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Goodness of fit in armitage doll poisson models

, : Goodness of fit in armitage doll poisson models. Biometrics 45(4): 1271-1280

We consider testing the adequacy of multistage models of cancer induction for Poisson event rates depending on age and exposure to environmental agents. The space of time and covariates is partitioned for comparison of observed and fitted event counts over regions of the partition. A test of fit based on the quadratic score statistic is proposed to assess overall residual error between observed and fitted counts. The limiting distribution of the test statistic is central chi-squared under the null hypothesis and noncentral chi-squared under local alternatives. Standardized residuals and tests of trend for individuals regions of the partition are given. The method is applied to lung cancer incidence rates among British physicians grouped by age, by amount of smoking, and by decile of estimated risk. The relation of the proposed method to chi-squared frequency tests and extensions to case-control studies are considered.


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