1/ One day everyone will recognize #selectionbias due to a #collider and the world will be a better place.
This time observational studies found a higher risk of omicron reinfection after a 3rd dose of #COVID19 vaccine. As usual, alarms went off.
Can you see the obvious bias?
2/ Those who receive a booster and get infected are, on average, more susceptible to infection than those who don't receive a booster and get infected.
So no surprise than those who receive a booster and get infected are more likely to get reinfected.
1/ Our findings on a fourth dose (2nd booster) of the Pfizer-BioNTech #COVID19 vaccine are now published.
Compared with 3 doses only, a fourth dose had 68% effectiveness against COVID-19 hospitalization during the Omicron era in persons over 60 years of age.
@ProfMattFox 1/
The odds ratio from a case-control study is an unbiased estimator of the
a. odds ratio in the underlying cohort when we sample controls among non-cases
b. rate ratio in the underlying cohort when we use with incidence density sampling
No rare outcome assumption required.
@ProfMattFox 2/
Because the odds ratio is approximately equal to the risk ratio when the outcome is rare, the odds ratio from a case-control study approximates the risk ratio in the underlying cohort when we sample controls among non-cases and the outcome is rare.
But...
@ProfMattFox 3/
... for an unbiased estimator of the risk ratio (regardless of the outcome being rare), we need a case-base design, not a classical case-control design.
Of course, all of the above only applies to time-fixed treatments or exposures.