Model Selection for Survival Individualized Treatment Rules Using the Jackknife Estimator

Abstract

Background: Precision medicine is an emerging field that involves the selection of treatments based onpatients’ individual prognostic data. It is formalized through the identification of individualized treatment rules(ITRs) that maximize a clinical outcome. When the type of outcome is time-to-event, the correct handling ofcensoring is crucial for estimating reliable optimal ITRs. Methods: We propose a jackknife estimator of the value function to allow for right-censored data for a binarytreatment. The jackknife estimator or leave-one-out-cross-validation approach can be used to estimate thevalue function and select optimal ITRs using existing machine learning methods. We address the issue ofcensoring in survival data by introducing an inverse probability of censoring weighted (IPCW) adjustment inthe expression of the jackknife estimator of the value function. In this paper, we estimate the optimal ITR byusing random survival forest (RSF) and Cox proportional hazards model (COX). We use a Z-test to comparethe optimal ITRs learned by RSF and COX with the zero-order model (or one-size-fits-all). Through simulationstudies, we investigate the asymptotic properties and the performance of our proposed estimator underdifferent censoring rates. We illustrate our proposed method on a phase III clinical trial of non-small cell lung cancer data. Results: Our simulations show that COX outperforms RSF for small sample sizes. As sample sizes increase,the performance of RSF improves, in particular when the underlying distribution of the failure times follows anon-linear pattern. The estimator is fairly normally distributed across different combinations of simulationscenarios and censoring rates. When applied to a non-small-cell lung cancer data set, our method determinesthe zero-order model (ZOM) as the best performing model. This finding highlights the possibility that tailoringmay not be needed for this cancer data set. Conclusion: The jackknife approach for estimating the value function in the presence of right-censored datashows satisfactory performance when there is small to moderate censoring. Winsorizing the upper and lowerpercentiles of the estimated survival weights for computing the IPCWs stabilizes the estimator.