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.
Pete Mack
This is not the way I would attack the problem. The question I would ask is: how many hospital cases of covid does it take to cost the state $1m? Or perhaps it should be how many hospital cases does it take to save $1m between state and insurers? Insurers also will pass on costs to the population in the next year.
Unique uid
I hadn’t heard of a QALY before, interesting.
My only observation would be: maybe a Federal/national lottery later this summer?
trnc
“My odds of dying of it are higher than winning the “vax a million” so I will still take my chances.”
https://newsbeyonddetroit.net/2021/06/01/first-winners-of-ohios-vax-a-million-covid-19-vaccination-lottery-revealed/
I’ve been assuming this is the attitude of most anti vaxxers, which is why I’ve been saying the state should have started with one thousand $1000 prizes from the first million and let that run it’s course, up the prizes for the next 3 million dollars and finish with 10 $100,000 prizes that only fully vaccinated people will be eligible for. Right now, not only are the odds too high for anyone not already planning to get the vaccine, there’s no incentive to get the second shot for the ones that require that.
Pittsburgh Mike
This article overlooks to me, a vaccinated person, the biggest benefit of the lottery/whatever programs: you’re decreasing the case numbers faster, which reduces the reservoir of the virus, which reduces the probability of a new bad variant.
A variant that requires respinning the vaccines a year earlier is expensive. Assume that a vaccine is normally good for 4 years, but a bad variant means you’re redoing say 3 billion shots after 2 years instead of 4. You’re averaging 1.5 billion shots/year instead of 750M, so you have 750M shots extra you’re giving out, which is 75 billion dollars just for the drugs. Add on the cost for people giving the shots, the administrative overheads, the sick time for recovering from side effects, the additional deaths from the new variant, the costs of new tests and using them to track the spread of the new variants, and the costs of additional lock downs, and you’re probably north of 100-200 billion dollars.
If you can reduce the chance of this variant getting established by 20% by reducing the size of the pool of sick people, you’ve probably saved say 30 billion dollars.
That’s a lot of money for lotteries :-)
Ohio Mom
I admit I didn’t like the lottery idea at first, mainly because I’ve never liked the idea of state-run lotteries. And I still would have preferred a payout scheme like the one tnrc@3 proposes, with more lower-priced prizes rather than only a handful of big ones.
But props to my (otherwise jerk of a) Governor for leading the way on lotteries. It appears to be working.
What is next though? Payouts for not getting any speeding tickets, not littering, etc.? It’s the libertarian idea that we owe nothing to one another, that everything should be transactional, that still rankles me.
David Anderson
@Pittsburgh Mike: Mike — you are right. I am pointing out the most simplistic modeling with no dynamic effects leads to cost-effectiveness under any but absurd assumptions.
Victor Matheson
@trnc: While I don’t doubt there is some of what you are saying, the health economists are banking on many of the people not getting the vaccine are just bad at math, so a lottery appeals perfectly to this subset of people.
Victor Matheson
@Ohio Mom: Yeah, I don’t think any economist is happy that we have to do this. But given the situation, this is a policy with a huge positive benefit cost ratio.
Edmund Dantes
@trnc: In California to fully realize your win requires you to have completed the vaccine regimen before claiming.
Keithly
@David Anderson: Could you define NNT? I believe it means number needed to treat, but it’s not otherwise obvious from context on my reading.
gvg
The people who like lotterys are not the most logical thinkers. In some hard to define way, I think it helps normalize getting vaccinated among the pool of not very deep thinkers. People who decide things based on emotions. It also associates getting the shots with something they are really familiar with. I think it makes vaccination less suspicious and new.
I don’t understand the appeal of lotteries either. I last bought tickets about 40 years ago. However, I am not typical and many people do it on a regular basis.
David Anderson
@Keithly:
NNT = Number needed to treat — so the number of people who have to get a vaccine to prevent an infection or an adverse outcome (those two numbers will vary greatly)
MattF
The choices individuals are making here are personal, e.g., ‘a million $$$’ vs. ‘walking across the street to the CVS’, similar to the choice of whether to buy a lottery ticket. They’re betting on an extreme event, and the state is offering one. That seems OK to me.
debbie
@Ohio Mom:
It was reported last week that vaccinations had increased between 40% and 50% for each age category. I think that’s pretty impressive.
artem1s
It’s possible an overlooked advantage of the lottery is that the state also gets to initiate a shadow tracking program with little or no political ramifications. It could be used as a central state verification system if the state has to deal with vaccine mandates that the RWNJ’s want to block. The universities are already initiating self reporting tracking of their staff and students so they can prep for mandating vaccines for fall semester.
Unfortunately DeWimp has allowed the Cult45 members of the state GQP to take over the party. Since the head of health and human services is no longer allowed to make decisions about COVID or anything else. So shadow tracking vital health care information is the best Ohio can hope for at this point.
Amir Khalid
Keboard acting up. Backspace kes and some lettter keys misbehaving. Couldn’ttt happen at a worse ttime. 14 das before I can do anytttthing. Gaah.
