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Abstract:
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To discover optimal treatment regimes for potentially censored outcomes, we propose a proportional hazards model with a single-index function to represent the interactions between treatment and covariates. This model is flexible enough to allow non-linear treatment-covariate interactions but still provides a simple and interpretable optimal treatment rule. The model enables one to assess how treatment effect varies across patients according to baseline variables and to derive the individualized treatment rule that reflects the baseline characteristics of each subject. We use the nonparametric maximum likelihood estimation approach, together with the B-spline approximation technique, to estimate the model parameters. We prove that the resulting estimators are consistent, asymptotically normal, and asymptotically efficient, and we provide consistent variance estimators. We also show how to estimate the treatment rule and the average treatment effect. In addition, we demonstrate through extensive simulation studies that the proposed methods perform well in realistic settings. Finally, we provide a detailed illustration with an AIDS clinical trial.
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