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: 1.52). 05/2008; 65(1):282-91. DOI: 10.1111/j.1541-0420.2007.01039.x
Source: PubMed

ABSTRACT A distributed lag model (DLagM) 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. DLagMs 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 DLagMs include unconstrained, polynomial, and penalized spline DLagMs. 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 suboptimal estimates. In this article, we propose a Bayesian DLagM (BDLagM) 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. We apply our BDLagM to its motivating data from the National Morbidity, Mortality, and Air Pollution Study to estimate the short-term health effects of particulate matter air pollution on mortality from 1987 to 2000 for Chicago, Illinois. In a simulation study, we compare our Bayesian approach with alternative methods that use unconstrained, polynomial, and penalized spline DLagMs. We also illustrate the connection between BDLagMs and penalized spline DLagMs. Software for fitting BDLagM models and the data used in this article are available online.

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    • "In this setting, interest lies in specifying plausible shapes for DL curves and in particular the " mortality displacement " effect, a phenomenon characterized by negative coefficients in the tail of the estimated lag structure. Zanobetti et al. (2000) propose a generalized model taking a penalized spline approach to modeling DL curves while Welty et al. (2009) discuss a Bayesian approach with penalties on parameters determined by carefully chosen priors. Others (Muggeo et al., 2008; Gasparrini et al., 2010) allow lag coefficients to change with temperature in addition to lying on a smooth curve, so that a surface of lag coefficients results. "
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    ABSTRACT: Summary The distributed lag model (DLM), used most prominently in air pollution studies, finds application wherever the effect of a covariate is delayed and distributed through time. We specify modified formulations of DLMs to provide computationally attractive, flexible varying-coefficient models that are applicable in any setting in which lagged covariates are regressed on a time-dependent response. We investigate the application of such models to rainfall and river flow and in particular their role in understanding the impact of hidden variables at work in river systems. We apply two models to data from a Scottish mountain river, and we fit to some simulated data to check the efficacy of our model approach. During heavy rainfall conditions, changes in the influence of rainfall on flow arise through a complex interaction between antecedent ground wetness and a time-delay in rainfall. The models identify subtle changes in responsiveness to rainfall, particularly in the location of peak influence in the lag structure.
    Biometrics 02/2013; DOI:10.1111/biom.12008 · 1.52 Impact Factor
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    • "This formulation does not impose any parametric shape on the coefficients, but constrains the coefficients at longer lags to approach zero. Common parametric shapes for the lagged effects of air pollution are polynomials or penalised splines, but as shown by Welty et al. (2009) these methods are prone to over-smooth and ignore the prior knowledge that pollution effects are likely to become smaller with increasing lag. The total effect of air pollution over all L days is L l=0 γ l . "
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    ABSTRACT: The health effects of environmental hazards are often examined using time series of the association between a daily response variable (e.g., death) and a daily level of exposure (e.g., temperature). Exposures are usually the average from a network of stations. This gives each station equal importance, and negates the opportunity for some stations to be better measures of exposure. We used a Bayesian hierarchical model that weighted stations using random variables between zero and one. We compared the weighted estimates to the standard model using data on health outcomes (deaths and hospital admissions) and exposures (air pollution and temperature) in Brisbane, Australia. The improvements in model fit were relatively small, and the estimated health effects of pollution were similar using either the standard or weighted estimates. Spatial weighted exposures would be probably more worthwhile when there is either greater spatial detail in the health outcome, or a greater spatial variation in exposure.
    09/2012; 3(3):225-34. DOI:10.1016/j.sste.2012.02.010
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    • "Following Welty et al. (2009) and Peng et al. (2009) "
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    ABSTRACT: As climate continues to change, scientists are left to analyze the effects these changes will have on the public. In this article, a flexible class of distributed lag models are used to analyze the effects of heat on mortality in four major metropolitan areas in the U.S. (Chicago, Dallas, Los Angeles, and New York). Specifically, the proposed methodology uses Gaussian processes as a prior model for the distributed lag function. Gaussian processes are adequately flexible to capture a wide variety of distributed lag functions while ensuring smoothness properties of process realizations. Additionally, the proposed framework allows for probabilistic inference of the maximum lag. Applying the proposed methodology revealed that mortality displacement (or, harvesting) was present for most age groups and cities analyzed suggesting that heat advanced death in some individuals. Additionally, the estimated shape of the DL functions gave evidence that prolonged heat exposure and highly variable temperatures pose a threat to public health.
    Journal of Agricultural Biological and Environmental Statistics 09/2012; 17(3):313-331. DOI:10.1007/s13253-012-0097-7 · 0.78 Impact Factor
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