Uncle Cosmo
I have maintained for years that humanity is going to extinct itself from its inability to emotionally comprehend, not (as Deadbeat Dad of the H-Bomb Edward Teller** once claimed) the exponential function, but basic probability and statistics. If polite society can use that miscomprehension as a force for good, I say huzzah!
** FTR Stanislaw Ulam did most of the heavy lifting on the socalled Teller-Ulam configuration. Teller spent most of his energy cheerleading for “the Super” and shivving Robert Oppenheimer, whose slide rule he couldn’t carry.
Ohio Mom
Debbie:
Like I said, props to DeWine (and whoever whispered the lottery idea into his ear in the first place). I can’t claim to be surprised at what motivates so many of our fellow Buckeyes.
catclub
I think you are looking at lottery odds rationally, and people really do not do that. They say ‘Somebody is gonna win, it might as well be me’ and buy a ticket.
catclub
wow! good!
Ken
@catclub: And in this case they don’t even have to come up with the dollar for the ticket. Though they do have to find an hour or two to get the vaccination, and allow for possibly not being able to work the next day, which from what I’ve read are among the major blockers for the “want to get it but haven’t yet” category.
Wag
An excellent analysis, as always. Thanks for the good work.
jmh
This analysis focuses on the value of individual lives saved (which is important). I think another significant factor is the ability to safely open the economy. This will have a large economic benefit in terms of, job creation, reopening supply chains etc. That’s economic so it will be easier to measure than other positive aspects like the general increase in mental well-being of being able to safely interact with folks again.
debbie
@Ohio Mom:
I am shameless enough to tell you that I was not ashamed to register for it!
edmund dantes
The setup for the California lottery is pretty good.
$50 incentive for those not already vaccinated on top of also getting entries. Plus chance at 50K prizes (one round is being drawn today and another next Friday)… plus the 10 large jackpot drawings of 1.5 million.
https://covid19.ca.gov/vax-for-the-win/
Can’t claim any until you complete your vaccine regimen.
Ohio Mom
Debbie:
Crossing my fingers for you! I see Kroger’s is also announcing a lottery — one prize is cash and another is a year’s worth of groceries.
I’m wondering how they would control for someone buying a big freezer and buying extra meat each week to fill it up. Because that would be my approach.
Major Major Major Major
I guess I’m not surprised that there are some “how can we afford this?” scolds out there but yeah, numbers seem pretty obvious & common-sensical! Thanks for the write-up.
debbie
@Ohio Mom:
You have to have gotten vaccinated at Krogers to qualify.
Goku (aka Amerikan Baka)
@Major Major Major Major:
The Dem Minority Leader of the OH statehouse is one of them. She said it was an irresponsible use of public funds, which I think is incredibly tone deaf. It’s clearly encouraging a bunch of people to be vaccinated
Ken
@Ohio Mom: The contest rules will specify the way the prize is awarded. The one time I checked, “year’s worth of groceries” was a weekly dollar amount. This is also needed for tax purposes.
Major Major Major Major
@Goku (aka Amerikan Baka): Tone-deaf is one thing; innumerate and short-sighted are much worse in political leaders!
VeniceRiley
It is too late but I truly wish they had tied the huge stimmies to getting vaccinated.
Ohio Mom
Debbie:
So all of us who were responsible citizens and got our vaccinations as soon as we could — which as I recall, means not at Kroger’s because they weren’t a site back then — are snubbed! Oh well, whatever gets us closer to as close as we can get to that elusive herd immunity.
Ken:
That makes sense, it’s not an episode of that old game show where contestants filled their carts as much as they could before the buzzer sounded.
Searcher
When I crossed the NY death statistics with the actuarial life tables last year, it came out to about 11-12 years lost per death. That leaves out “quality adjusted” and a detailed analysis of co-morbitities but 11+ QALY for 40s-60s (cutting out the 70+s) still seems aggressively low.
Brachiator
I like some of the targeted incentives for the already vaccinated. Something like “free Dodger tickets” if you provide proof that you were vaccinated within the last two weeks.”
Another Scott
@Amir Khalid: Do you have any “canned air”? Maybe a buildup of crumbs under the keys?
Good luck!
Cheers,
Scott.
sab
@gvg: In my head I already have the money spent.
Amir Khalid
@Another Scott:
We’re in lockdown here. Dunno if I can get any.
?BillinGlendaleCA
@Amir Khalid: Have you tried turning it upside down and shaking it
ETA: IIRC, you have a laptop, shut it down first
ETA2: Even with a laptop, it’s usually a good idea to keep a standalone keyboard handy.
Uncle Cosmo
@Amir Khalid: Vacuum cleaner, soft brush attachment, on the keyboard & exhaust areas for air? Also you can try removing the battery and vacuuming out the contacts & such there, then replacing it.
David Anderson
@Searcher: I agree, everything in this post is absurdly low where the assumption is biased towards assume non-cost-effectiveness.