Score tests based on a finite mixture model of Markov processes under intermittent observation

The polytomous discrimination index for prediction involving multistate processes under intermittent observation

With the increasing importance of predictive modeling in health research comes the need for methods to rigorously assess predictive accuracy. We consider the problem of evaluating the accuracy of predictive models for nominal outcomes when outcome data are coarsened at random. We first consider the problem in the context of a multinomial response modeled by polytomous logistic regression. Attention is then directed to the motivating setting in which class membership corresponds to the state occupied in a multistate disease process at a time horizon of interest. Here, class (state) membership may be unknown at the time horizon since disease processes are under intermittent observation. We propose a novel extension to the polytomous discrimination index to address this and evaluate the predictive accuracy of an intensity-based model in the context of a study involving patients with arthritis from a registry at the University of Toronto Centre for Prognosis Studies in Rheumatic Diseases.