Sufficient Dimension Reduction for Populations with Structured Heterogeneity

TL;DR

This paper introduces a semiparametric sufficient dimension reduction method to improve risk modeling for heterogeneous populations, enhancing estimation accuracy and interpretability in health system data.

Contribution

The paper presents a novel flexible approach that accounts for heterogeneity and leverages related subpopulations, improving estimation and interpretability in high-dimensional settings.

Findings

Method improves estimation performance in simulations.

Approach is robust to assumption deviations.

Demonstrated predictive power on health system data.

Abstract

A key challenge in building effective regression models for large and diverse populations is accounting for patient heterogeneity. An example of such heterogeneity is in health system risk modeling efforts where different combinations of comorbidities fundamentally alter the relationship between covariates and health outcomes. Accounting for heterogeneity arising combinations of factors can yield more accurate and interpretable regression models. Yet, in the presence of high dimensional covariates, accounting for this type of heterogeneity can exacerbate estimation difficulties even with large sample sizes. To handle these issues, we propose a flexible and interpretable risk modeling approach based on semiparametric sufficient dimension reduction. The approach accounts for patient heterogeneity, borrows strength in estimation across related subpopulations to improve both estimation efficiency and interpretability, and can serve as a useful exploratory tool or as a powerful predictive model. In simulated examples, we show that our approach often improves estimation performance in the presence of heterogeneity and is quite robust to deviations from its key underlying assumptions. We demonstrate our approach in an analysis of hospital admission risk for a large health system and demonstrate its predictive power when tested on further follow-up data.