PUB - Publikationen an der Universität Bielefeld

The article discusses duration time models with multiple duration observations per individual and different competing events marking the end of a duration time. The dependence between two (or more) duration times observed for each individual is incorporated in a mixed model approach including frailty effects for each individual. The frailties are multivariate, with a separate component for each competing risk. As frailty distribution the article suggests a flexible and numerically handy mixture of gamma distributions. The model itself is based on the classical Cox approach by modeling the hazard functions. Instead of assuming proportional hazards, however, we allow covariate effects to vary functionally with time. The latter are fitted using, penalized splines in combination with mixed models technology. The modeling exercise allows to analyze data on unemployment, where duration time is the length of an unemployment spell and the competing events are the different reasons for leaving the state of unemployment, for example, full time or half time reemployment, respectively. The R code to compute the competing risk model and some other useful functions along with documentation are available in the online supplements.