Hypothesis testing in the polychotomous logistic model with an application to detecting gastrointestinal cancer

We discuss the use of the trichotomous logistic model to discriminate between patients with gastrointestinal (GI) cancer, patients with benign GI disease and 'normal' subjects, using symptoms and the concentrations of some serum proteins that are potentially indicative of malignancy as covariates. A parsimonious model can be obtained by invoking an indistinguishability hypothesis which is appropriate when a covariate is considered to have no predictive value between categories. It is shown that the polychotomous model can be re-parameterised under the null hypothesis to give a 'reduced form', which can be fitted by maximum likelihood. The validity of the use of the same methods for retrospective sampling is discussed. The approach is illustrated by the development of a logistic model to identify symptomatic and asymptomatic subjects with a high risk of GI cancer.