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.
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.
基金
Funded by Fundamental Research Funds for the Central Universities (Grant No.BUPT2012RC0708)
