Modeling variation in mixture effects over space with a Bayesian spatially varying mixture model.

Mixture analysis is an emerging statistical tool in epidemiological research that seeks to estimate the health effects associated with mixtures of several exposures. This approach acknowledges that individuals experience many simultaneous exposures and it can estimate the relative importance of components in the mixture. Health effects due to mixtures may vary over space driven by to political, demographic, environmental, or other differences. In such cases, estimating a global mixture effect without accounting for spatial variation would induce bias in effect estimates and potentially lower statistical power. To date, no methods have been developed to estimate spatially varying chemical mixture effects. We developed a Bayesian spatially varying mixture model that estimates spatially varying mixture effects and the importance weights of components in the mixture, while adjusting for covariates. We demonstrate the efficacy of the model through a simulation study that varies the number of mixtures (one and two) and spatial pattern (global, one-dimensional, radial) and magnitude of mixture effects, showing that the model is able to accurately reproduce the spatial pattern of mixture effects across a diverse set of scenarios. Finally, we apply our model to a multi-center case-control study of non-Hodgkin lymphoma (NHL) in Detroit, Iowa, Los Angeles, and Seattle. We identify significant spatially varying positive and inverse associations with NHL for two mixtures of pesticides in Iowa and do not find strong spatial effects at the other three centers. In conclusion, the Bayesian spatially varying mixture model represents a novel method for modeling spatial variation in mixture effects.