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Poisson regression

# Poisson regression - POISSON REGRESSION 2 Example applying...

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POISSON REGRESSION

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Example applying the Poisson distribution A retrospective occupational follow-up study was conducted among workers of a telecommunications company in the State of New York. The authors wanted to test the null hypothesis that there was no association between exposure to magnetic fields and the occurrence of breast cancer among men. Male telephone workers, who were actively employed in the company during 1976-1980, were matched to the cancer registry of New York to identify breast cancer cases. Person-years and cases were counted only if the person was still working for the telephone company during the study period. The annual rate of breast cancer among all men in New York was 0.15/100,000 during the study period. Two cases were observed among 50,582 male telecommunications workers who had contributed 206,067 person years of follow-up (Matanonski GM, et al. Electromagnetic field exposure and male breast cancer, Lancet 1991; 337: 737). 2
Summary of data Observe 2 cases over 206,067 person years Expect (under H 0 ): 206,067[(0.15)/100,000] = 0.31 cases over 206,067 person years Expected cases = (Total person time) × (Rate) μ = Lλ μ = expected events L = person time λ = underling rate 3

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Poisson distribution Let Y be a random variable which can take on the values 0, 1, 2, 3, … (e.g., Y = the number of cases) P(Y=y) = ! y e y μ μ - where y=0, 1, 2, 3, … The Poisson distribution is defined in terms of a single parameter ( μ ) Once a value of μ is assumed, then the distribution is specified 4
Male breast cancer example (continued) Under H 0 (no association between male breast cancer and magnetic field exposure): μ = 0.31 Let Y = the number of breast cancer cases, assume Y is distributed Poisson P(Y=0) = ! 0

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Poisson regression - POISSON REGRESSION 2 Example applying...

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