Ranking and Selection with Covariates: Simulation for Personalized Decision Making

Abstract

A typical decision making problem in practice is to select the best from a finite set of alternatives, whose performances are unknown and can only be learned from sampling. This is referred to as the ranking and selection (R&S) problem in simulation literature. Since the samples may be expensive to acquire, the R&S problem is usually solved by designing a sampling procedure that ensures certain probability of correct selection with minimal samples. Motivated by the emerging popularity of personalized decision making in various areas such as healthcare, e-commerce, and wealth management as customer-specific data grows exponentially, in this talk we introduce a new paradigm called R&S with covariates, where the best alternative is not universal but varies as a function of observable covariates. The goal is then to use sampling to compute a decision rule that specifies the best alternative for each subsequent individual after observing her covariates. We demonstrate the usefulness of our methodology via a case study in personalized medicine for selecting the best cancer treatment regimen. We show that by leveraging disease-related personal information, R&S-C can improve substantially the expected quality-adjusted life years for some groups of patients through providing patient-specific treatment regimen.