Valid and Efficient Two-Stage Latent Subgroup Analysis with Observational Data

TL;DR

This paper develops a robust, efficient two-stage method for latent subgroup analysis in observational data, addressing bias from misclassification and high-dimensional confounders, with proven consistency and practical validation.

Contribution

It introduces a spectral method-based two-stage approach that achieves valid subgroup analysis despite misclassification, high-dimensional confounders, and noninformative items.

Findings

Method achieves consistent estimation of subgroup effects.

Approach is computationally efficient and robust.

Validated through simulations and real educational data.

Abstract

Subgroup analysis evaluates treatment effects across multiple sub-populations. When subgroups are defined by latent memberships inferred from imperfect measurements, the analysis typically involves two inter-connected models, a latent class model and a subgroup outcome model. The classical one-stage framework, which models the joint distribution of the two models, may be infeasible with observational data containing many confounders. The two-stage framework, which first estimates the latent class model and then performs subgroup analysis using estimated latent memberships, can accommodate potential confounders but may suffer from bias issues due to misclassification of latent subgroup memberships. This paper focuses on latent subgroups inferred from binary item responses and addresses when and how a valid two-stage latent subgroup analysis can be made with observational data. We investigate the maximum misclassification rate that a valid two-stage framework can tolerate. Introducing a spectral method perspective, we propose a two-stage approach to achieve the desired misclassification rate with the blessing of many item responses. Our method accommodates high-dimensional confounders, is computationally efficient and robust to noninformative items. In observational studies, our methods lead to consistent estimation and valid inference on latent subgroup effects. We demonstrate its merit through simulation studies and an application to educational assessment data.