Generalized additive model (GAM) with natural cubic splines (NS) has been commonly used as a standard analytical tool in time series studies of health effects of air pollution. Standard model selection procedures used in GAM ignore the uncertainty in model fitting. This may lead to biased estimates of the health effects, in particular lagged effects. Moreover, the degrees of smoothing to adjust for time-varying confounders estimated from data-driven methods were found to give biased estimates. We applied Bayesian model averaging (BMA) approach to account for model uncertainty and proposed also a generalized linear mixed model with natural cubic splines (GLMM + NS) to adjust for time-varying confounders. As the posterior model probability derived from BMA contains a hyperparameter to account for model uncertainty and has potential usefulness in this type of studies, we first conducted a sensitivity analysis with simulation studies for BMA with different calibrated hyperparameters. Our results indicated the importance of selecting the optimum degree of lagging for variables, not based on only maximizing the likelihood, but by considering the possible effects of lagging and biological plausibility. Our proposed model, GLMM + NS, was found to produce more precise estimates of the health effects of current day level of PM10 than the commonly used generalized linear models with natural cubic splines (GLM + NS) in our simulation studies. However, more in depth analyses with special attention to inferential procedures in readily available software are needed to have any definitive conclusion about the performance of our proposed model. An illustrative example is provided using data from 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 and five previous days. Assessing the effect of air pollution on human health is an important public health problem. There are some inconsistencies in the literature as to the magnitude of this effect. The proposed statistical methods are expected to better characterize the true effect of air pollution.
