Estimation for optimal treatment regimes with survival data under semiparametric model

In this paper, we consider a semiparametric model to find the optimal treatment regimes. A-learning type equation method is proposed to construct a doubly robust estimating equation for the parameters of interest in the optimal treatment. To overcome bias from the censoring time, we consider the inverse probability censoring weighting method in estimating equation. The resulting estimator is shown to be consistent and asymptotic normal when either the baseline effect model for covariates or the propensity score is correctly specified. Also, numerical simulations and an application with real data illustrate the proposed method.