BCH-GEE Approach to Examine the Association Between Time-Varying Food Environment Classes and Multi-Level Health Outcomes.

While the creation of latent classes and how they transition over time is useful in describing heterogeneity in a population, examining their relation to other external variables, such as distal outcomes, is often of main interest. There are multiple methods of determining the association between latent classes and distal outcomes. Using modal class assignment as a predictor of the distal outcome is the simplest approach, but these associations suffer from bias due to classification error when assigning latent classes. Other common methods, including the biased-adjusted 3-step maximum likelihood or BCH approaches, remove the bias but struggle computationally when estimating associations using complex data structures, such as a larger number of time points or multilevel distal outcomes. We propose a biased-adjusted 3-step BCH-GEE approach that can be used for a multilevel repeated cross-sectional design. In this approach, latent transition analysis is used to model time-varying latent classes, followed by ascertainment of classification errors, and weighted GEE to estimate the association between the latent classes and the multilevel distal outcomes. Simulation studies show that the proposed method corrects the bias of the effect estimates that otherwise occur due to the classification error when assigning latent classes. We use this method to examine the association between time-varying school neighborhood unhealthy food environment classes in California and measures of students' body mass index in 5th grade over an 8 year time-frame. Results show that children attending schools in neighborhood environments with a higher density of unhealthy food outlets have higher body mass index.