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UBC Theses and Dissertations

Overdispersion in poisson regression McNeney, W. Brad


Investigation of a possible relationship between air quality and human health in the community of Prince George, British Columbia was undertaken after a public opinion poll in 1972 discovered that poor air quality was the number one concern of the residents of Prince George. An analysis which attempted to identify such relationships using a data set including air quality measurements and hospital admissions for the period April 1, 1984 to March 31, 1986 is discussed in Knight, Leroux, Millar, and Petkau (1988). A similar analysis using emergency room visits during the same period rather than hospital admissions is described in Knight, Leroux, Millar, and Petkau (1989). The data set described here was collected to carry out a follow-up study to the emergency room visits analysis. The main part of the analyses carried out involved the use of Poisson regression models with a minor extension to account for over-dispersion in the data. The results of the analysis were not consistent with either the earlier study or with the expectations of the investigators. For example, higher levels of one of the air quality variables was found to be associated with a decrease in the number of emergency room visits for respiratory disease in the winter, but an increase in emergency room visits for respiratory disease in the fall. A mechanism to explain such effects is difficult to imagine. These counter-intuitive results motivated a simulation study to assess the methods used in the analysis and to compare these to other possible estimators and test statistics that can be employed in the analysis of over-dispersed Poisson data.

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