Treatment Effect Estimation Under Additive Hazards Models With High-Dimensional Confounding

Abstract

Estimating treatment effects for survival outcomes in the high-dimensional setting is critical for many biomedical applications and any application with censored observations. This article establishes an “orthogonal” score for learning treatment effects, using observational data with a potentially large number of confounders. The estimator allows for root-n, asymptotically valid confidence intervals, despite the bias induced by the regularization. Moreover, we develop a novel hazard difference (HDi), estimator. We establish rate double robustness through the cross-fitting formulation. Numerical experiments illustrate the finite sample performance, where we observe that the cross-fitted HDi estimator has the best performance. We study the radical prostatectomy’s effect on conservative prostate cancer management through the SEER-Medicare linked data. Last, we provide an extension to machine learning both approaches and heterogeneous treatment effects. Supplementary materials for this article are available online.

Keywords:

• Causal inference
• Double robustness
• Orthogonal score
• Survival analysis

Supplementary Material

In supplementary materials contain complete proofs of the theoretical claims made in the main text.