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#ANOTHER WORD FOR YOU HAVE NO CONTROL HOW TO#
Let’s be clear: This post is not intended to discuss the substantial content of these topics such as how well vaccines work these issues are presented purely as examples for how to statistically deal with correlations in observational data. We might assume that: If the older people with pre-existing conditions would not have gotten the vaccine, they would probably nevertheless have a higher mortality rate (maybe even higher than with the vaccine) as opposed to the younger and healthier and unvaccinated persons, which would mean there is no causal effect (or, if anything, a causal effect in the other direction, meaning the death rate might actually be lower due to the vaccine).
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If we define causation in a counterfactual way, causality means that if X had not happened, Y would also not have happened, all other things being equal. As a result, getting the vaccine is correlated with a higher death rate, but not because of the vaccine, but because the effect of third variables. And, being older and having pre-existing diseases is also associated with higher mortality rates, irrespective of vaccination. Rather, we might suspect that older people and persons with pre-existing conditions (such as cancer or obesity) have higher vaccination rates as compared with younger and healthy persons. But we might suspect that getting the vaccine is not the actual cause for the higher mortality rate among the vaccinated. Let’s look at our second example: There is a correlation between getting a vaccine and having an increased risk of dying. But we can mitigate the problem with the methods shown in this article. This means that if you do not have data from a randomized experiment, but rather from real-world observations where you did not have control over the data-generating process, you usually cannot interpret correlations as causations. data where you have not controlled the assignment of the treatment (here: smoking), but rather people have assigned themselves to the groups which might be associated with a multitude of other factors. Often, you have to resort to using observational data, i.e.
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However, for obvious reasons, randomized experiments are often not possible to conduct in real-world scenarios.
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If you were able to recruit a group of 10,000 non-smokers, randomly divide them into two groups, force the first group to start smoking heavily and the other to refrain from it, and observe the number of covid infections in both groups over the following months, you could be quite confident to identify a causal effect of smoking on the risk of catching covid with a simple comparison of counts and maybe a t-test for statistical significance. So what does imply causation? In general, randomized control trials (RCT) are considered the gold standard for causal inference in science. Why does correlation not imply causation?īy now you certainly have heard of the phrase “correlation does not imply causation”. Let’s first try to understand what might be wrong with these two examples. The answers to these questions can be found below. Does the vaccine increase your chance of dying? What? Does smoking reduce your risk of getting Covid?Īnother example: I recently saw a post on Twitter with a line graph showing that, in the UK, persons aged 18 to 59 who were vaccinated against the coronavirus had a higher risk of dying (from any cause) in the next 21 days as opposed to unvaccinated persons aged 18 to 59. But: Among the heavy smokers among these patients, only 6% have Covid-19. In a hospital, 9% of all patients have Covid-19.