Evaluating Goodness of Fit of Poisson Regression Models in Cohort Studies

Relative and absolute risk models are often used in epidemiologic studies to describe the effect of exposure on age-specific mortality rates. Poisson regression analysis is used to obtain maximum likelihood estimates of unknown parameters and to assess goodness of fit of the models. It is common practice to base both estimation and the evaluation of goodness of fit on certain marginal totals. This approach is potentially misleading for relative risk models and is totally inappropriate for absolute risk models. To illustrate the situation, we present an example using data on smoking and lung cancer. In the example, the goodness-of-fit tests based on the marginal totals indicate that neither the absolute risk nor the relative risk model can be rejected, whereas the age-specific test statistics strongly reject both models. The validity of the marginal test is based on an assumption (i.e., of no exposure by age interaction) that is not satisfied in the example. We describe a more general approach to model evaluation that provides the analyst with summary information for various models of interest and provides guidance on how to identify good descriptive models.