Martingale R-learner: Estimating Time-varying Heterogeneous Treatment Effects for Time-to-event Outcomes

Thomas M. Menino Convention & Exhibition Center 

Biological research and clinical evidence suggest that treatment response may vary substantially across individuals with different characteristics, such as comorbidities, genetic variants, environmental, or socio-economic factors. Future precision medicine requires accurate assessment of explainable variability in treatment effects, known as heterogeneous treatment effects (HTE), to guide optimal clinical decisions at the individual level. Measuring HTE by the ratio of survival probabilities under the structural failure time model, we develop a martingale R-learner to estimate HTE. Our martingale R-learner incorporates flexible estimators for (1) marginal survival or cumulative hazards for the association between outcome and confounders, and (2) time-varying propensity scores in risk sets, which enables leveraging advances in machine learning. To reduce the impact of estimation bias in these two nuisance models on HTE, we propose a Neyman-orthogonal score based on an orthogonal decomposition of conditional model martingale residuals into residuals of the propensity score and the marginal model martingale. The resulting martingale R-learner attains an oracle property, i.e., estimation errors of the nuisance models have no impact on HTE if their estimators are consistent at rate o(n^(-1/4)). Numerical experiments across various settings demonstrate empirical performance consistent with the theory. We investigate the effect of alcohol on dementia through the Honolulu-Asia Aging Study data.

Heterogeneous treatment effects

Causal inference

Survival analysis

Orthogonal score