Stage-specific cancer incidence: an artificially mixed multinomial logit model.

Early detection of prostate cancer using the prostate-specific antigen test led to a sharp spike in the incidence of the disease accompanied by an equally sharp improvement in patient prognoses as evaluated at the point of advanced diagnosis. Observed outcomes represent age at diagnosis and stage, a categorical prognostic variable combining the actual stage and the grade of tumor. The picture is summarized by the stage-specific cancer incidence that represents a joint survival-multinomial response regressed on factors affecting the unobserved history of the disease before diagnosis (mixture). Fitting the complex joint mixed model to large population data is a challenge. We develop a stable and structured MLE approach to the problem allowing for the estimates to be obtained iteratively. Factorization of the likelihood achieved by our method allows us to work with only a fraction of the model dimension at a time. The approach is based on generalized self-consistency and the quasi-EM algorithm used to handle the mixed multinomial part of the response through Poisson likelihood. The model provides a causal link between the screening policy in the population and the stage-specific incidence. Copyright 2009 John Wiley & Sons, Ltd.