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 assumed to be represented by multiple exposures, where membership of the observed exposures to latent groups is unknown. Our model assumes that one measured exposure 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 Development 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.