of shots needed to be administered to avoid something bad, in this situation either a case or a death. The NNT(case) and NNT(death) are both functions of community prevalence and individual socio-demographic characteristics. Community prevalence is a function of how many people have been vaccinated, social behavior, physical environment and a whole lot of other variables. If we think that the marginal deaths that are being avoided due to extra vaccination at this point are people who are in their 40s, 50s or 60s, their expected lifespans absent COVID is decades with pretty decent health and easily a 11+ QALY left to live if they had not died of COVID. If a lottery can prevent one death a week, it is likely cost effective even before we consider that one death is likely the last stream of medical interventions that include several ICU admissions, a dozen hospital admissions, a hundred people getting infected, a few people with long COVID which all have very real economic and quality of life costs that vaccinations help avoid.
This is quick and dirty, but the short version is that it takes absolutely heroic assumptions about either QALY valuation, the marginal deaths, or lack of increased take-up of vaccines for million dollar lotteries to not be cost effective in the short run much less the long run.