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Abstract:
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Poisson regression models with population size as offset terms are often used to model incidence rates and test for significant differences between subpopulations. However, in some situations the subpopulation sizes can only be estimated from complex survey samples resulting in random offset terms. Correspondingly, the incidence rates have two sources of random variation: the Poisson process that generates the disease incidence and the sampling error from the survey. In this paper, we examined and compared two strategies to obtain accurate estimation of the variance of such incidence rates using disease counts from the Active Bacterial Core Surveillance system and population counts from the National Health Interview Survey. The first strategy is based on a delta method applicable to functions of data vectors estimated from independent surveys. The second strategy involves generating random samples of the case and population counts based on mean and variance estimates from the surveillance and survey data. Both methods of estimating variance provide similar results.
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