Moderation analysis for evaluating differential treatment effects serves as the bedrock of precision medicine, which is of growing interest in many fields. In the analysis of data with binary outcomes, we observe an interesting symmetry property concerning the ratio of odds ratios, which suggests that heterogeneous treatment effects could be equivalently estimated via a role exchange between the outcome and treatment variable in logistic regression models. We then obtain refined inference on moderating effects by rearranging data and combining two models into one via a generalized estimating equation approach. The improved efficiency is helpful in addressing the lack-of-power problem that is common in the search for important moderators. We investigate the proposed method by simulation and provide an illustration with data from a randomized trial on wart treatment.
Keywords: Heterogeneous treatment effects; logistic regression; moderation; odds ratio; treatment-by-covariates interactions.