This paper reviews empirical Bayes methods for disease mapping. A distinction is made between spatial models (which take into account the geographical distribution of disease) and nonspatial models. Several estimators are presented, and methods of estimation are described. Empirical Bayes methods are compared with full Bayes methods, and we argue that both have their place.
Get full access to this article
View all access options for this article.
References
1.
Lawson AB , Williams FLR.An introductory guide to disease mapping. Chichester: John Wiley & Sons , Ltd, 2001.
Clayton D , Kaldor J.Empirical Bayes estimates of age-standardized relative risks for use in disease mapping . Biometrics1987; 43: 671-681 .
4.
Bithell JF.A classification of disease mapping methods . Statistics in Medicine2000; 19: 2203-2215 .
5.
Smans M , Este`ve J.Practical approaches to disease mapping. In Elliott P , Cuzick J , English D , Stern R eds. Geographical and environmental epidemiology: methods for small-area studies. Oxford: Oxford University Press , 1992.
6.
Muehrcke PC , Muehrcke JO.Map use: reading, analysis, and interpretation. third edition. Madison, WI: JP Publications , 1992.
7.
Breslow NE , Day NE.Indirect standardisation and multiplicative models of rates with reference to the age adjustment of cancer incidence and relative frequency data . Journal of Chronic Diseases1975; 28: 289-303 .
8.
Manton KG , Woodbury MA , Stallard E , Riggan WB , Creason JP , Pellom AC.Empirical Bayes procedures for stabilizing maps of United-States cancer mortality-rates . Journal of the American Statistical Association1989; 84: 637-650 .
9.
Mollié A.Bayesian and empirical Bayes approaches to disease mapping. In Lawson A , Biggeri A , Böhning D , Lesaffre E , Viel J-F , Bertollini R eds. Disease mapping and risk assessment for public health. Chichester: John Wiley & Sons, Ltd , 1999: 15-29.
10.
Haining R.Spatial data analysis: theory and practice. Cambridge: Cambridge University Press , 2003.
11.
Dempster AP , Laird NM , Rubin DB.Maximum likelihood from incomplete data via the EM algorithm . Journal of the Royal Statistical Society: Series B1977; 39: 1-38 .
12.
Clayton D , Bernardinelli L.Bayesian methods for mapping disease risk. In Elliott P , Cuzick J , English D , Stern R eds. Geographical and environmental epidemiology: methods for small-area studies. Oxford: Oxford University Press , 1992: 205-220.
13.
Tsutakawa RK.Mixed model for analyzing geographic variability in mortality rates . Journal of the American Statistical Association1988; 83: 37-42 .
14.
Goldstein H.Multilevel statistical models. third edition. London: Arnold , 2003.
15.
Leyland AH , Goldstein H , eds. Multilevel modelling of health statistics. Chichester: John Wiley & Sons, Ltd , 2001.
16.
Leyland AH.Spatial analysis. In Leyland AH , Goldstein H eds. Multilevel modelling of health statistics. Chichester: John Wiley & Sons, Ltd , 2001.
17.
Langford IH , Day RD.Poisson regression. In Leyland AH , Goldstein H eds. Multilevel modelling of health statistics. Chichester: John Wiley & Sons, Ltd , 2001: 45-57.
18.
Lawson AB , Browne WJ , Vidal Rodeiro CL.Disease mapping with WinBUGS and MLwiN. Chichester: John Wiley & Sons, Ltd , 2003.
19.
Leyland AH.Increasing inequalities in premature mortality in Great Britain . Journal of Epidemiology and Community Health2004; 58: 296-302 .
20.
Langford IH , Bentham G , McDonald A-L.Multi-level modelling of geographically aggregated health data: a case study on malignant melanoma mortality and UV exposure in the European community . Statistics in Medicine1998; 17: 41-57 .
21.
Tsutakawa RK , Shoop GL , Marienfeld CJ.Empirical Bayes estimation of cancer mortality rates . Statistics in Medicine1985; 4: 201-212 .
22.
Marshall RJ.Mapping disease and mortality rates using empirical Bayes estimators . Applied Statistics1991; 40: 283-294 .
23.
