A Parsimonious Personalized Dose Finding Model via Dimension Reduction

TL;DR

This paper introduces a dimension reduction framework for personalized dose finding that simplifies the estimation process, avoids inverse probability weighting, and improves efficiency in high-dimensional settings.

Contribution

It proposes a novel parsimonious dose finding model that reduces dimensionality, directly maximizes the value function, and employs an orthogonality constrained optimization algorithm.

Findings

The proposed methods outperform existing approaches in simulations.

The framework effectively reduces the covariate space in dose decision models.

Application to a warfarin dataset demonstrates practical utility.

Abstract

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 a lower-dimensional subspace of the covariates. We exploit that the individualized dose rule can be defined in a subspace spanned by a few linear combinations of the covariates, leading to a more parsimonious model. The proposed framework does not require the inverse probability of the propensity score under observational studies due to a direct maximization of the value function. This distinguishes us from the outcome weighted learning framework, which also solves decision rules directly. Under 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, the results on the asymptotic normality of the proposed estimators are established, respectively. We also derive the consistency and convergence rate for the value function under the estimated optimal dose rule. We evaluate the performance of the proposed approaches through extensive simulation studies and a warfarin pharmacogenetic dataset.