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A statistical framework for ecological and aggregate studies

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  • Jonathan Wakefield
  • Ruth Salway

Abstract

Inference from studies that make use of data at the level of the area, rather than at the level of the individual, is more difficult for a variety of reasons. Some of these difficulties arise because frequently exposures (including confounders) vary within areas. In the most basic form of ecological study the outcome measure is regressed against a simple area level summary of exposure. In the aggregate data approach a survey of exposures and confounders is taken within each area. An alternative approach is to assume a parametric form for the within‐area exposure distribution. We provide a framework within which ecological and aggregate data studies may be viewed, and we review some approaches to inference in such studies, clarifying the assumptions on which they are based. General strategies for analysis are provided including an estimator based on Monte Carlo integration that allows inference in the case of a general risk–exposure model. We also consider the implications of the introduction of random effects, and the existence of confounding and errors in variables.

Suggested Citation

  • Jonathan Wakefield & Ruth Salway, 2001. "A statistical framework for ecological and aggregate studies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(1), pages 119-137.
    • Handle: RePEc:bla:jorssa:v:164:y:2001:i:1:p:119-137
    DOI: 10.1111/1467-985X.00191
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    Cited by:

    1. Aleš Urban & Katrin Burkart & Jan Kyselý & Christian Schuster & Eva Plavcová & Hana Hanzlíková & Petr Štěpánek & Tobia Lakes, 2016. "Spatial Patterns of Heat-Related Cardiovascular Mortality in the Czech Republic," IJERPH, MDPI, vol. 13(3), pages 1-19, March.
    2. Ying C. MacNab, 2018. "Some recent work on multivariate Gaussian Markov random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 497-541, September.
    3. Judge, George G. & Miller, Douglas J. & Cho, Wendy K. T., 2003. "An Information Theoretic Approach to Ecological Estimation and Inference," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt7h03r00q, Department of Agricultural & Resource Economics, UC Berkeley.
    4. Judge, George G. & Miller, Douglas J. & Cho, Wendy K. T., 2003. "An Information Theoretic Approach to Ecological Estimation and Inference," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt7h03r00q, Department of Agricultural & Resource Economics, UC Berkeley.
    5. Jon Wakefield, 2003. "Sensitivity Analyses for Ecological Regression," Biometrics, The International Biometric Society, vol. 59(1), pages 9-17, March.
    6. Katherine A. Guthrie & Lianne Sheppard & Jon Wakefield, 2002. "A Hierarchical Aggregate Data Model with Spatially Correlated Disease Rates," Biometrics, The International Biometric Society, vol. 58(4), pages 898-905, December.
    7. Leon-Gonzalez, Roberto & Tseng, Fu Min, 2011. "Socio-economic determinants of mortality in Taiwan: Combining individual and aggregate data," Health Policy, Elsevier, vol. 99(1), pages 23-36, January.
    8. Yi Liu & Gavin Shaddick & James V. Zidek, 2017. "Incorporating High-Dimensional Exposure Modelling into Studies of Air Pollution and Health," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 559-581, December.
    9. Francesca Dominici & Lianne Sheppard & Merlise Clyde, 2003. "Health Effects of Air Pollution: A Statistical Review," International Statistical Review, International Statistical Institute, vol. 71(2), pages 243-276, August.
    10. Gillian A. Lancaster & Mick Green & Steven Lane, 2006. "Reducing bias in ecological studies: an evaluation of different methodologies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(4), pages 681-700, October.
    11. Joan G. Staniswalis, 2008. "Incorporating Marginal Covariate Information in a Nonparametric Regression Model for a Sample of R×C Tables," Biometrics, The International Biometric Society, vol. 64(4), pages 1054-1061, December.
    12. Christopher Jackson & And Nicky Best & Sylvia Richardson, 2008. "Hierarchical related regression for combining aggregate and individual data in studies of socio‐economic disease risk factors," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 159-178, January.
    13. Jon Wakefield, 2004. "Ecological inference for 2 × 2 tables (with discussion)," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(3), pages 385-445, July.
    14. Duncan Lee & Chris Robertson & Colin Ramsay & Kate Pyper, 2020. "Quantifying the impact of the modifiable areal unit problem when estimating the health effects of air pollution," Environmetrics, John Wiley & Sons, Ltd., vol. 31(8), December.

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