Bayesian Profile Regression to Deal With Multiple Highly Correlated Exposures and a Censored Survival Outcome. First Application in Ionizing Radiation Epidemiology

Abstract

As multifactorial and chronic diseases, cancers are among these pathologies for which the exposome concept is essential to gain more insight into the associated etiology and, ultimately, lead to better primary prevention strategies for public health. Indeed, cancers result from the combined influence of many genetic, environmental and behavioral stressors that may occur simultaneously and interact. It is thus important to properly account for multifactorial exposure patterns when estimating specific cancer risks at individual or population level. Nevertheless, the risk factors, especially environmental, are still too often considered in isolation in epidemiological studies. Moreover, major statistical difficulties occur when exposures to several factors are highly correlated due, for instance, to common sources shared by several pollutants. Suitable statistical methods must then be used to deal with these multicollinearity issues. In this work, we focused on the specific problem of estimating a disease risk from highly correlated environmental exposure covariates and a censored survival outcome. We extended Bayesian profile regression mixture (PRM) models to this context by assuming an instantaneous excess hazard ratio disease sub-model. The proposed hierarchical model incorporates an underlying truncated Dirichlet process mixture as an attribution sub-model. A specific adaptive Metropolis-Within-Gibbs algorithm—including label switching moves—was implemented to infer the model. This allows simultaneously clustering individuals with similar risks and similar exposure characteristics and estimating the associated risk for each group. Our Bayesian PRM model was applied to the estimation of the risk of death by lung cancer in a cohort of French uranium miners who were chronically and occupationally exposed to multiple and correlated sources of ionizing radiation. Several groups of uranium miners with high risk and low risk of death by lung cancer were identified and characterized by specific exposure profiles. Interestingly, our case study illustrates a limit of MCMC algorithms to fit full Bayesian PRM models even if the updating schemes for the cluster labels incorporate label-switching moves. Then, although this paper shows that Bayesian PRM models are promising tools for exposome research, it also opens new avenues for methodological research in this class of probabilistic models.