Why my analyses of Moderna and AstraZeneca's mortality were conservative
Recently, I showed that mortality rates among Czech women who had taken the Moderna or AstraZeneca COVID-19 vaccines were higher than those who had taken the Pfizer vaccine. The analyses were conservative, and here I show why.
The results in the two columns on the left are the same ones I recently posted and have controlled for, i.e., included a dummy variable for the number of doses each woman had taken at each time point of analysis (Note 1). There may be reasonable arguments for this, since individuals who took one or a few doses differ from those who took more; older individuals consistently took more doses than younger individuals, but within age cohorts, individuals with initially better health took more doses than those with poorer health. If the number of doses taken of the different drugs varied, as is the case, women took an average of 2.74 Pfizer doses, 2.48 Moderna doses, and 1.26 AstraZeneca doses; the approach can correct for these differences (Note 2).
However, “survival bias” or “survivorship bias” argues against including the number of doses taken as a control variable. For example, if Moderna and AstraZeneca are more dangerous than Pfizer, not only will more people die from the former two drugs, but those who survive their initial dose or doses will then be more robust than those who survive the initial dose or doses of Pfizer. The phenomenon is known among smokers, where the most vulnerable die early, while the more resilient survive longer. One may then experience reduced mortality among older smokers compared to non-smokers. The reason, rather than smoking becoming healthier with age, is that the most vulnerable smokers have already died and are therefore no longer included in the comparison group.
Since I have already shown that Moderna and AstraZeneca were probably more lethal than Pfizer, “survival bias” is a natural consequence, especially in those who took the first two drugs. By using the aforementioned control variable, I hold the analyses constant for the remaining survivors after each dose, which will be increasingly robust, especially among those who took Moderna or AstraZeneca, with the highest mortality rate at the outset. One implication is that differences in mortality between the drugs may be masked (Note 3).
In the columns on the right, I therefore present analyses that do NOT control for different doses at different analysis times, i.e., only WHETHER a woman has taken Pfizer, Moderna, or AstraZeneca, and ignore the number of doses. The analyses on the right are therefore not tainted by possible “survival bias”, and we see that the hazard rates for both Moderna and, especially, AstraZeneca have increased considerably (Note 4).
Whether the latter analyses on the right provide completely correct estimates is debatable, as I do not have access to other data beyond age that could correct for differences between Moderna, AstraZeneca, and Pfizer vaccinees. But as pointed out, “I have little reason to think that someone with particularly good or poor health has systematically chosen one type of vaccine over another.”
The conclusion is then that, due to “survival bias”, there is reason to believe that the most accurate estimates are consistently closer to those reported on the right in the table than to those on the left. That is, the mortality from Moderna and, especially, AstraZeneca was considerably higher than Pfizer’s, as shown in my previous conservative estimates.
A final point is that the clear changes in estimates, with and without the aforementioned control variable, not only make “survival bias” probable, but in themselves make it probable that Moderna and AstraZeneca were more deadly than Pfizer, despite the lack of data on possible underlying unobserved explanations. The reason is that a relatively high degree of “survival bias” among Moderna and especially AstraZeneca vaccinees makes a selection process more likely, with the most robust surviving after repeated doses. An implication is that more robust people died after taking the initial dose or doses of Moderna and especially AstraZeneca compared to Pfizer.
Norwegian version here.
Notes
1. Confidence intervals (CIs) are in parentheses. Numbers in bold are statistically significant (95% CIs), i.e., the mortality rate among women who received Moderna was significantly higher than among those who received Pfizer.
2. I have no sure answer to the fact that women, on average, took fewer doses of Moderna and especially AstraZeneca than Pfizer, but one explanation could be relatively high mortality or extensive side effects that resulted in fewer booster doses. An additional explanation for AstraZeneca may be that skepticism towards the drug increased in the Czech Republic after it was put on hold in several EU countries as early as March 2021. However, I have not found information that AstraZeneca was officially banned in the Czech Republic before it was withdrawn from the world market, allegedly due to “market considerations”, in May 2024. For information, I have analyzed Czech data through 2023.
3. For simplicity, let’s assume two drugs, A and B, where 40 out of 100 died from A and 80 out of 100 died from B. That is, B is twice as deadly as A, all else being equal. If we further assume that all deaths occurred after the first dose, and that all survivors will later take a second dose, then 40 out of 40, i.e. 100% of those who only took the first dose of A will have died, while 80 out of 80, i.e. also 100% of those who only took the first dose of B will have died. In other words, equal mortality among those who only took the first dose of A or B. Similarly, all 60 survivors who took the second dose of A will survive, as will the 20 survivors who took the second dose of B, i.e., 0% mortality for both drugs. If we control for and hold the effect constant across doses, we only look at mortality within each dose category, not between them. The consequence may be that we mistakenly assume A and B have the same mortality: 100% mortality among those who received only the first dose of A and B, and 0% mortality among those who received the second dose of A and B. However, the reality is that B has twice the mortality rate as A.
4. The only exception is the lower hazard rate among women who took AstraZeneca in the youngest age cohort, but here the low number of deaths in general and among those who took this drug in particular may have led to unstable estimates that should not be given too much weight. Another explanation may be that younger women who took multiple doses of AstraZeneca initially had significantly worse health than those who took multiple doses of Pfizer.