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Regression of Area Mortality Rates on Explanatory Variables: What Weighting is Appropriate?

Stuart J. Pocock, Derek G. Cook and Shirley A. A. Beresford
Journal of the Royal Statistical Society. Series C (Applied Statistics)
Vol. 30, No. 3 (1981), pp. 286-295
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2346353
Stable URL: http://www.jstor.org/stable/2346353
Page Count: 10
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Regression of Area Mortality Rates on Explanatory Variables: What Weighting is Appropriate?
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Abstract

One can often gain insight into the aetiology of a disease by relating mortality rates in different areas to explanatory variables. Multiple regression techniques are usually employed, but unweighted least squares may be inappropriate if the areas vary in population size. Also, a fully weighted regression, with weights inversely proportional to binomial sampling variances, is usually too extreme. This paper proposes an intermediate solution via maximum likelihood which takes account of three sources of variation in death rates: sampling error, explanatory variables and unexplained differences between areas. The method is also adapted for logit (death rates), standardized mortality ratios (SMRs) and log (SMRs). Two examples are presented.

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