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:延长治疗存活模式能够将影响事件概率(或`长期'生存)的共变数与只影响事件时间(或`短期'生存)的共变数区分开来,我们提议将约束性累积危险模式普遍化,处理时间(外)共变共变的累加条件,共同影响长期和短期生存。选择惩罚参数是这一框架内的一个挑战。提出了基于巴耶西亚P-斯派模型拉普差近似值的快速算法。该方法的动机是生育研究,妇女的特点,如就业状况和收入(仅举几个例子)在个别跟踪过程中可以以非三轨和频繁的方式变化。这一方法还借鉴了德国养恤基金的登记数据,该数据使我们能够研究妇女时间变化的收入如何与第一次分娩过渡相关。