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While sample sizes in randomized clinical trials are large enough to estimatethe average treatment effect well, they are often insufficient for estimationof treatment-covariate interactions critical to studying data-driven precisionmedicine. Observational data from real world practice may play an importantrole in alleviating this problem. One common approach in trials is to predictthe outcome of interest with separate regression models in each treatment arm,and estimate the treatment effect based on the contrast of the predictions.Unfortunately, this simple approach may induce spurious treatment-covariateinteraction in observational studies when the regression model is misspecified.Motivated by the need of modeling the number of relapses in multiple sclerosispatients, where the ratio of relapse rates is a natural choice of the treatmenteffect, we propose to estimate the conditional average treatment effect (CATE)as the ratio of expected potential outcomes, and derive a doubly robustestimator of this CATE in a semiparametric model of treatment-covariateinteractions. We also provide a validation procedure to check the quality ofthe estimator on an independent sample. We conduct simulations to demonstratethe finite sample performance of the proposed methods, and illustrate theiradvantages on real data by examining the treatment effect of dimethyl fumaratecompared to teriflunomide in multiple sclerosis patients.

Estimation and Validation of Ratio-based Conditional Average Treatment Effects Using Observational Data