Bootstrap-after-Bootstrap Model Averaging for Reducing Model Uncertainty in Model Selection for Air Pollution Mortality Studies

BACKGROUND: Concerns have been raised about findings of associations between particulate matter (PM) air pollution and mortality that have been based on a single “best” model arising from a model selection procedure, because such a strategy may ignore model uncertainty inherently involved in searching through a set of candidate models to find the best model. Model averaging has been proposed as a method of allowing for model uncertainty in this context. OBJECTIVES: To propose an extension (double BOOT) to a previously described bootstrap model-averaging procedure (BOOT) for use in time series studies of the association between PM and mortality. We compared double BOOT and BOOT with Bayesian model averaging (BMA) and a standard method of model selection [standard Akaike’s information criterion (AIC)]. METHOD: Actual time series data from the United States are used to conduct a simulation study to compare and contrast the performance of double BOOT, BOOT, BMA, and standard AIC. RESULTS: Double BOOT produced estimates of the effect of PM on mortality that have had smaller root mean squared error than did those produced by BOOT, BMA, and standard AIC. This performance boost resulted from estimates produced by double BOOT having smaller variance than those produced by BOOTand BMA. CONCLUSIONS: Double BOOT is a viable alternative to BOOT and BMA for producing estimates of the mortality effect of PM.