A parsimonious personalized dose-finding model via dimension reduction

Abstract

Summary Learning an individualized dose rule in personalized medicine is a challenging statistical problem. Existing methods often suffer from the curse of dimensionality, especially when the decision function is estimated nonparametrically. To tackle this problem, we propose a dimension reduction framework that effectively reduces the estimation to an optimization on a lower-dimensional subspace of the covariates. We exploit the fact that the individualized dose rule can be defined in a subspace spanned by a few linear combinations of the covariates to obtain a more parsimonious model. Owing to direct maximization of the value function, the proposed framework does not require the inverse probability of the propensity score under observational studies. This distinguishes our approach from the outcome-weighted learning framework, which also solves decision rules directly. Within the same framework, we further propose a pseudo-direct learning approach that focuses more on estimating the dimensionality-reduced subspace of the treatment outcome. Parameters in both approaches can be estimated efficiently using an orthogonality-constrained optimization algorithm on the Stiefel manifold. Under mild regularity assumptions, results on the asymptotic normality of the proposed estimators are established. We also derive the consistency and convergence rate of the value function under the estimated optimal dose rule. We evaluate the performance of the proposed approaches through extensive simulation studies and analysis of a pharmacogenetic dataset.