Semisupervised D-Learning for Optimal Individualized Treatment Regimes

In precision medicine, linear treatment decision classes have attracted widespread attention due to their simple structures and good interpretability. However, linear decision models may often be misspecified in practical applications. To address this issue, we develop an imputation-based semisupervised D-learning method that leverages information from unlabelled data to enhance the efficiency of estimating optimal individualized treatment regimes (ITRs), especially when the linear decision model is misspecified. Specifically, we estimate the imputation function using a projection-based dimension reduction approach, adjust for the bias in imputation estimates via a residual refitting step, and estimate the decision function based on the debiased imputation function. To mitigate potential bias due to overfitting, cross-validation is incorporated. Theoretical results show that the semisupervised D-learning method achieves (Formula presented.) -consistent parameter estimates with asymptotic normality. Numerical experiments on both simulated and real datasets demonstrate the superior performance of our proposed approach.