Default Status Prediction in Credit Data using Mixture Cure Models

Abstract

In survival analysis, it may happen that some subjects in the study never experience the event of interest and are hence, considered to be cured. In credit data, cured individuals are the loans that never get defaulted. One of the common models to study such cured survival data are the mixture cure models which assume that the population of interest consists of two sub-populations, the cured sub-population and the uncured one. These models are comprised of two components, the incidence, which models the probability of cure of an individual, and the latency, which models the survival distribution for uncured sub-population. Often, one is interested in the cure status of an individual. For example, in credit data, a useful question is whether a loan would default or not default. We propose a classifier for this prediction using the estimator for the probability of cure. To evaluate the predictive performance of this classifier, we use the receiver operating characteristic (ROC) curves. But as the cure status of a subject is usually unknown, we discuss the modification of the ROC curves estimators to consider the latent cured status. Finally, we illustrate this methodology on two credit data sets, the German credit data and the Bondora credit data, and compare different parametric approaches with the semi-parametric approach of the single-index model for the incidence and the Cox proportional hazards model for the latency. We also discuss the concept of effects of covariates on the model, and propose two methodologies of significance tests for the single-index Cox proportional hazards mixture cure model.