Fitting epidemiologic follow-up studies with cumulative damage models

The use of an extended version of the cumulative damage model to identify and quantify cancer risk arising from a specified exposure is outlined. For this, a strategy to fit the model to individual data coming from epidemiologic follow-up studies is described. Two statistical problems are addressed: first, the regularity of the model has to be ascertained to allow the application of maximum-likelihood and likelihood-ratio methods for parameter estimation and testing. Second, a statistical test has to be found that permits testing goodness of fit in the setting of parameter estimation with individual data. As an example, these methods are applied to the data of a cohort study on mortality among stainless steel welders in the Federal Republic of Germany. The results show that the model fits the data well and confirms a carcinogenic effect of stainless steel welding among welders. Some distinguishing characteristics of the model, especially its prediction of a potentially decreasing relative risk despite ongoing carcinogenic exposure, are discussed.