Abstract
Prevalence and mortality rates of asthma among children have been increasing over the past twenty years, particularly among African American children and children of lower socioeconomic status. In this paper we investigate the link between ambient ozone and pediatric ER visits for asthma in the Atlanta metro area during the summers of 1993, 1994, and 1995. Our statistical model allows for several demographic and meteorologic covariates, spatial and spatio-temporal autocorrelation, and errors in the ozone estimates (which are obtained from a kriging procedure to smooth ozone monitoring station data). As with most recent Bayesian analyses we employ a MCMC computing strategy, highlighting convergence problems we encountered due to the high collinearity of several predictors included in early versions of our model. After providing our choice of prior distributions, we present our results and consider the issues of model selection and adequacy. In particular, we offer graphical displays which suggest the presense of unobserved spatially varying covariates outside the city of Atlanta, and reveal the value of our errors in covariates approach, respectively. Finally, we summarize our findings, discuss limitations of (and possible remedies for) both our data set and analytic approach, and compare frequentist and Bayesian approaches in this case study.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bernardinelli, L. and Montomoli, C. (1992). Empirical Bayes versus fully Bayesian analysis of geographical variation in disease risk. Statistics in Medicine, 11, 983–1007.
Bernardinelli, L., Pascutto, C., Best, N.G. and Gilks, W.R. (1997). Disease map-ping with errors in covariates. Statistics in Medicine, 16, 741–752.
Besag, J., Green, P.J., Higdon, D. and Mengersen, K. (1995). Bayesian computation and stochastic systems (with discussion). Statistical Science, 10, 3–66.
Besag, J., York, J.C., and Mollié, A. (1991). Bayesian image restoration, with two applications in spatial statistics (with discussion). Annals of the Institute of Statistical Mathematics, 43, 1–59.
Carlin, B.P. and Louis, T.A. (1996). Bayes and Empirical Bayes Methods for Data Analysis. London: Chapman and Hall.
Carroll, R.J., Ruppert, D. and Stefanski, L.A. (1995). Measurement Error in Nonlinear Models. London: Chapman and Hall.
Centers for Disease Control (1992). Asthma — United States, 1980–1990. Morbidity and Mortality Weekly Report, 41, 733–735.
Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scat-terplots. Journal of the American Statistical Association, 74, 829–836.
Evans, R., Mullally, D.I., Wilson, R.W., Gergen, P.J., Rosenberg, H.M., Grauman, J.S., Chevarly, F.M., and Feinleib, M. (1987). National trends in the morbidity and mortality of asthma in the US. Chest, 91, 65S–74S.
Gelfand, A.E. and Smith, A.F.M. (1990). Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398–409.
Gelman, A. and Rubin, D.B. (1992). Inference from iterative simulation using multiple sequences (with discussion), Statistical Science, 7, 457–511.
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953). Equations of state calculations by fast computing machines. J. Chemical Physics, 21, 1087–1091.
Thurston, G.D., Ito, K., Kinney, P.L., and Lippmann, M. (1992). A multi-year study of air pollution and respiratory hospital admissions in three New York State metropolitan areas: Results for the 1988 and 1989 summers. J. Expos. Anal. Environ. Epidemiol. 2, 429–450.
Tolbert, P., Mulholland, J., MacIntosh, D., Xu, F., Daniels, D., Devine, O., Carlin, B.P., Butler, A., Wilkinson, J., Russell, A., Nordenberg, D., Frumkin, H., Ryan, B., Manatunga, A., and White, M. (1997). Spatio-temporal analysis of air quality and pediatric asthma emergency room visits. To appear Proc. A.S.A. Section on Statistics and the Environment, Alexandria, VA: American Statistical Association.
Waller, L.A., Carlin, B.P., Xia, H., and Gelfand, A.E. (1997). Hierarchical spatiotemporal mapping of disease rates. J. Amer. Statist. Assoc. 92, 607–617.
Xia, H. and Carlin, B.P. (1998). Spatio-temporal models with errors in covariates: Mapping Ohio lung cancer mortality. To appear Statistics in Medicine.
Xia, H., Carlin, B.P., and Waller, L.A. (1997). Hierarchical models for mapping Ohio lung cancer rates. Environmetrics, 8, 107–120.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this paper
Cite this paper
Carlin, B.P., Xia, H., Devine, O., Tolbert, P., Mulholland, J. (1999). Spatio-Temporal Hierarchical Models for Analyzing Atlanta Pediatric Asthma ER Visit Rates. In: Gatsonis, C., et al. Case Studies in Bayesian Statistics. Lecture Notes in Statistics, vol 140. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1502-8_7
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1502-8_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98640-1
Online ISBN: 978-1-4612-1502-8
eBook Packages: Springer Book Archive