Time-varying exogenous covariates with frequently changing values in double additive cure survival models: an application to fertility

Extended cure survival models enable to separate covariates that affect the long-term probability of an event (or long-term survival) from those only affecting the dynamics of events (or short-term survival). We propose to generalize the bounded cumulative hazard model to handle exogenous covariates frequently changing values over time and jointly impacting long- and short-term survival. The selection of the penalty parameters tuning the smoothness of additive terms is a challenge in that framework. A fast algorithm based on Laplace approximations in Bayesian P-spline models is proposed. The methodology is motivated by fertility studies where women’s characteristics such as the employment status and the income (to cite a few) can vary in a non-trivial and frequent way during the individual follow-up. The method is furthermore illustrated by drawing on register data from the German Pension Fund which enabled us to study how women’s time-varying earnings relate to first birth transitions.