Ranking and Selection with Covariates for Personalized Decision Making
This work addresses personalized decision-making in fields like healthcare by enabling selection of optimal alternatives based on individual covariates, though it is incremental as it builds on existing ranking and selection methods.
The paper tackles the problem of ranking and selection with covariates (R&S-C) for personalized decision-making, where the best alternative varies based on observable covariates, and develops two-stage procedures with statistical guarantees, demonstrating in a case study that it can substantially improve patients' expected quality-adjusted life years by providing patient-specific treatment regimens.
We consider a problem of ranking and selection via simulation in the context of personalized decision making, where the best alternative is not universal but varies as a function of some observable covariates. The goal of ranking and selection with covariates (R&S-C) is to use simulation samples to obtain a selection policy that specifies the best alternative with certain statistical guarantee for subsequent individuals upon observing their covariates. A linear model is proposed to capture the relationship between the mean performance of an alternative and the covariates. Under the indifference-zone formulation, we develop two-stage procedures for both homoscedastic and heteroscedastic simulation errors, respectively, and prove their statistical validity in terms of average probability of correct selection. We also generalize the well-known slippage configuration, and prove that the generalized slippage configuration is the least favorable configuration for our procedures. Extensive numerical experiments are conducted to investigate the performance of the proposed procedures, the experimental design issue, and the robustness to the linearity assumption. Finally, we demonstrate the usefulness of R&S-C via a case study of selecting the best treatment regimen in the prevention of esophageal cancer. We find that by leveraging disease-related personal information, R&S-C can substantially improve patients' expected quality-adjusted life years by providing patient-specific treatment regimen.