Inconsistency between overall and subgroup analyses.

Suppose we have a sample of subjects in two treatment groups. To study the difference of the treatment effects, we can analyse the data using all subjects (overall analysis). We may also divide the subjects into several subgroups based on some covariates of interest (eg, gender), and study the treatment effects within each subgroup. The results of these two analyses may be different or even in opposite directions. In this paper, we give a general sufficient condition of consistency between the overall and subgroup analyses.