Misspecification of within-area exposure distribution in ecological Poisson models
Ecological studies enable investigation of geographic variations in exposure to environmental variables, across groups, in relation to health outcomes measured on a geographic scale. Such studies are subject to ecological biases, including pure specification bias which arises when a nonlinear individual exposure-risk model is assumed to apply at the area level. Introduction of the within-area variance of exposure should induce a marked reduction in this source of ecological bias. Assuming several measurements per area of exposure and no confounding risk factors, we study the model including the within-area exposure variability when Gaussian within-area exposure distribution is assumed. The robustness is assessed when the within-area exposure distribution is misspecified. Two underlying exposure distributions are studied: the Gamma distribution and an unimodal mixture of two Gaussian distributions. In case of strong ecological association, this model can reduce the bias and improve the precision of the individual parameter estimates when the within-area exposure means and variances are correlated. These different models are applied to analyze the ecological association between radon concentration and childhood acute leukemia in France.
KeywordsEcological association Ecological bias Robustness Within-area exposure variability
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- Best NG, Ickstad K, Wolpert RL and Briggs DJ (2000). Combining models of health and exposure data: the SAVIAH study. In: Elliott, P, Wakefield, J, Best, NG, and Briggs, D (eds) Spatial Epidemiology, methods and applications, pp 393–414. Oxford University Press, Oxford Google Scholar
- Best NG, Ickstad K, Wolpert RL, Cookings S, Elliott P, Bennett J and Reed S (2002). Modeling the impact of traffic related air pollution on childhood respiratory illness (with discussion). Case Stud Bayesian Stat vol V: 183–259 Google Scholar
- Clavel J, Goubin A, Auclerc MF, Auvrignon A, Waterkeyn C, Patte C, Baruchel A, Leverger G, Nelken B, Philippe N, Sommelet D, Vilmer E, Bellec S, Perrillat-Menegaux F and Hémon D (2004). Incidence of childhood leukemia and non-hodgkin’s lymphoma in France - national registry of childhood leukemia and lymphoma, 1990–1999. E J Cancer Prev 13: 97–103 CrossRefGoogle Scholar
- Diggle PJ, Tawn JA and Moyeed RA (1998). Model-based geostatisctics. Appl Stat 47: 299–350 Google Scholar
- Elliott P, Cuzick J, English D and Stern R (1992). Geographical and environmental epidemiology: methods for small-area studies. Oxford University Press, Oxford Google Scholar
- Fortunato L, Guihennuec-Jouyaux C, Laurier D, Tirmarche M, Clavel J, Hémon D (2006) Introduction of within-area risk factor distribution in ecological Poisson regression models. Under Revision for Volume Edition of European SeminarGoogle Scholar
- Kelsall J, Wakefield J (1999) Discussion of “Bayesian models for spatially correlated disease and exposure data” by Best NG, Arnold RA, Thomas A, Waller LA, Conlon EM. In: Bayesian Statistics 6, Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds), Oxford University Press, OxfordGoogle Scholar
- Plummer M and Clayton D (1996). Estimation of population exposure in ecological studies (with discussion). J R Stat Soc Ser B 58: 113–126 Google Scholar
- Spiegelhalter DJ, Thomas A and Best NG (2001). WinBUGS Version 1.4, User Manual. Medical Research Council Biostatistics Unit, Cambridge, and Imperial College School of Medicine, London, UK Google Scholar