The usually reliable Zvi writes:

If you have had one shot of the Johnson & Johnson vaccine, should you then get a shot of Pfizer or Moderna? If it is available, absolutely, yes you should.

When people give orders like this instead of making assertions about matters of fact, I have to assume that if there's no stated cost-benefit calculation, then no cost-benefit calculation was performed. So I have to do my own.

[UPDATE: Here's a spreadsheet with somewhat more precise numbers. If you make a copy you can adjust some parameters to see how they affect the total.]

Based on the experience of people I know I expect to lose about a day to vaccine symptoms if I get a second shot. While many people I know had no serious symptoms, I lost a day to J&J, a few other people I'm in regular contact with (a fairly small group) got wiped out for a day with other COVID vaccines, and my sister was sick for over a week.

What's the benefit?

I previously estimated that the expected cost of COVID to an unprotected person in my risk category is around a month due to the risk of death, plus 2 weeks due to likely symptoms if infected. If you're in a different risk category you should substitute the numbers that apply to you, but hopefully my model makes this easier to calculate.

A single shot of just about any vaccine seems to reduce morbidity by around 2/3 and mortality by around 95%. Let's assume that the protection from any two shots is independent (though I'd expect that mixing treatments gives better results than two of the same). High-dose vitamin D is probably about as effective as a single vaccine shot so no need to deal with it separately.

One treatment reduces days lost to death per case by 95% * 30 = 28.5, and days lost to illness per case by 67% * 15 = 10, for a total of 38.5 days saved.

How likely am I to get COVID? As of today the current case rate in New York where I live is around 5 per 100,000, which amounts to a 1 - .99995^365 = 2% chance a typical person gets COVID in the next year. But the population is heterogeneous - around 2/3 of the population is vaccinated. Call unvaccinated_rate the rate at which unvaccinated people are diagnosed with COVID. Assume that each vaccine shot reduces your risk by 2/3, i.e. vaccine_relative_risk = 1/3. If half of the vaccinated have only one dose and half have two, then we can estimate 2% = unvaccinated_rate * (vaccine_relative_risk^0 + vaccine_relative_risk^1 + vaccine_relative_risk^2) / 3. That gives us unvaccinated_rate = 4%.

Quick check - in NY state, the first wave infected around 2% of residents and the second wave infected another 9%. Their geometric mean is 4.6%. Since as calculated above I naively expect the current state of vaccination to halve the risk, that leads to extrapolations of 1% if the next wave is like the first, 4.5% if it's like the second, and 2% if it's about halfway in between.

4% * 38.5 = 1.5 days of benefit for my first treatment, barely more than my expected day lost.

How about for the second treatment? Expected days lost to death are reduced by 95% * 5% * 30 = 1.5, with pretty much zero remaining. Expected days lost to illness are reduced by (2/3) * (1/3) * 15 = 3, with two days remaining. In other words, with two treatments, getting COVID is like getting a very mild flu. The probability that I realize this benefit is unvaccinated_rate * vaccine_relative_risk = 1%, so the expected benefit is 4.5 * 1% = .045 days of life, for a net loss of .955 days of life.

Note that even if Delta is twice as severe and we should expect a large wave that multiplies the effective risk by 10, the resulting 20x multiple doesn't justify the time cost to me of going somewhere to get a vaccine, before even counting side effects. On the other hand, if you're in a higher risk category, you might want to estimate the benefit to yourself of a third treatment.

Strictly from a personal health perspective, since high-dose vitamin D* has no serious adverse side effects, it wouldn't make sense for me right now to get even one vaccine shot. I got the single-shot J&J vaccine mostly because the infection rate used to be higher, the low infection rate depends on people getting the vaccine, I want to be able to honestly tell people I'm vaccinated, and I want a vaccine card in case I need it to travel.

* This summer I've been taking less, but mostly because I got the J&J, not because I expect sunlight to be enough. My Fitzpatrick Type III skin can produce around 400 IU in 6 minutes (another estimate of the equivalence between vitamin D and sunlight) of peak direct sunlight with my shirt off, so to get the 7600 IU/day maintenance dose from the Spanish RCT, I'd have to get about 2 hours of peak sun daily.

Zvi MowshowitzSo from my perspective, it's interesting that you interpret this as 'giving orders' and as conspicuously missing a cost/benefit calculation. Expanding to include context, the intended meaning of the OP's statement was supposed to be this:

One J&J shot + One Pfizer/Moderna shot is similarly effective to two Pfizer/Moderna shots.

One J&J shot is similarly effective to one Pfizer/Moderna shot.

So the two calculations are the same - if you can get a second shot after getting J&J, you should treat it the same (for health purposes) as if you'd had one shot of Pfizer/Moderna and were considering skipping the second one. The idea that J&J counts as vaccinated with one dose, but mRNA requires two doses, is not based in physical reality.

Having, as a mathematician, reduced it to the previous problem, I considered the question solved.

In terms of the calculation, if you really think it's mild flu, and that long Covid isn't a thing at all, and you have a full day's loss to the vaccine shot which I think is too high, then yes that would get one a potentially different answer.

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