DINA: Estimating Heterogenous Treatment Effects in Exponential Family and Cox Model

We propose to use the difference in natural parameters (DINA) to quantify the heterogeneous treatment effect for the exponential family, a.k.a. the hazard ratio for the Cox model, in contrast to the difference in means. For responses such as binary outcome and survival time, DINA is of more practical interest and convenient for modeling the covariates' influences on the treatment effect. We introduce a DINA estimator that is insensitive to confounding and non-collapsibility issues, and allows practitioners to use powerful off-the-shelf machine learning tools for nuisance estimation. We use extensive simulations to demonstrate the efficacy of the proposed method with various response distributions and censoring mechanisms. We also apply the proposed method to the SPRINT dataset to estimate the heterogeneous treatment effect, testify the method's robustness to nuisance estimation, and conduct placebo evaluation.