Modeling the effects of multiple exposures with unknown group memberships: a Bayesian latent variable approach

We propose a Bayesian latent variable model to allow estimation of the covariate- adjusted relationships between an outcome and a small number of latent exposure variables, using data from multiple observed exposures. Each latent variable is as- sumed to be represented by multiple exposures, where membership of the observed exposures to latent groups is unknown. Our model assumes that one measured ex- posure variable can be considered as a sentinel marker for each latent variable, while membership of the other measured exposures is estimated using MCMC sampling based on a classical measurement error model framework. We illustrate our model using data on multiple cytokines and birth weight from the Seychelles Child Devel- opment Study, and evaluate the performance of our model in a simulation study. Classification of cytokines into Th1 and Th2 cytokine classes in the Seychelles study revealed some differences from standard Th1/Th2 classifications. In simulations, our model correctly classified measured exposures into latent groups, and estimated model parameters with little bias and with coverage that was similar to the oracle model.