Beyond Berkson: Further Light on the Selection Bias

The Berkson effect shows that two independent diseases, A and B, become negatively correlated if they are confined within the walls of a hospital. We explain that, simply by adding a third disease, C, the negative correlation may flip into a positive one, and we identify the point where this happens. That leads to a necessary and sufficient condition for a positive as well as a negative correlation between A and B. We further explain that a flip from negative to positive is impossible if C is independent of A, of B, and of the disjunction of A and B: with these three independences in place, the Berkson effect remains in force. However, if only two of the three independences hold, the effect is not guaranteed.