AISM 54, 827-839
© 2002 ISM

Efficient non-iterative and nonparametric estimation of heterogeneity variance for the standardized mortality ratio

Dankmar Böhning1, Uwe Malzahn1, Jesus Sarol, Jr.2, Sasivimol Rattanasiri3 and Annibale Biggeri4

1Department of Epidemiology, Free University Berlin, Haus 562, Fabeckstr. 60-62, 14195 Berlin, Germany, e-mail:
2Department of Epidemiology and Biostatistics, College of Public Health, University of the Philippines Manila, Manila, Philippines, e-mail:
3Department of Biostatistics, Faculty of Public Health, Mahidol University, Bangkok, Thailand, e-mail:
4Department of Statistics, University of Florence, 50134 Florence, Italy, e-mail:

(Received December 5, 2000; revised August 6, 2001)

Abstract.    In this paper the situation of extra population heterogeneity in the standardized mortality ratio is discussed from the point-of-view of an analysis of variance. First, some simple non-iterative ways are provided to estimate the variance of the heterogeneity distribution without estimating the heterogeneity distribution itself. Next, a wider class of linear unbiased estimators is introduced and their properties investigated. Consistency is shown for a wide sub-class of estimators charactererized by the fact that the associated linear weights are within some positive, finite bounds. Furthermore, it is shown that an efficient estimator is often provided when the weights are proportional to the expected counts.

Key words and phrases:    Population heterogeneity, random effects model, moment estimator, variance separation, standardized mortality ratio.

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