title: Estimators for longitudinal latent exposure models: examining measurement model assumptions.
abstract: Latent variable (LV) models are increasingly being used in environmental epidemiology as a way to summarize multiple environmental exposures and thus minimize statistical concerns that arise in multiple regression. LV models may be especially useful when multivariate exposures are collected repeatedly over time. LV models can accommodate a variety of assumptions but, at the same time, present the user with many choices for model specification particularly in the case of exposure data collected repeatedly over time. For instance, the user could assume conditional independence of observed exposure biomarkers given the latent exposure and, in the case of longitudinal latent exposure variables, time invariance of the measurement model. Choosing which assumptions to relax is not always straightforward. We were motivated by a study of prenatal lead exposure and mental development, where assumptions of the measurement model for the time-changing longitudinal exposure have appreciable impact on (maximum-likelihood) inferences about the health effects of lead exposure. Although we were not particularly interested in characterizing the change of the LV itself, imposing a longitudinal LV structure on the repeated multivariate exposure measures could result in high efficiency gains for the exposure-disease association. We examine the biases of maximum likelihood estimators when assumptions about the measurement model for the longitudinal latent exposure variable are violated. We adapt existing instrumental variable estimators to the case of longitudinal exposures and propose them as an alternative to estimate the health effects of a time-changing latent predictor. We show that instrumental variable estimators remain unbiased for a wide range of data generating models and have advantages in terms of mean squared error. Copyright © 2017 John Wiley & Sons, Ltd.
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, 48109, MI, U.S.A.
authors.forename: Brisa N
authors.identifier: 0000-0002-4824-7200
authors.initials: BN
authors.lastname: Sánchez
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, 48109, MI, U.S.A.
authors.forename: Sehee
authors.initials: S
authors.lastname: Kim
authors.affiliation: Center for Clinical Epidemiology and Biostatistics, University of Pennsylvania School of Medicine, Philadelphia, PA, U.S.A.
authors.forename: Mary D
authors.initials: MD
authors.lastname: Sammel
mesh_terms: D015415:Biomarkers / Q000032:analysis; D002648:Child; D002657:Child Development / Q000187:drug effects; D004781:Environmental Exposure / Q000009:adverse effects / Q000706:statistics & numerical data*; D005260:Female; D006801:Humans; D007855:Lead Poisoning / Q000150:complications; D016013:Likelihood Functions; D008137:Longitudinal Studies; D015233:Models, Statistical; D011247:Pregnancy; D011297:Prenatal Exposure Delayed Effects / Q000139:chemically induced / Q000453:epidemiology
chemical_list: D015415:Biomarkers
keywords: estimating equations; instrumental variables; measurement model invariance