Noncollapsibility, confounding, and sparse-data bias. Part 2: What should researchers make of persistent controversies about the odds ratio?

Abstract

A previous note illustrated how the odds of an outcome have an undesirable property for risk summarization and communication: Noncollapsibility, defined as a failure of a group measure to represent a simple average of the measure over individuals or subgroups. The present sequel discusses how odds ratios amplify odds noncollapsibility and provides a basic numeric illustration of how noncollapsibility differs from confounding of effects (with which it is often confused). It also draws a connection of noncollapsibility to sparse-data bias in logistic, log-linear, and proportional-hazards regression.