Abstract
We develop a new Bayesian two-stage space-time mixture model to investigate the effects of air pollution on asthma. The two-stage mixture model proposed allows for the identification of temporal latent structure as well as the estimation of the effects of covariates on health outcomes. In the paper, we also consider spatial misalignment of exposure and health data. A simulation study is conducted to assess the performance of the 2-stage mixture model. We apply our statistical framework to a county-level ambulatory care asthma data set in the US state of Georgia for the years 1999–2008.
Similar content being viewed by others
References
Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2004), Hierarchical Modeling and Analysis for Spatial Data, Boca Raton: Chapman & Hall/CRC.
Berkson, J. (1950), “Are There Two Regressions?” Journal of the American Statistical Association, 45, 164–180.
Bernardinelli, L., Clayton, D. G., Pascutto, C., Montomoli, C., Ghislandi, M., and Songini, M. (1995), “Bayesian Analysis of Space-Time Variation in Disease Risk,” Statistics in Medicine, 14, 2433–2443.
Besag, J., York, J., and Mollie, A. (1991), “Bayesian Image Restoration, With Two Applications in Spatial Statistics (with discussion),” Annals of the Institute of Statistical Mathematics, 43, 1–59.
Castro, M., Schechtman, B. K., Halstead, J., and Bloomberg, G. (2001), “Risk Factors for Asthma Morbidity and Mortality in a Large Metropolitan City,” Journal of Asthma, 38, 625–635.
Celeux, G., Forbes, F., Robert, C., and Titterington, M. (2006), “Deviance Information Criteria for Missing Data Models,” Bayesian Analysis, 1, 651–674.
Centers for Disease Control and Prevention (2008), National Health Interview Survey Raw Data, 2008, Atlanta: U.S. Department of Health and Human Services, CDC.
— (2011), “Vital Signs, May 2011: Asthma in the US,” Atlanta, GA: CDC. Available at http://www.cdc.gov/vitalsigns/pdf/2011-05-vitalsigns.pdf.
Choi, J., Fuentes, M., and Reich, B. J. (2009), “Spatial-Temporal Association Between Fine Particulate Matter and Daily Mortality,” Computational Statistics & Data Analysis, 53, 2989–3000.
Choi, J., Lawson, A. B., Cai, B., and Hossain, M. M. (2011), “Evaluation of Bayesian Spatial-Temporal Latent Models in Small Area Health Data,” Environmetrics, 22, 1008–1022.
Clayton, D., Bernardinelli, L., and Montomoli, C. (1993), “Spatial Correlation in Ecological Analysis,” International Journal of Epidemiology, 22, 1193–1202.
Congdon, P. (2005), Bayesian Models for Categorical Data, New York: Wiley.
Dey, D., Chen, M. H., and Chang, H. (1997), “Bayesian Approach for Nonlinear Random Effects Models,” Biometrics, 53, 1239–1252.
Dockery, D. W., and Pope, C. A. III (1994), “Acute Respiratory Effects of Particulate Air Pollution,” Annual Review of Public Health, 15, 107–132.
Eisner, D. M., Katz, P. P., Yelin, H. E., Shiboski, C. S., and Blanc, D. P. (2001), “Risk Factors for Hospitalization Among Adults With Asthma: The Influence of Sociodemographic Factors and Asthma Severity,” Respiratory Research, 2, 53–60.
Ellison-Loschmann, L., Sunyer, J., Plana, E., Pearce, N., Zock, J. P., Jarvis, D., Janson, C., Anto, J. M., and Kogevinas, M. (2007), “Socioeconomic Status, Asthma and Chronic Bronchitis in a Large Community-Based Study,” European Respiratory Journal, 29, 897–905.
Friedman, M. S., Powell, K. E., Hutwagner, L., Graham, L. M., and Teague, W. G. (2001), “Impact of Changes in Transportation and Commuting Behaviors During the 1996 Summer Olympic Games in Atlanta on Air Quality and Childhood Asthma,” Journal of the American Medical Association, 285, 897–905.
Fuentes, M., and Raftery, A. E. (2005), “Model Evaluation and Spatial Interpolation by Bayesian Combination of Observations With Outputs From Numerical Models,” Biometrics, 61, 36–45.
Fuentes, M., Song, H., Ghosh, S. K., Holland, D. M., and Davis, J. M. (2006), “Spatial Association Between Speciated Fine Particles and Mortality,” Biometrics, 62, 855–863.
Gelfand, A. E., and Vounatsou, P. (2002), “Proper Multivariate Conditional Autoregressive Models for Spatial Data Analysis,” Biostatistics, 4, 11–25.
Gelman, A. (2004), “Parameterization and Bayesian Modelling,” Journal of the American Statistical Association, 99, 537–545.
— (2006), “Prior Distributions for Variance Parameters in Hierarchical Models,” Bayesian Analysis, 1, 515–533.
Geweke, J. (1992), “Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments,” in Bayesian Statistics 4, eds. J. M. Bernado, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford: Oxford University Press.
Gotway, C. A., and Young, L. J. (2002), “Combining Incompatible Spatial Data,” Journal of the American Statistical Association, 97, 632–648.
