An estimating equations approach to fitting latent exposure models with longitudinal health outcomes

TL;DR

This paper introduces a robust estimating equations method for fitting latent exposure models with longitudinal health data, addressing variance misspecification issues and improving estimation stability in environmental health studies.

Contribution

It develops a novel estimating equations approach that is robust to variance misspecification, generalizes existing methods, and compares efficiency of different weighting schemes.

Findings

Method performs nearly as well as maximum likelihood under correct model specification.

Two weighting schemes are proposed and their efficiencies are compared.

Applied to in-utero lead exposure data, demonstrating practical utility.

Abstract

The analysis of data arising from environmental health studies which collect a large number of measures of exposure can benefit from using latent variable models to summarize exposure information. However, difficulties with estimation of model parameters may arise since existing fitting procedures for linear latent variable models require correctly specified residual variance structures for unbiased estimation of regression parameters quantifying the association between (latent) exposure and health outcomes. We propose an estimating equations approach for latent exposure models with longitudinal health outcomes which is robust to misspecification of the outcome variance. We show that compared to maximum likelihood, the loss of efficiency of the proposed method is relatively small when the model is correctly specified. The proposed equations formalize the ad-hoc regression on factor scores procedure, and generalize regression calibration. We propose two weighting schemes for the equations, and compare their efficiency. We apply this method to a study of the effects of in-utero lead exposure on child development.