Prediction and classification when the diagnostic classes are related

Abstract

We consider prediction and classification into diagnostic classes which consist of individuals who can suffer from multiple diseases. For instance, in a cardiovascular context a patient can need bypass surgery, or a valve replacement, or both. The popular multigroup logistic model is suitable for prediction into nominal classes, but does not employ the underlying structure of the classes. Hence, this model is not entirely suitable for this situation. Also, computational difficulties often occur with the multigroup logistic model when the classes are of the above nature. A modified form of the model, applicable to some economic applications, is not appropriate for most medical applications. Instead, we suggest the n-way Dale model, also called the marginal logistic model. It is shown that this model is computationally more stable, although more involved, and allows better interpretation of the parameters. To illustrate our ideas the POPS data set is taken, where the child's abilities at the age of 2 is predicted from risk factors at delivery. A simulation study is performed to indicate the gain in classification ability in comparison with the multigroup logistic model. It is also shown that in terms of the parameter estimates the Dale model is more sensitive to the choice of the sampling scheme than the multigroup logistic model.