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

Abstract

While sample sizes in randomized clinical trials are large enough to estimate the average treatment effect well, they are often insufficient for estimation of treatment-covariate interactions critical to studying data-driven precision medicine. Observational data from real world practice may play an important role in alleviating this problem. One common approach in trials is to predict the 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-covariate interaction in observational studies when the regression model is misspecified. Motivated by the need of modeling the number of relapses in multiple sclerosis (MS) patients, where the ratio of relapse rates is a natural choice of the treatment effect, we propose to estimate the conditional average treatment effect (CATE) as the ratio of expected potential outcomes, and derive a doubly robust estimator of this CATE in a semiparametric model of treatment-covariate interactions. We also provide a validation procedure to check the quality of the estimator on an independent sample. We conduct simulations to demonstrate the finite sample performance of the proposed methods, and illustrate their advantages on real data by examining the treatment effect of dimethyl fumarate compared to teriflunomide in MS patients. Supplementary materials for this article are available online.

KEYWORDS:

• Conditional average treatment effect
• Doubly robust estimation
• Heterogeneous treatment effect
• Observational study
• Precision medicine

Supplementary Materials

The supplementary materials provide additional results for showing optimality of the weights for the contrast regression under Poisson distributed outcomes, details regarding constructing symmetric contrast regression estimating equations, and proofs of Theorem 2. They also provide extensions for estimating and validating relative treatment effects for survival outcomes, along with experimental results for these settings.

Acknowledgments

The authors thank Hongseok Namkoong and the anonymous reviewers for helpful comments.

Additional information

Funding

SY is partially supported by the Stanford Graduate Fellowship and NHLBI award R01HL144555-01. Dr. Tian’s research is partially supported by R01HL089778-05 and 1UL1TR003142 from National Institutes of Health, USA.