Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Research Article
  • Published:

Bootstrap model averaging in time series studies of particulate matter air pollution and mortality

Abstract

The consensus from time series studies that have investigated the mortality effects of particulate matter air pollution (PM) is that increases in PM are associated with increases in daily mortality. However, recently concerns have been raised that the observed positive association between PM and mortality may be an artefact of model selection due to multiple hypothesis testing. This problem arises when a number of models are investigated, but only the “best” model is reported and all subsequent inference is based on this model, ignoring the model selection process. In this paper, we introduce the use of the bootstrap as a means of addressing the problems of model selection in PM mortality time series studies. Using the bootstrap to perform inference about the effect of PM on mortality is a process based on a set of models rather than on a single model. It is shown that using the bootstrap to overcome the problems of model selection is competitive with the existing methodology of Bayesian model averaging.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1

Similar content being viewed by others

References

  • Akaike H. Information theory and an extension of the maximum likelihood principle. Second International Symposium on Information Theory, 1973, pp. 267–281.

  • Bell L.M., Samet J.M., and Dominici F. Time-series studies of particulate matter. Annu Rev Public Health 2004: 25: 247–280.

    Article  Google Scholar 

  • Buckland S.T., Burnham K.P., and Augustin N.H. Model selection: an integral part of inference. Biometrics 1997: 53: 603–618.

    Article  Google Scholar 

  • Chock D.P., Winkler S.L., and Chen C. A study of the association between daily mortality and ambient air pollutant concentrations in Pittsburgh, Pennsylvania. J Air Waste Manage Assoc 2000: 50: 1481–1500.

    Article  CAS  Google Scholar 

  • Clyde M. Model uncertainty and health effect studies for particulate matter. Environmetrics 2000: 11: 745–763.

    Article  CAS  Google Scholar 

  • Cox L. Statistical issues in the study of air pollution involving airborne particulate matter. Environmetrics 2000: 11: 611–626.

    Article  Google Scholar 

  • Crosignani P., Borgini A., Cadum E., Mirabelli D., and Porro E. New directions: air pollution — how many victims? Correspondence. Atmos Environ 2002: 36: 4705–4760.

    Article  CAS  Google Scholar 

  • Daniels M.J., Dominici F., Samet J.M., and Zeger S.L. Estimating the particulate matter-mortality dose–response curves and threshold levels: an analysis of daily time-series for the 20 largest US cities. Am J Epidemiol 2000: 152: 397–406.

    Article  CAS  Google Scholar 

  • Davison A.C., and Hinkley D.V. Bootstrap Methods and Their Application. Cambridge University Press, Cambridge, 1997.

    Book  Google Scholar 

  • Dominici F., McDermott A., Daniels M., Zeger S.L., and Samet J.M. Mortality among residents of 90 cities. In: Revised Analysis of Time-series Studies of Air Pollution and Health, Research Report 94. Health Effects Institute, Cambridge, MA, 2003, pp. 9–24.

    Google Scholar 

  • Filleul L., Le Tertre A., Baldi I., and Tessier J.F. Difference in the relation between daily mortality and air pollution among elderly and all-ages populations in southwestern France. Environ Res 2004: 94: 249–253.

    Article  CAS  Google Scholar 

  • Hastie T.J., and Tibshirani R.J. Generalized Additive Models. Chapman & Hall, London, 1990.

    Google Scholar 

  • Health Effects Institute. Revised analysis of time-series studies of air pollution and health. Research Report 94 Health Effects Institute, Cambridge, MA, 2003.

  • Kelsall J.E., Samet J.M., Zeger S.L., and Xu J. Air pollution and mortality in Philadelphia, 1974–1988. Am J Epidemiol 1997: 146: 750–762.

    Article  CAS  Google Scholar 

  • Kim H., Kim Y., and Hong Y.C. The lag-effect pattern in the relationship of particulate air pollution to daily mortality in Seoul, Korea. Int J Biometeorol 2003: 48: 25–30.

