Bootstrap model averaging in time series studies of particulate matter air pollution and mortality

Abstract

The consensus from time series studies that have investigated the mortality effects of particulate matter air pollution (PM) is that increases in PM are associated with increases in daily mortality. However, recently concerns have been raised that the observed positive association between PM and mortality may be an artefact of model selection due to multiple hypothesis testing. This problem arises when a number of models are investigated, but only the ''best'' model is reported and all subsequent inference is based on this model, ignoring the model selection process. In this paper, we introduce the use of the bootstrap as a means of addressing the problems of model selection in PM mortality time series studies. Using the bootstrap to perform inference about the effect of PM on mortality is a process based on a set of models rather than on a single model. It is shown that using the bootstrap to overcome the problems of model selection is competitive with the existing methodology of Bayesian model averaging.

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

“…In the paragraphs that follow, we describe Akaike’s information criterion (AIC; Akaike 1973) and outline the bootstrap (BOOT) method used by Martin and Roberts (2006) and our extension that refines this method.…”

“…Based on our earlier work, the stationary bootstrap is implemented using a mean block length of size 10 (Martin and Roberts 2006). Lahiri (2003) provides additional information on the use of resampling methods for dependent data.…”

“…Model averaging in both Bayesian and frequentist forms has been proposed as a means of allowing for model uncertainty in time series studies of PM and mortality (Clyde 2000; Koop and Tole 2004, 2006; Martin and Roberts 2006). Model-averaging procedures assign probabilities or weights to each candidate model that reflect the degree to which the model is supported by the data.…”

“…Clyde (2000) and Koop and Tole (2004, 2006) implemented Bayesian model-averaging (BMA) techniques to estimate the association between air pollution and mortality. Martin and Roberts (2006) implemented model averaging using a bootstrap-based procedure and showed that it is competitive with BMA in that context. Previous investigations have also used the bootstrap in the context of time series studies of air pollution, including investigations of the effect of concurvity in generalized additive models (Figueiras et al 2005; Ramsay et al 2003).…”

“…In this paper, we discuss a double bootstrap model-averaging (double BOOT) approach that extends and improves the bootstrap model-averaging (BOOT) procedure that was implemented in Martin and Roberts (2006).…”