Article

# Bayesian distributed lag models: estimating effects of particulate matter air pollution on daily mortality.

Department of Preventive Medicine, Northwestern University, Feinberg School of Medicine, 680 North Lake Shore Drive, Suite 1102, Chicago, Illinois 60611, USA.

Biometrics (Impact Factor: 1.41). 05/2008; 65(1):282-91. DOI: 10.1111/j.1541-0420.2007.01039.x Source: PubMed

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**ABSTRACT:**Case-crossover designs are widely used to study short-term exposure effects on the risk of acute adverse health events. While the frequentist literature on this topic is vast, there is no Bayesian work in this general area. The contribution of this paper is twofold. First, the paper establishes Bayesian equivalence results that require characterization of the set of priors under which the posterior distributions of the risk ratio parameters based on a case-crossover and time-series analysis are identical. Second, the paper studies inferential issues under case-crossover designs in a Bayesian framework. Traditionally, a conditional logistic regression is used for inference on risk-ratio parameters in case-crossover studies. We consider instead a more general full likelihood-based approach which makes less restrictive assumptions on the risk functions. Formulation of a full likelihood leads to growth in the number of parameters proportional to the sample size. We propose a semi-parametric Bayesian approach using a Dirichlet process prior to handle the random nuisance parameters that appear in a full likelihood formulation. We carry out a simulation study to compare the Bayesian methods based on full and conditional likelihood with the standard frequentist approaches for case-crossover and time-series analysis. The proposed methods are illustrated through the Detroit Asthma Morbidity, Air Quality and Traffic study, which examines the association between acute asthma risk and ambient air pollutant concentrations.Biometrics 11/2013; · 1.41 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**As public awareness of consequences of environmental exposures has grown, estimating the adverse health effects due to simultaneous exposure to multiple pollutants is an important topic to explore. The challenges of evaluating the health impacts of environmental factors in a multipollutant model include, but are not limited to: identification of the most critical components of the pollutant mixture, examination of potential interaction effects, and attribution of health effects to individual pollutants in the presence of multicollinearity. In this paper, we reviewed five methods available in the statistical literature that are potentially helpful for constructing multipollutant models. We conducted a simulation study and presented two data examples to assess the performance of these methods on feature selection, effect estimation and interaction identification using both cross-sectional and time-series designs. We also proposed and evaluated a two-step strategy employing an initial screening by a tree-based method followed by further dimension reduction/variable selection by the aforementioned five approaches at the second step. Among the five methods, least absolute shrinkage and selection operator regression performs well in general for identifying important exposures, but will yield biased estimates and slightly larger model dimension given many correlated candidate exposures and modest sample size. Bayesian model averaging, and supervised principal component analysis are also useful in variable selection when there is a moderately strong exposure-response association. Substantial improvements on reducing model dimension and identifying important variables have been observed for all the five statistical methods using the two-step modeling strategy when the number of candidate variables is large. There is no uniform dominance of one method across all simulation scenarios and all criteria. The performances differ according to the nature of the response variable, the sample size, the number of pollutants involved, and the strength of exposure-response association/interaction. However, the two-step modeling strategy proposed here is potentially applicable under a multipollutant framework with many covariates by taking advantage of both the screening feature of an initial tree-based method and dimension reduction/variable selection property of the subsequent method. The choice of the method should also depend on the goal of the study: risk prediction, effect estimation or screening for important predictors and their interactions.Environmental Health 10/2013; 12(1):85. · 2.71 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In applications where covariates and responses are observed across space and time, a common goal is to quantify the effect of a change in the covariates on the response while adequately accounting for the spatio-temporal structure of the observations. The most common approach for building such a model is to confine the relationship between a covariate and response variable to a single spatio-temporal location. However, oftentimes the relationship between the response and predictors may extend across space and time. In other words, the response may be affected by levels of predictors in spatio-temporal proximity to the response location. Here, a flexible modeling framework is proposed to capture such spatial and temporal lagged effects between a predictor and a response. Specifically, kernel functions are used to weight a spatio-temporal covariate surface in a regression model for the response. The kernels are assumed to be parametric and non-stationary with the data informing the parameter values of the kernel. The methodology is illustrated on simulated data as well as a physical data set of ozone concentrations to be explained by temperature.Spatial statistics. 12/2012; 2:15-32.

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