A nearly unavoidable mechanism for collider bias with index-event studies

Factors suspected of causing certain chronic diseases and death are often associated with lower mortality among those with disease. For end-stage renal disease, examples include high cholesterol and homocysteine. Here, we consider obesity, thought to cause both end-stage renal disease and premature mortality, but which is associated with lower mortality among end-stage renal disease patients. Such seeming paradoxes could reflect collider (index event) bias due to selection of a diseased population for study. However, previous descriptions are incomplete, as they posit an uncontrolled factor causing both end-stage renal disease (the index event) and death. Here, we explicitly note that death can precede end-stage renal disease onset. The target population is obese persons with end-stage renal disease, effects of interest are seemingly controlled direct effects, the usual estimator is a conditional risk ratio, and remaining at risk until the onset of end-stage renal disease is a collider. Collider bias is then expected if any mortality risk factor is uncontrolled, even if no factor also affects end-stage renal disease. The bias is similar to, but differs from, that associated with competing risks. Because control of every mortality risk factor is implausible, bias of the standard estimator is practically unavoidable. Better awareness of these issues by clinicians and researchers is needed if observational research is to usefully guide care of this vulnerable patient population.