Analysis of Time-to-Event Data With Two Time Scales. An Application to Transitions out of Cohabitation

Models for time-to-event data are based on transition rates between states, and to define such hazards of experiencing an event, the time scale over which the process evolves needs to be identified. In many applications, however, more than one time scale might be of importance. Here, we demonstrate how to model a hazard jointly over two time dimensions. The model assumes a smooth bivariate hazard function, and the function is estimated by two-dimensional P -splines. We provide an R package for the analysis of event history data with two time scales. As an example, we model transitions from cohabitation to marriage or separation simultaneously over the age of the individual and the duration of the cohabitation. We use data from the German Family Panel (pairfam) and demonstrate that considering the two time scales as equally important provides additional insights about the transition from cohabitation to marriage or separation.