Controls who experienced hypothetical causal intermediates should not be excluded from case-control studies

It has been suggested that controls with adenomatous polyps of the colon and rectum should be excluded from case-control studies of cigarette smoking and colorectal cancer. A claim has been made that the presence of such controls creates a bias toward the null. The polyps are an intermediate step in a hypothetical causal pathway between the exposure and the disease. Thus, the recommendation logically extends to the exclusion of all controls who experienced hypothetical causal intermediates from all case-control studies. It is shown, in the simple case of an exposure that acts solely through the pathway involving the intermediate, that such exclusions create a bias away from the null. The rationale for recommending the detrimental exclusions appears to stem from a variant of the "trohoc fallacy": the mistaken view of case-control studies as comparisons between diseased and healthy groups and not as comparisons between groups that differ by exposure.