As mentioned before, the team who did the research tying Covid-19 vaccinations to car accidents convinced themselves that they have found a real effect. They attempted a variety of confirmatory analyses. In the prior post, I described how they conducted variants of the basic analysis by analyzing subgroups and by modifying the outcome metrics.
It's instructive to look at several other validation strategies and discuss their strengths and weaknesses.
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Every observational study delivers the following table, usually called Table 1 because it's the first table in the paper:
Table 1 compares the characteristics of the treatment group and the control group. In the traffic accidents study, the two comparison groups are the vaccinated and the unvaccinated residents of Ontario (after exclusions). For a randomized clinical trial, in which vaccination status would be randomly assigned, the two columns of Table 1 should look statistically the same. For an observational study, in which vaccination status is self-selected (or influenced by biases such as public-health priorities), the differences between the two columns provide hints as to the magnitude and direction of biases.
The first thing to notice is vaccinated residents outnumbered unvaccinated about 5 times. The features are divided into three groups: demographics, prior medical conditions (e.g. diagnoses of cancer in the past year), and something labeled "general". The "general" collection includes clinical contacts, hospital admissions, and emergency room visits in the prior year. These are important variables because prior health status is a likely source of self-selection bias.
The researchers have this to say about Table 1:
The 2 groups spanned a diverse range of demographics, with comparable general health care utilization (Table 1). The largest relative differences were that those who had not received a COVID vaccine were more likely to be younger, living in a rural area, and below the middle socioeconomic quintile. Those who had not received a vaccine also were more likely to have a diagnosis of alcohol misuse or depression and less likely to have a diagnosis of sleep apnea, diabetes, cancer, or dementia. About 4% had a past COVID diagnosis, with no major imbalance between the 2 groups.
This language is highly typical of how researchers opine on the likely sources of bias, i.e. those characteristics that differ between the comparison groups. Now pay attention to the last sentence: About 4% had a past COVID diagnosis, with no major imbalance between the 2 groups.
The actual data from Table 1 show 4.1% of vaccinated people had a documented Covid-19 infection in the past year, compared to 3.5% of unvaccinated. That's a relative ratio of 1.17. Given the large sample size (millions of people), a 0.6% difference in infection rates is highly significant! If we randomly selected 4/5 of the population to be vaccinated, the difference in infection rates between them and the unvaccinated would typically be much smaller than 0.6%.
So the claim of no major imbalance on Covid-19 prior infection is incorrect. It is also inconsistent because in the main analysis, based on 95% confidence intervals on relative risk, they declared they have found a significant correlation between vaccination status and traffic accidents. The same method would have found the difference between 3.5% and 4.1% prior infection rate to be highly significant. Indeed, if we apply the same method to all rows of Table 1, quite a few would also be found significantly different.
The prior-year emergency visits metric is of particular interest because the primary outcome being analyzed in this study was "emergency visits for individuals injured in traffic crashes". The unvaccinated group had a much higher prior rate of 26% compared to 20% for vaccinated, a relative ratio of almost 1.3, clearly significant. The analysts did not adjust for any of the variables in the general collection in their logistic regression, perhaps because they thought the two groups have "comparable general health care utilization," which as I just explained, is incorrect.
It's ok - in fact, expected - that the unvaccinated group would differ from the vaccinated group on some metrics. It's the opposite that should raise doubt. If the two columns are effectively equivalent, then the two comparison groups resemble those found in randomized trials. If we believe that, we're claiming that obvious sources of bias due to self-selection and public-health policy have not resulted in observed bias.
The biggest weakness of Table 1 analysis is missing variables. The comparisons are made only on the measured covariates. In the case of Covid-19, the measured covariates are whatever can be found in large government databases, collected for purposes other than conducting a study of traffic accidents and Covid-19 vaccination. The researchers said: "The available databases lacked information on driver skill, functional status, personality traits, traffic infractions, political affiliation, and self-identified ethnicity." Several of these variables are clearly pivotal for our present study.
