Methods for detecting disease clustering,with consideration of childhood leukaemia

Abstract

In trying to interpret reports of disease clusters in specific localities, it is valuable to know whether the disease in question has a general tendency to cluster spatially. Methods for investigating localized disease clustering were the subject of a comparative study organized by the International Agency for Research on Cancer some years ago. This paper addresses some further aspects of one of the methods used in this exercise, namely the Potthoff-Whittinghill (P-W) test. Particular consideration is given to methodology for estimating the magnitude of overdispersion and for detecting whether one area, in particular, has an undue influence on the evidence for overdispersion using the P-W test, the extent to which is possible to detect clustering over regions of differing sizes using a components-of-variance approach and how adjustment for overdispersion might affect tests for raised disease rates in specific locations. These points are illustrated using data on childhood leukaemia incidence and reference is made to other analyses of the geographical distribution of childhood leukaemia that are based on this approach.

Get full access to this article

View all access options for this article.

References

Committee on Medical Aspects of Radiation in the Environment (COMARE) . The incidence of cancer and leukaemia in young people in the vicinity of the Sellafield site, West Cumbria: further studies and an update of the situation since the publication of the report of the Black Advisory Group in 1984. Fourth report, Department of Health, Wetherby , 1996.

Committee on Medical Aspects of Radiation in the Environment (COMARE) . Investigation of the possible increased incidence of leukaemia in young people near the Dounreay Nuclear Establishment, Caithness, Scotland. Second report, HMSO, London , 1988.

Committee on Medical Aspects of Radiation in the Environment (COMARE) . Report on the incidence of childhood cancer in the West Berkshire and North Hampshire area, in which are situated the Atomic Weapons Research Establishment, Aldermaston and the Royal Ordnance Factory, Burghfield. Third report, HMSO, London , 1989.

Knox EG. Childhood cancers and atmospheric carcinogens . Journal of Epidemiology and Community Health 2005; 59: 101-105 .

Potthoff RF , Whittinghill M. Testing for homogeneity. I. The binomial and multinomial distributions . Biometrika 1966; 53: 167-182 .

Potthoff RF , Whittinghill M. Testing for homogeneity. II. The Poisson distribution . Biometrika 1966; 53: 183-190 .

Muirhead CR , Ball AM. Contribution to the discussion of the Royal Statistical Society meeting on cancer near nuclear installations . Journal of the Royal Statistical Society, Series A 1989; 152: 376-376 .

Muirhead CR , Butland BK. Methods for investigating localized clustering of disease. Testing for over-dispersion using an adapted form of the Potthoff-Whittinghill method . Methods for investigating localized clusting of disease IARC Scientific Publications 1996; 135: 40-52 (with discussion 155-63).

Alexander FE , Boyle P eds. Methods for investigating localized clustering of disease. IARC Scientific Publications No. 135. International Agency for Research on Cancer, Lyon , 1996.

10.

Wray NR , Alexander FE , Muirhead CR , Pukkala E , Schmidtmann I , Stiller C. A comparison of some simple methods to identify geographical areas with excess incidence of a rare disease such as childhood leukaemia . Statistics in Medicine 1999; 18: 1501-1516 .

11.

Paul SR , Liang KY , Self SG. On testing departure from the binomial and multinomial assumptions . Biometrics 1989; 45: 231-236 .

12.

Kim BS , Margolin BH. Testing goodness of fit of a multinomial model against overdispersed alternatives . Biometrics 1992; 48: 711-719 .

13.

Black RJ , Sharp L , Urquhart JD. Analysing the spatial distribution of disease using a method of constructing geographical areas of approximately equal population size. Methods for investigating localized clustering of disease . IARC Scientific Publications, 1996; 135: 28-39 (with discussion 155-62).

14.

Cox DR , Hinkley DV. Theoretical statistics. Chapman and Hall , 1974.

15.

Dean CB. Testing for overdispersion in Poisson and binomial regression models . Journal of the American Statistical Association 1992; 87: 451-457 .

16.

Breslow NE. Extra-Poisson variation in log-linear models . Applied Statistics 1984; 33: 38-44 .

17.

Breslow NE. Tests of hypotheses in over-dispersed Poisson regression and other quasi-likelihood models . Journal of the American Statistical Association 1990; 85: 565-571 .

18.

Clayton D , Kaldor J. Empirical Bayes estimates of age-standardised relative risks for use in disease mapping . Biometrics 1987; 43: 671-681 .

19.

Collings BJ , Margolin BH. Testing goodness of fit for the Poisson assumption when observations are not identically distributed . Journal of the American Statistical Association 1985; 80: 411-418 .

20.

Dean C , Lawless JF. Tests for detecting over-dispersion in Poisson regression models . Journal of the American Statistical Association 1989; 84: 467-472 .

21.

Morton R. Analysis of extra-multinomial data derived from extra-Poisson variables conditional on their total . Biometrika 1992; 78: 1-6 .

22.

Alexander FE , Wray N , Boyle P et al. Clustering of childhood leukaemia: a European study in progress . Journal of Epidemiology and Biostatistics 1996; 1: 13-24 .

23.

Muirhead CR.

Childhood leukemia in metropolitan regions in the United States: a possible relation to population density?

Cancer Causes and Control 1995; 6: 383-388 .

24.

Tsutakawa RK , Shoop GL , Marienfeld CJ. Empirical Bayes estimation of cancer mortality rates . Statistics in Medicine 1985; 4: 201-212 .

25.

Estève J , Benhamou E , Raymond L. Statistical methods in cancer research. Volume IV, Descriptive epidemiology. IARC Scientific Publications No. 128. International Agency for Research on Cancer, Lyon , 1994.

26.

Committee on Medical Aspects of Radiation in the Environment (COMARE) . The incidence of childhood cancer around nuclear installations in Great Britain. Tenth report. 2005. http://www.comare.org.uk/documents/COMARE10thReport.pdf

27.

Jablon S , Hrubec Z , Boice JD , Stone BJ. Cancer in populations living near nuclear facilities. NIH Publication No. 90-874. National Institutes of Health, Washington, D.C . 1990.

28.

Alexander FE , Boyle P , Carli PM et al. Spatial clustering of childhood leukaemia: summary results from the EUROCLUS project . British Journal of Cancer 1998; 77: 818-824 .

29.

Alexander FE , Boyle P , Carli PM et al. Population density and childhood leukaemia: results of the EUROCLUS Study . European Journal of Cancer 1999; 35: 439-444 .