  Extended cure survival models enable to separate covariates that affect the
probability of an event (or `long-term' survival) from those only affecting the
event timing (or `short-term' survival). We propose to generalize the bounded
cumulative hazard model to handle additive terms for time-varying (exogenous)
covariates jointly impacting long- and short-term survival. The selection of
the penalty parameters 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.

Methodology