Bayesian model averaging approach in health effects studies: Sensitivity analyses using PM₁₀ and cardiopulmonary hospital admissions in Allegheny County, Pennsylvania and simulated data

Generalized Additive Models (GAMs) with natural cubic splines (NS) as smoothing functions have become a standard analytical tool in time series studies of health effects of air pollution. However, standard model selection procedures ignore the model uncertainty that may lead to biased estimates, in particular those of the lagged effects. We addressed this issue by Bayesian model averaging (BMA) approach which accounts for model uncertainty by combining information from all possible models where GAMs and NS were used. Firstly, we conducted a sensitivity analysis with simulation studies for Bayesian model averaging with different calibrated hyperparameters contained in the posterior model probabilities. Our results indicated the importance of selecting the optimum degree of lagging for variables, based not only on maximizing the likelihood, but also by considering the possible effects of concurvity, consistency of degree of lagging, and biological plausibility. This was illustrated by analyses of the Allegheny County Air Pollution Study (ACAPS) where the quantity of interest was the relative risk of cardiopulmonary hospital admissions for a 20 μg/m³ increase in PM₁₀ values for the current day. Results showed that the posterior means of the relative risk and 95% posterior probability intervals were close to each other under different choices of the prior distributions. Simulation results were consistent with these findings. It was also found that using lag variables in the model when there is only same day effect, may underestimate the relative risk attributed to the same day effect.