Estimating cumulative spatial risk over time with low-rank kriging multiple membership models

Many health outcomes result from accumulated exposures to one or more environmental factors. Accordingly, spatial risk studies have begun to consider multiple residential locations of participants, acknowledging that participants move and thus are exposed to environmental factors in several places. However, novel methods are needed to estimate cumulative spatial risk for disease while accounting for other risk factors. To this end, we propose a Bayesian model (LRK-MMM) that embeds a multiple membership model (MMM) into a low-rank kriging (LRK) model in order to estimate cumulative spatial risk at the point level while allowing for multiple residential locations per subject. The LRK approach offers a more computationally efficient means to analyze spatial risk in case-control study data at the point level compared with a Bayesian generalized additive model, and as increased precision in spatial risk estimates by analyzing point locations instead of administrative areas. Through a simulation study, we demonstrate the efficacy of the model and its improvement upon an existing multiple membership model that uses area-level spatial random effects to estimate risk. The results show that our proposed method provides greater spatial sensitivity (improvements ranging from 0.12 to 0.54) and power (improvements ranging from 0.02 to 0.94) to detect regions of elevated risk for disease across a range of exposure scenarios. Finally, we apply our model to case-control data from the New England bladder cancer study to estimate cumulative spatial risk while adjusting for many covariates.