Estimating mixture effects and cumulative spatial risk over time simultaneously using a Bayesian index low-rank kriging multiple membership model

The exposome is an ideal in public health research that posits that individuals experience risk for adverse health outcomes from a wide variety of sources over their lifecourse. There have been increases in data collection in the various components of the exposome, but novel statistical methods are needed that capture multiple dimensions of risk at once. We introduce a Bayesian index low-rank kriging (LRK) multiple membership model (MMM) to simultaneously estimate the health effects of one or more groups of exposures, the relative importance of exposure components, and cumulative spatial risk over time using residential histories. The model employs an MMM to consider all residential locations for subjects weighted by duration and LRK to increase computational efficiency. We demonstrate the performance of the Bayesian index LRK-MMM through a simulation study, showing that the model accurately and consistently estimates the health effects of one or several group indices and has high power to identify a region of elevated spatial risk due to unmeasured environmental exposures. Finally, we apply our model to data from a multicenter case-control study of non-Hodgkin lymphoma (NHL), finding a significant positive association between one index of pesticides and risk for NHL in Iowa. Additionally, we find an area of significantly elevated spatial risk for NHL in Los Angeles. In conclusion, our Bayesian index LRK-MMM represents a step forward toward bringing the ideals of the exposome into practice for environmental risk analyzes.