The analysis of ratios and cross-product ratios of poisson variates with application to incidence rates |
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Authors: | John J Gart |
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Institution: | Mathematical Statistics and Applied Mathematics Section , National Cancer Institute Bethesda , Md, 20014, U.S.A. |
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Abstract: | The incidence of most diseases is low enough that in. large populations the number of new cases may be considered a Poisson variate. This paper explores models and methods for analyzing such data Specific cases are the estimation and testing of ratios and the cross-product ratios, both simple and stratified* We assume the Poisson means are exponential functions of the relevant parameters. The resulting sets of sufficient statistics are partitioned into a test statistic and a vector of statistics related to the nuisance parameters . The methods derived are based on the conditional distribution of the test statistic given the other sufficient statistics. The analyses of stratified cross-product ratios are seen to be analogues of the noncentral distribution associated with theanalysis of the common odds ratio in several 2×2 tables. The various methods are illustrated in numerical examples involving incidence rates of cancer in two metropolitan areas adjusting for both age and sex. |
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Keywords: | minimal sets of sufficient statistics conditional maximum likelihood estimation conditional tests |
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