title: A comparison of non-iterative and iterative estimators of heterogeneity variance for the standardized mortality ratio.
abstract: 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.
authors.affiliation: 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@zedat.fu-berlin.de
authors.forename: Dankmar
authors.initials: D
authors.lastname: Böhning
authors.forename: Jesus
authors.initials: J
authors.lastname: Sarol
authors.forename: Sasivimol
authors.initials: S
authors.lastname: Rattanasiri
authors.forename: Chukiat
authors.initials: C
authors.lastname: Viwatwongkasem
authors.forename: Annibale
authors.initials: A
authors.lastname: Biggeri
mesh_terms: D001604:Berlin / Q000453:epidemiology; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006509:Hepatitis B / Q000453:epidemiology; D006515:Hepatitis B virus; D006801:Humans; D007226:Infant Mortality / Q000639:trends; D007231:Infant, Newborn; D016013:Likelihood Functions; D009026:Mortality; D006113:United Kingdom