Identifying the optimal treatment decision rule, where the best treatment for an individual varies according to his/her characteristics, is of great importance when treatment effect heterogeneity exists. We develop methods for estimating the optimal treatment decision rule based on data with survival time as the primary endpoint. Our methods are based on a flexible semiparametric accelerated failure time model, where only the treatment contrast (ie, the difference in means between treatments) is parameterized and all other aspects are unspecified. An individual's treatment contrast is firstly estimated robustly by an augmented inverse probability weighted estimator (AIPWE). Then the optimal decision rule is estimated by minimizing the loss between the treatment contrast and the AIPWE contrast. Two loss functions with different strategies to account for censoring are proposed. The proposed loss functions distinguish from existing ones in that they are based on treatment contrasts, which completely determine the optimal treatment rule. Our methods can further incorporate a penalty term to select variables that are only important for treatment decision making, while taking advantage of all covariates predictive of outcomes to improve performance. Comprehensive simulation studies have been conducted to evaluate performances of the proposed methods relative to existing methods. The proposed methods are illustrated with an application to the ACTG 175 clinical trial on HIV-infected patients.
Keywords: augmented inverse probability weighted estimator; decision rule; doubly robust; optimal treatment regime; subgroup identification; variable selection.
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