A Bayesian Partial Membership Model for Multiple Exposures with Uncertain Group Memberships

We present a Bayesian partial membership model that estimates the associations between an outcome, a small number of latent variables, and multiple observed exposures where the number of latent variables is specified a priori. We assign one observed exposure as the sentinel marker for each latent variable. The model allows non-sentinel exposures to have complete membership in one latent group, or partial membership across two or more latent groups. MCMC sampling is used to determine latent group partial memberships for the non-sentinel exposures, and estimate all model parameters. We compare the performance of our model to competing approaches in a simulation study and apply our model to inflammatory marker data measured in a large mother-child cohort of the Seychelles Child Development Study (SCDS). In simulations, our model estimated model parameters with little bias, adequate coverage, and tighter credible intervals compared to competing approaches. Under our partial membership model with two latent groups, SCDS inflammatory marker classifications generally aligned with the scientific literature. Incorporating additional SCDS inflammatory markers and more latent groups produced similar groupings of markers that also aligned with the literature. Associations between covariates and birth weight were similar across latent variable models and were consistent with earlier work in this SCDS cohort. Supplementary materials accompanying this paper appear online.

Automated summary

We propose a Bayesian partial membership model for estimating associations between outcome, latent variables, and observed exposures. The model allows for complete or partial membership of non-sentinel exposures across latent groups. Using MCMC sampling, we estimate partial memberships and model parameters. The model performs well in simulations and aligns with scientific literature in the analysis of inflammatory marker data.