Hypothesis Tests for Neyman's Bias in Case-Control Studies

Survival bias is a long recognized problem in case-control studies, and many varieties of bias can come under this umbrella term. We focus on one of them, termed Neyman's bias or 'prevalence-incidence bias'. It occurs in case-control studies when exposure affects both disease and disease-induced mortality, and we give a formula for the observed, biased odds ratio under such conditions. We compare our result with previous investigations into this phenomenon and consider models under which this bias may or may not be important. Finally, we propose three hypothesis tests to identify when Neyman's bias may be present in case-control studies. We apply these tests to three data sets, one of stroke mortality, another of brain tumors, and the last of atrial fibrillation, and find some evidence of Neyman's bias in the former two cases, but not the last case.