A robust covariate-balancing method for estimating individualized treatment with censored data

One of the most essential aspects of precision medicine is the identification of optimal individualized treatment regimen, which recommends treatment decisions to maximize a patient's expected survival time based on their individual characteristics with censored data. Typically, the expected survival time is required to be estimated first, which is usually based on the posited weighting models (propensity score model and censoring model) or the posited outcome model. However, if any of the above models is misspecified, the estimated treatment regimen is not reliable. In this paper, we consider the contrast value function defined for survival analysis, and propose two robust covariate-balancing estimators of the contrast value function by balancing the covariates of patients through censoring probability and survival function of censoring time in the weights, respectively. Theoretical results prove that the proposed estimators are doubly robust and asymptotically normal under standard regularity conditions. A large number of simulations show the superiority of our methods over the existing methods. We further apply the proposed methods to the China Rural Hypertension Control Project to identify the individualized medication regimens for hypertensive patients by tailoring their individual characteristics to maximize the expected survival time. The results indicate that the estimated optimal treatment regimen improves patients' survival probability over the 36-month follow-up period.