Welcome to MAA-Wisconsin Spring 2010 Meeting!
Leah Welty (Northwestern University Medical School)
Bayesian Distributed Lag Models: Estimating the Effects of Particulate Matter Air Pollution on Daily Mortality
A distributed lag model (DLM) is a regression model that includes lagged exposure variables as covariates; its corresponding distributed lag (DL) function describes the relationship between the lag and the coefficient of the lagged exposure variable. DLMs have recently been used in environmental epidemiology for quantifying the cumulative effects of weather and air pollution on mortality and morbidity. Standard methods for formulating DLMs include unconstrained, polynomial, and penalized spline DLMs. These methods may fail to take full advantage of prior information about the shape of the DL function for environmental exposures, or for any other exposure with effects that are believed to smoothly approach zero as lag increases, and are therefore at risk of producing sub-optimal estimates.
We propose a Bayesian DLM (BDLM) that incorporates prior knowledge about the shape of the DL function and also allows the degree of smoothness of the DL function to be estimated from the data. In a simulation study, we compare our Bayesian approach with alternative methods that use unconstrained, polynomial and penalized spline DLMs. We also show that BDLMs encompass penalized spline DLMs: under certain assumptions, imposing a prior on the DL coefficients is analogous to smoothing the DL coefficients with a penalty specified by the prior. We apply our BDLM to data from the National Morbidity,Mortality, and Air Pollution Study (NMMAPS) to estimate the short term health effects of particulate matter air pollution on mortality from 1987--2000 for Chicago, Illinois.
Dr. Welty earned a BS in
mathematics from the
Dr. Welty's research interests include applications of statistics to psycho-social, medical and environmental sciences, and in particular the formulation of statistical models for outcomes correlated over time and space.