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.

翻译：扩展的治愈生存模型能够将影响事件发生概率（或“长期”存活）的协变量与仅影响事件发生时间（或“短期”存活）的协变量区分开来。本文提出对有界累积风险模型进行推广，以处理同时影响长期和短期存活的时变（外生）协变量的加性项。在该框架中，惩罚参数的选择是一个挑战。我们提出了一种基于贝叶斯P样条模型中拉普拉斯近似的快速算法。该方法受生育率研究的启发，其中女性特征（如就业状况和收入等）在个体随访期间可能以非平凡且频繁的方式发生变化。此外，本文利用德国养老基金的登记数据对该方法进行了说明，使我们能够研究女性时变收入与首次生育转变之间的关系。