Collapsibility of odds ratios for a continuous outcome variable

摘要

The sign of an association measure between two varibles may be strongly affected and even be reversed after marginalization over a backgruoud variable, which is the well-known Yule-Simpson paradox.Odds ratios are strongly collapsible over a background variable if they remain unchanged no matter how the background variable is partially pooled.In this paper, we firstly give some definitions and notations about odds ratios between a dichotomous explanatory variable and a continuous response variable.Then, we present conditions for simple collapsibility of odds ratios.Further, necessary and sufficient conditions are given for strong collapsibility of odds ratios for continuous outcome variable.