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Biostatistics 5:61-74 (2004)
© 2004 Oxford University Press

A comparison of non-iterative and iterative estimators of heterogeneity variance for the standardized mortality ratio

Dankmar Böhning*, Jesus Sarol, Sasivimol Rattanasiri, Chukiat Viwatwongkasem and Annibale Biggeri

Biometry and Epidemiology, Institute for International Health, Joint Center for Health Sciences and Humanitites, Free University Berlin/Humboldt University at Berlin, Haus 562, Fabeckstr. 60-62, 14195 Berlin, Germany boehning{at}zedat.fu-berlin.de
Department of Epidemiology and Biostatistics, College of Public Health, University of the Philippines at Manila, Manila, Philippines
Clinical Epidemiology Unit, Faculty of Medicine, Ramathibodi Hospital, Mahidol University, Bangkok, Thailand
Department of Biostatistics, Faculty of Public Health, Mahidol University, Bangkok, Thailand
Department of Statistics, University of Florence, 50134 Florence, Italy

*To whom correspondence should be addressed.

This paper continues work presented in Böhning et al. (2002b, Annals of the Institute of Statistical Mathematics 54, 827–839, henceforth BMSRB) where a class of non-iterative estimators of the variance of the heterogeneity distribution for the standardized mortality ratio was discussed. Here, these estimators are further investigated by means of a simulation study. In addition, iterative estimators including the Clayton–Kaldor procedure as well as the pseudo-maximum-likelihood (PML) approach are added in the comparison. Among all candidates, the PML estimator often has the smallest mean square error, followed by the non-iterative estimator where the weights are proportional to the external expected counts. This confirms the theoretical result in BMSRB in which an asymptotic efficiency could be proved for this estimator (in the class of non-iterative estimators considered). Surprisingly, the Clayton–Kaldor iterative estimator (often recommended and used by practitioners) performed poorly with respect to the MSE. Given the widespread use of these estimators in disease mapping, medical surveillance, meta-analysis and other areas of public health, the results of this study might be of considerable interest.

Keywords: Comparative simulation study; DerSimonian–Laird estimator; Heterogeneity variance estimators; Iterative and non-iterative estimators; Moment estimator; Population heterogeneity; Standardized mortality ratio


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