Semi-varying coefficient multinomial logistic regression for disease progression risk prediction

This paper proposes a risk prediction model using semi-varying coefficient multinomial logistic regression. We use a penalized local likelihood method to do the model selection and estimate both functional and constant coefficients in the selected model. The model can be used to improve predictive modelling when non-linear interactions between predictors are present. We conduct a simulation study to assess our method's performance, and the results show that the model selection procedure works well with small average numbers of wrong-selection or missing-selection. We illustrate the use of our method by applying it to classify the patients with early rheumatoid arthritis at baseline into different risk groups in future disease progression. We use a leave-one-out cross-validation method to assess its correct prediction rate and propose a recalibration framework to evaluate how reliable are the predicted risks.