Hodges, J., and Reich, B. (2010), “Adding Spatially-Correlated Errors Can Mess up the Fixed Effect You Love,” American Statistician, 64, 325–334.
Ibrahim, J., Chen, M. H., and Sinha, D. (2001), Bayesian Survival Analysis, New York: Springer.
Jasra, A., Holmes, C. C., and Stephens, D. A. (2005), “Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling,” Statistical Science, 20, 50–67.
Knorr-Held, L. (2000), “Bayesian Modelling of Inseparable Space-Time Variation in Disease Risk,” Statistics in Medicine, 19, 2555–2567.
Knorr-Held, L., and Besag, J. (1998), “Modelling Risk From a Disease in Time and Space,” Statistics in Medicine, 17, 2045–2060.
Lawson, A. B., Song, H. R., Cai, B., Hossain, M. M., and Huang, K. (2010), “Space-Time Latent Component Modeling of Geo-referenced Health Data,” Statistics in Medicine, 29, 2012–2027.
Lin, M., Chen, Y., Burnett, R. T., Villeneuve, P. J., and Krewski, D. (2002), “The Influence of Ambient Coarse Particulate Matter on Asthma Hospitalization in Children: Case-Crossover and Time-Series Analyses,” Environmental Health Perspectives, 110, 575–581.
Lin, S., Liu, X., Le, L. H., and Hwang, S. A. (2008), “Chronic Exposure to Ambient Ozone and Asthma Hospital Admissions Among Children,” Environmental Health Perspectives, 116, 1725–1730.
Ma, B., Lawson, A. B., and Liu, Y. (2007), “Evaluation of Bayesian Models for Focused Clustering in Health Data,” Environmetrics, 18, 871–887.
Mugglin, A. S., Cressie, N., and Gemmell, I. (2002), “Hierarchical Statistical Modelling of Influenza Epidemic Dynamics in Space and Time,” Statistics in Medicine, 21, 2703–2721.
Paciorek, C. (2010), “The Importance of Scale for Spatial-Confounding Bias and Precision of Spatial Regression Estimators,” Statistical Science, 25, 107–125.
Pleis, J. R., Lucas, J. W., and Ward, B. W. (2009), “Summary Health Statistics for US Adults: National Health Interview Survey, 2008,” Vital Health Statistics, 10(242), National Center for Health Statistics.
Ponka, A., and Virtanen, M. (1996), “Asthma and Ambient Air Pollution in Helsinki,” Journal of Epidemiology and Community Health, 50(Suppl 1), s59–s62.
Reich, B., Hodges, J., and Zadnik, V. (2006), “Effects of Residual Smoothing on the Posterior of the Fixed Effects in Disease-Mapping Models,” Biometrics, 62, 1197–1206.
Richardson, S., Abellan, J., and Best, N. (2006), “Bayesian Spatio-Temporal Analysis of Joint Patterns of Male and Female Lung Cancer Risks in Yorkshire (U.K.),” Statistical Methods in Medical Research, 15, 97–118.
Sheppard, L. (2003), “Ambient Air Pollution and Nonelderly Asthma Hospital Admissions in Seattle, Washington, 1987–1994,” in Revised Analyses of Time-Series Studies of Air Pollution and Health, Boston: Health Effects Institute, pp. 227–230.
Spiegelhalter, D. J., Best, N., Carlin, B. P., and van der Linde, A. (2002), “Bayesian Measures of Model Complexity and Fit (with discussion),” Journal of the Royal Statistical Society B, 64, 583–639.
Stephens, M. (2000), “Dealing With Label Switching in Mixture Models,” Journal of the Royal Statistical Society B, 62, 795–809.
Stieb, D. M., Burnett, R. T., Beveridge, R. C., and Brook, J. R. (1996), “Association Between Ozone and Asthma Emergency Department Visits in Saint John, New Brunswick, Canada,” Environmental Health Perspectives, 104, 1354–1360.
Tolbert, P. E., Mulholland, J. A., Maclntosh, D. L., Xu, F., Daniels, D., Devine, O. J., Carlin, B. P., Klein, M., Dorley, J., Butler, A. J., Nordenberg, D. F., Frumkin, H., Ryan, P. B., and White, M. C. (2000), “Air Quality and Pediatric Emergency Room Visits for Asthma in Atlanta, Georgia,” American Journal of Epidemiology, 151, 798–810.
Tzala, T., and Best, N. (2008), “Bayesian Latent Variable Modelling of Multivariate Spatio-Temporal Variation in Cancer Mortality,” Statistical Methods in Medical Research, 17, 97–118.
Xia, H., Carlin, B. P., and Waller, L. A. (1997), “Hierarchical Models for Mapping Ohio Lung Cancer Rates,” Environmetrics, 8, 107–120.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lawson, A.B., Choi, J., Cai, B. et al. Bayesian 2-Stage Space-Time Mixture Modeling With Spatial Misalignment of the Exposure in Small Area Health Data. JABES 17, 417–441 (2012). https://doi.org/10.1007/s13253-012-0100-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13253-012-0100-3