Lawson AB , Biggeri AB , Böhning D , Lesaffre E , Viel JF , Clark A , Schlattman P , Divino F.Disease mapping models: an empirical evaluation . Statistics in Medicine2000; 19: 2217-2241 .
24.
Schlattmann P , Bohning D.Mixture models and disease mapping . Statistics in Medicine1993; 12: 1943-1950 .
25.
Heisterkamp SH , Doornbos G , Gankema M.Disease mapping using empirical Bayes and Bayes methods on mortality statistics in the Netherlands . Statistics in Medicine1993; 12: 1895-1913 .
26.
Böhning D , Schlattmann P.Disease mapping with hidden structures using mixture models. In Lawson A , Biggeri A , Böhning D , Lesaffre E , Viel J-F , Bertollini R eds. Disease mapping and risk assessment for public health. Chichester: John Wiley & Sons, Ltd , 1999: 49-60.
Besag J , Mollié A.Bayesian mapping of mortality rates . Bulletin of the International Statistical Institute, 47th Session1989; 53: 127-128 .
31.
Mollié A , Richardson S.Empirical Bayes estimates of cancer mortality rates using spatial models . Statistics in Medicine1991; 10: 95-112 .
32.
Besag J , York J , Mollié A.Bayesian image restoration, with two applications in spatial statistics . Annals of the Institute of Statistical Mathematics1991; 43: 1-20 .
33.
Langford IH , Leyland AH , Rasbash J , Goldstein H.Multilevel modelling of the geographical distributions of diseases . Applied Statistics1999; 48: 253-268 .
34.
Leyland AH , Langford IH , Rasbash J , Goldstein H.Multivariate spatial models for event data . Statistics in Medicine2000; 19: 2469-2478 .
35.
Biggeri A , Dreassi E , Lagazio C , Böhning D.A transitional non-parametric maximum pseudo-likelihood estimator for disease mapping . Computational Statistics and Data Analysis2003; 41: 617-629 .
36.
de Leeuw J , Kreft IGG.Software for multilevel analysis. In Leyland AH , Goldstein H eds. Multilevel modelling of health statistics. Chichester: John Wiley & Sons, Ltd , 2001.
37.
Biggeri A , Marchi M , Lagazio C , Martuzzi M , Böhning D.Non-parametric maximum likelihood estimators for disease mapping . Statistics in Medicine2000; 19: 2539-2554 .
38.
Goldstein H.Multilevel mixed linear model analysis using iterative generalised least squares . Biometrika1986; 73: 43-56 .
McCullagh P , Nelder JA.Generalized linear models, second edition. London: Chapman & Hall , 1989.
41.
Breslow NE , Clayton D.Approximate inference in generalized linear mixed models . Journal of the American Statistical Association1993; 88: 9-25 .
42.
Goldstein H , Rasbash J.Improved approximations for multilevel models with binary responses . Journal of the Royal Statistical Society Series A1996; 159: 505-513 .
43.
Louis TA.Estimating a population of parameter values using Bayes and empirical Bayes methods . Journal of the American Statistical Association1984; 79: 393-398 .
44.
Ghosh M.Constrained Bayes estimation with applications . Journal of the American Statistical Association1992; 87: 533-540 .
45.
Devine OJ , Louis TA.A constrained empirical Bayes estimator for incidence rates in areas with small populations . Statistics in Medicine1994; 13: 1119-1133 .
46.
Bernardinelli L , Montomoli C.Empirical Bayes versus fully Bayesian analysis of geographical variation in disease risk . Statistics in Medicine1992; 11: 983-1007 .
47.
Yasui Y , Liu H , Benach J , Winget M.An empirical evaluation of various priors in the empirical Bayes estimation of small area disease risks . Statistics in Medicine2000; 19: 2409-2420 .
48.
Cislaghi C , Biggeri A , Braga M , Lagazio C , Marchi M.Exploratory tools for disease mapping in geographical epidemiology . Statistics in Medicine1995; 14: 2363-2381 .
49.
Leroux BG.Modelling spatial disease rates using maximum likelihood . Statistics in Medicine2000; 19: 2321-2332 .
50.
Spiegelhalter DJ , Thomas A , Best N , Lunn D.WinBUGS User Manual Version 1.4. Cambridge: MRC Biostatistics Unit , 2003.
