EFFICIENT NON-ITERATIVE AND NONPARAMETRIC ESTIMATION OF HETEROGENEITY VARIANCE FOR THE STANDARDIZED MORTALITY RATIO

DANKMAR BÖHNING^{1}, UWE MALZAHN^{1}, JESUS SAROL, JR.^{2}, SASIVIMOL RATTANASIRI^{3} AND ANNIBALE BIGGERI^{4}

1Department of Epidemiology, Free University Berlin, Haus 562, Fabeckstr. 60-62, 14195 Berlin,

Germany, e-mail: boehning@zedat.fu-berlin.de 2Department of Epidemiology and Biostatistics, College of Public Health, University of the Philippines Manila, Manila, Philippines, e-mail: jsarol@nwave.net

3Department of Biostatistics, Faculty of Public Health, Mahidol University, Bangkok, Thailand,

e-mail: r sasivimol@hotmail.com 4Department of Statistics, University of Florence, 50134 Florence, Italy, e-mail: abiggeri@stat.ds.unifi.it

(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.