In addition, Table 1 analysis addresses only biases acting independently. Some biases act in complex ways. When I analyzed prior emergency visits, the observed data appeared to indicate a healthy user bias in the vaccinated group. But this factor interacts with the age bias, which was also present. The vaccinated group was quite markedly older than the unvaccinated group. If older people are more likely to need emergency medical service than younger, then the emergency visit bias is even more pronounced since younger, unvaccinated people have a lower baseline emergency room usage than the older, vaccinated group. If younger people are more likely to need emergency medical service older, then age could explain some of the observed bias in emergency room usage. In other words, these factors should be interpreted simultaneously. In fact, any adjustment in the regression model should contain interaction effects, but this is rarely done.
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The researchers also used "positive controls" and "negative controls" to convince themselves they have properly removed bias from this observational dataset. The idea is to process the data in the same way but substitute other metrics instead of the traffic accidents outcome. These other metrics are chosen because the researchers are 100% sure of the direction of the effect: for positive controls, they claim they knew ex-ante that the alternate outcomes are definitely affected by Covid-19 vaccination status while for negative controls, they claim they knew ex-ante that the alternate outcomes are definitely independent of Covid-19 vaccination status.
For negative control, they presented an analysis of constipation.
There were 2,985 cases of constipation during the month of August in the study population, and the relative risk was 1.03 meaning the unvaccinated group's risk was 3% above that of the vaccinated. This difference is not significant because the confidence interval of 0.94 to 1.14 crosses the 1.00 reference level. In other words, the data provided no evidence that unvaccinated people differ from vaccinated people in terms of experiencing constipation.
This type of validation analysis has many shortcomings. First, it's a single outcome. We don't know if this was pre-specified. Even if pre-specified, it could still show the desired result by chance since there are hypothetically hundreds or thousands of possible negative control candidates. If it's not pre-specified, it's hard to know if other candidates were tried and failed the test.
Perhaps because of reviewer feedback, the research team added several other negative controls, namely, fall, water craft, appendicitis and conjunctivitis. Perhaps because these were not in the original analyses, they did not discuss these other negative controls in the article.
I excerpted the table of results below.
The last column presents the confidence interval of the relative risk, and the second last column from the right shows the point estimate of the relative risk.
The second problem is inconclusiveness. Notice the point estimates of all five negative controls are tightly clustered between 0.90 and 1.14, and every confidence interval except "falls" shows a statistically insignificant difference between the vaccinated and unvaccinated groups. How should one interpret the result of "falls"? The researchers were silent on that one. When a negative control (constipation) shows insignificance, as expected, they were quick to say this finding validated the study conclusion but when a negative control shows a significant difference, it appeared that they explained it away, probably arguing it's a chance observation.
The third problem is over-confidence. How do they know that vaccination could have zero impact on constipation? I imagine this relies on some kind of structural biological argument, such as that mRNA does not act on certain bodily systems. Remember that statistical analyses describe correlations, not causation. We have to rule out ex-ante not just a direct causal relation between vaccination and constipation but any kind of correlation. That's actually a deep assumption, not as simple as it looks.
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Positive controls are even harder to grapple with because we have to believe ex-ante that vaccination status will certainly result in some given outcome, in this case, "covid pneumonia".
The use of "covid pneumonia" implies the absolute belief that vaccinations reduce covid pneumonia in the analysis population. A few aborted clinical trials and many observational studies do not constitute incontrovertible evidence. Imagine if the data showed no significant difference in covid pneumonia between the unvaccinated and vaccinated. What would be the conclusion? That the methodology is invalidated? That the assumption of causation was incorrect?
These validation analyses using positive or negative controls have limited utility. They produce a situation in which the only possible conclusion is supporting the study - if these analyses do not support the study, we don't know how to interpret them so we throw them out and find another metric to act as control. (As a practical matter, no one would publish the paper if the authors include "failed" controls. See my prior post on the file drawer effect.)
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The next tactic used for validation is propensity score matching. I'll discuss that in the next post.
Prior posts about this study: 1, 2, 3
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