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 latent variable itself, imposing a longitudinal latent variable 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 (IV) 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 IV estimators remain unbiased for a wide range of data generating models and have advantages in terms of mean squared error.

Early Life Exposure in Mexico to ENvironmental Toxicants (ELEMENT) Project

“…Given the complex data structure in the ELEMENT study, including longitudinal follow-up, multiple exposures and high-dimensional data, ELEMENT has served as fertile ground for statistical methods development and innovations in data sharing. To date, methods arising from ELEMENT data include: structural equation models90–93; models to identify timing of vulnerability94 ; methods for gene—environment interactions in the context of multiple correlated exposures95 96; methods to identify complex interactions among multiple exposures,97 metabolomics determinants of metabolic risk,87 methods to characterise growth trajectories20 98 and derive dietary patterns19; and methods for data integration across multiple cohorts 99 100. Current and ongoing work involves the use of novel dimension reduction and simulation techniques to analyse accelerometry and dental imaging data.…”

Addressing unmeasured confounders in cohort studies: Instrumental variable method for a time‐fixed exposure on an outcome trajectory

“…We showed in this work how the two‐stage approach frequently used in IV methodology for cross‐sectional or survival outcomes (Burgess et al., 2017; Tchetgen Tchetgen et al., 2015) could be adapted to study the association between a time‐fixed exposure and the subsequent trajectory of an outcome using the mixed model theory. Previous contributions dealing with repeated data over time had systematically focused on time‐dependent exposures (rather than time‐fixed) and associations with either the level of a time‐fixed outcome (Sánchez et al., 2017) or the level of a repeated outcome at a given time using distributed lag models (Hogan & Lancaster, 2004; O'Malley, 2012). To our knowledge, the use of a mixed model with an IV approach in epidemiology was limited to the analysis of a complex clinical trial to treat noncompliance over time (Bond et al., 2007), the issue of measurement error of time‐dependent exposures with regression calibration (Strand et al., 2014), and the issue of between/within unmeasured confounding in cross‐sectional grouped data (Li et al., 2015).…”

Making Better Numbers through Bioethnographic Collaboration

“…Brisa has come to think of ethnography's big data as useful for understanding causality, which has been elusive in biostatistics, owing to the many assumptions about directionality that statistical models must make in order to make inference possible (Hubbard et al 2019;Kreiger and George 2016). Fortunately, when I met her, Brisa had already been working to develop multivariate statistical methods for measuring variables at spatially relevant scales, and she has come to think that the unruliness of ethnographic big data might help with her goals (Sánchez et al 2017). She now considers knowing "too much" about ELEMENT families and these neighborhoods as a means to build more realistic assumptions into statistical models, enabling more reliable constructs, valid measurements, and big judgment.…”

“…Fortunately, when I met her, Brisa had already been working to develop multivariate statistical methods for measuring variables at spatially relevant scales, and she has come to think that the unruliness of ethnographic big data might help with her goals (Sánchez et al. 2017). She now considers knowing “too much” about ELEMENT families and these neighborhoods as a means to build more realistic assumptions into statistical models, enabling more reliable constructs, valid measurements, and big judgment.…”