In applied time-to-event analysis, a flexible parametric approach is to model the hazard rate as a piecewise constant function of time. However, the change points and values of the piecewise constant hazard are usually unknown and need to be estimated. In this paper, we develop a fully data-driven procedure for piecewise constant hazard estimation. We work in a general counting process framework which nests a wide range of popular models in time-to-event analysis including Cox's proportional hazards model with potentially high-dimensional covariates, competing risks models as well as more general multi-state models. To construct our estimator, we set up a regression model for the increments of the Breslow estimator and then use fused lasso techniques to approximate the piecewise constant signal in this regression model. In the theoretical part of the paper, we derive the convergence rate of our estimator as well as some results on how well the change points of the piecewise constant hazard are approximated by our method. We complement the theory by both simulations and a real data example, illustrating that our results apply in rather general event histories such as multi-state models.

翻译：在应用生存分析中，一种灵活的参数化方法是将风险率建模为时间的分段常数函数。然而，分段常数风险的变化点与取值通常未知，需要估计。本文提出了一种完全数据驱动的分段常数风险估计方法。我们在一般计数过程框架下展开工作，该框架涵盖了生存分析中多种流行模型，包括可能包含高维协变量的Cox比例风险模型、竞争风险模型以及更一般的多状态模型。为构建估计量，我们首先为Breslow估计量的增量建立回归模型，随后运用融合套索技术来逼近该回归模型中的分段常数信号。在理论部分，我们推导了估计量的收敛速率，并给出了关于分段常数风险变化点被本方法逼近程度的若干结果。我们通过模拟实验和真实数据案例对理论进行了补充，证明我们的结果适用于多状态模型等相当普遍的事件历史过程。