Prediction Models for Time Discrete Competing Risks

The classical approach to the modeling of discrete time competing risks consists of fitting multinomial logit models where parameters are estimated using maximum likelihood theory. Since the effects of covariates are specific to the target events, the resulting models contain a large number of parameters, even if there are only few predictor variables. Due to the large number of parameters classical maximum likelihood estimates tend to deteriorate or do even not exist. Regularization techniques might be used to overcome these problems. This article explores the use of two different regularization techniques, namely penalized likelihood estimation methods and random forests, for modeling time discrete competing risks using both, extensive simulation studies and studies on real data. The simulation results as well as the application on three real world data sets show that the novel approaches perform very well and distinctly outperform the classical (unpenalized) maximum likelihood approach.