Constrained optimization for stratified treatment rules with multiple responses of survival data

Abstract

For data analysis, learning treatment rules in stratified medicine require the optimization of multiple responses. A common approach is to use a multi-objective function to find the optimal setting of the controllable factors. For patients, the optimal setting is a treatment regimen that yields the optimal value of potential responses. However, subclasses of patients are often stratified by their covariates. Thus, this paper proposes a new model called constrained optimization for stratified treatment rules (COSTAR) with multiple responses. This model incorporates covariates to build separate models for optimal responses and stratifies the patients with the balancing score from covariates. The optimal solution enables us to choose the optimal treatment for each subclass of patients. Theoretical results guarantee the identifiability of the solutions with conditional optimal values of multiple responses from survival probabilities. Examples of experiments with factorial designs and survival data validate the efficacy of the proposed method. The results suggest that this method improves the significance of the parameters and the adjusted R2 in fitting on the primary response, while the unsupervised clustering method (i.e., k-means) does not. This method, with the fitting model, is more interpretable than the conventional method and provides optimal treatment rules for stratified patients.