Estimation of an Exposure Effect on Outcome Rate of Change in Observational Study Settings

Abstract

Mixed models for longitudinal analysis have several well-established benefits, including gaining information from unbalanced data and depending on less restrictive assumptions about missing data than other methods such as semi-parametric methods (e.g. generalized estimating equations). While there are multiple longitudinal analysis methods to estimate the effect of exposure on an outcome's rate of change, in many applications linear mixed models with a model for the baseline outcome and longitudinal change may provide the best rate of change estimates. These models also give two distinct exposure effect estimates: the cross-sectional effect at baseline and the longitudinal effect of interest. We conduct simulations to evaluate characteristics of longitudinal exposure effect estimates from the modeled baseline mixed model (i.e. mixed model with separate cross-sectional and longitudinal effects) and competing methods of rate of change analysis. We also compare the longitudinal and cross-sectional effect estimates from the modeled baseline mixed model. We apply our insights to an analysis of how ambient air pollution affects the progression of a measure of coronary heart disease in a subset of the MESA Air study. The modeled baseline model avoids bias caused by controlling for the outcome's measured baseline as a covariate when the exposure affects the baseline outcome and the outcome is measured with error. The modeled baseline estimates are also more precise in comparison to models that use scaled change since baseline as the outcome variable. In the modeled baseline model, we find the cross-sectional exposure effect estimate is primarily influenced by characteristics of the baseline measurements, while the longitudinal estimate is influenced by characteristics of both the baseline and temporal changes in the follow-up data. Exposure qualities and model parameterization may induce a correlation in these two exposure estimates. We recommend deemphasizing the cross-sectional estimate and focusing on the longitudinal estimate as the cross-sectional effect estimate is generally more dependent on characteristics of the study design and are expected to be more prone to confounding. Our work provides strong support for the use of the modeled baseline mixed model in environmental epidemiology and more broadly in many non-randomized longitudinal study contexts.