Parallel Bayesian MCMC Imputation for Multiple Distributed Lag Models: A Case Study in Environmental Epidemiology

Time series data are frequently used to study the short-term effects of particulate matter air pollution on mortality. Distributed lag models, are regression models having daily mortality count as outcome and air pollution levels on the same day and on several previous days as exposure variables. Distributed lag models allow to estimate the cumulative effect of air pollution exposure over few days in the past and therefore provide a more realistic measure of the health effects of air pollution than single lag models. However, estimation of the cumulative effect in distributed lag models can be difficult because at many locations air pollution levels are collected at a cruder time scale than the daily mortality counts. This chapter presents a hierarchical model for estimating the distributed lag total effect of air pollution on daily mortality when the pollutant data has patterned missingness. We pay particular attention to the implementation of the MCMC sampler. A novel parallel computing approach is introduced that exploits conditional independence relationships in the full conditionals used for sampling. Proportional decreases in run times over the nonparallelized version of the sample near the inverse of the number of compute nodes available are observed.