Day 677: Immortal Time

Immortal time has nothing to do with the FDA doubling down and asking a federal judge for 75 years to release Pfizer's COVID vaccine approval application under an FOIA request. Seriously.

Here at PlagueBlog headquarters, we find it hard to resist the temptation to pronounce it "immortal time" like some sci-fi concept, but it's really "immortal time": the time during which a subject in the treatment group cannot die from the disease being treated.

Immortal time is generally due to a delay in the treatment process that causes patients to count as untreated for some interval, during which they can die of the disease or other causes. This makes the treatment look more effective against the disease (or against the proxy of all-cause mortality) than it actually is. Depending on the length of immortal time and the fragility of the patient population, this can be a significant statistical issue.

While the initial Pfizer trial was too brief and front-loaded with healthy people to need immortal time correction, population statistics for COVID vaccine rollouts do need adjustments for the long window (at least 14 days) of vaccinated but unprotected time. Patients in this window frequently find themselves in the unvaccinated column—though who is in which column is its own vexing issue with COVID data. Since the old and infirm get priority for vaccination, they can artificially inflate efficacy of the vaccine, or even create efficacy where none actually exists.

Troubling though immortal time is, it is only one of many statistical gotchas in calculating vaccine efficacy. Several of these issues are explained in a recent blog post and paper by Norman Fenton and Martin Neil, with regards to ONS England data.

Correlating unvaccinated mortality with vaccine roll out we see curious patterns (dotted line the proportion of people getting first and second doses). Why are the unvaccinated dying after NOT getting the 1st dose? Why are the single dosed dying after NOT getting the 2nd dose?

Plenty of evidence that the vaccinated who die within 14 days of vaccination may be categorized as unvaccinated. Then someone who dies within 14 days of first dose is miscategorised as unvaccinated and a similar thing could occur post second dose.

This theory could be described as "safe but ineffective", as opposed to the more common "unsafe but effective" theories that attribute excess deaths (regardless of how they are categorized) to vaccine side-effects. However, the authors do find some excess deaths to account for, and postulate that vaccines are, in fact, increasing mortality—but through innate risks of vaccination rather than adverse effects per se:

However, in interpreting these results it is important to avoid an overly simplistic understanding of the processes at play before and after vaccination. On the one hand, after vaccination the vaccinee is reported to endure a weakened immune response, [19], [21], for a period of up to 28 days [20] and may be in danger of infection from Covid or some other infectious agent at any time during that period. On the other hand, infection prior to vaccination, where Covid remaining symptomless for a period of up to three days, might endanger the vaccinee after vaccination because vaccination is supposed to be prohibited for 3-4 weeks after contracting Covid.

P.S. Massachusetts cases are up three fifths of a percentage point again today. We're approaching 6000 daily cases and looking a lot like this time last December.