    Article  Google Scholar 

  • Koop G., and Tole L. An investigation of thresholds in air pollution-mortality effects. University of Leicester, Department of Economics, Working Paper No. 04.20, 2004b.

  • Koop G., and Tole L. Measuring the health effects of air pollution: to what extent can we really say that people are dying from bad air? J Environ Econ Manage 2004a: 47: 30–54.

    Article  Google Scholar 

  • Kwon H.J., Cho S.H., Nyberg F., and Pershagen G. Effects of ambient air pollution on daily mortality in a cohort of patients with congestive heart failure. Epidemiology 2001: 12: 413–419.

    Article  CAS  Google Scholar 

  • Lumley T., and Sheppard L. Assessing seasonal confounding and model selection bias in air pollution epidemiology using positive and negative control analyses. Environmetrics 2000: 11: 705–717.

    Article  CAS  Google Scholar 

  • McCullagh P, and Nelder J.A. Generalized Linear Models. Chapman & Hall, London, 1989.

    Book  Google Scholar 

  • Moolgavkar S.H. Air pollution and daily mortality in two US counties: season-specific analyses and exposure–response relationships. Inhal Toxicol 2003: 15: 877–907.

    Article  CAS  Google Scholar 

  • Ostro B.D., Hurely S., and Lipsett M.J. Air pollution and daily mortality in the Coachella Valley, California: a study of PM10 dominated by coarse particles. Environ Res 1999: 81: 231–238.

    Article  CAS  Google Scholar 

  • Peng R.D., Dominici F., and Louis T.A. Model choice in multi-city time series studies of air pollution and mortality. Vol. 55, John Hopkins University, Department of Biostatistics, Working Papers, 2004a.

  • Peng R.D., Welty L.J., and McDermott A. The national morbidity, mortality, and air pollution study database in R. Vol. 44, John Hopkins University, Department of Biostatistics, Working Papers, 2004b.

  • Roberts S. Biologically plausible particulate air pollution mortality concentration–response functions. Environ Health Perspect 2004a: 112: 309–313.

    Article  Google Scholar 

  • Roberts S. Interactions between particulate air pollution and temperature in air pollution mortality time series studies. Environ Res 2004b: 96: 328–337.

    Article  CAS  Google Scholar 

  • Roberts S. An investigation of distributed lag models in the context of air pollution and mortality time series analysis. J Air Waste Manage Assoc 2005: 55: 273–282.

    Article  Google Scholar 

  • Schwartz J. The distributed lag between air pollution and daily deaths. Epidemiology 2000: 11: 320–326.

    Article  CAS  Google Scholar 

  • Smith M ., and Kohn R . Nonparametric regression using Bayesian variable selection. J Econometrics 1996: 75: 317–343.

    Article  Google Scholar 

  • Smith R.L., Davis J.M., Sacks J., Speckman P., and Styer P. Regression models for air pollution and daily mortality: analysis of data from Birmingham, Alabama. Environmetrics 2000: 11: 719–743.

    Article  CAS  Google Scholar 

  • Styer P., McMillan N., Gao F., Davis J., and Sacks J. Effect of outdoor airborne particulate matter on daily death counts. Environ Health Perspect 1995: 103: 490–497.

    Article  CAS  Google Scholar 

  • Sullivan E.M. Estimating the association between ambient particulate matter and elderly mortality in Phoenix and Seattle using Bayesian model averaging. NRCSE Technical Report Series, No. 054 2000.

  • Vedal S., Brauer M., White R., and Petkau J. Air pollution and daily mortality in a city with low levels of pollution. Environ Health Perspect 2003: 111: 45–51.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Steven Roberts.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martin, M., Roberts, S. Bootstrap model averaging in time series studies of particulate matter air pollution and mortality. J Expo Sci Environ Epidemiol 16, 242–250 (2006). https://doi.org/10.1038/sj.jea.7500454

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/sj.jea.7500454

Keywords

This article is cited by

Search

Quick links