Semi-competing risks refers to the survival analysis setting where the occurrence of a non-terminal event is subject to whether a terminal event has occurred, but not vice versa. Semi-competing risks arise in a broad range of clinical contexts, with a novel example being the pregnancy condition preeclampsia, which can only occur before the `terminal' event of giving birth. Models that acknowledge semi-competing risks enable investigation of relationships between covariates and the joint timing of the outcomes, but methods for model selection and prediction of semi-competing risks in high dimensions are lacking. Instead, researchers commonly analyze only a single or composite outcome, losing valuable information and limiting clinical utility -- in the obstetric setting, this means ignoring valuable insight into timing of delivery after preeclampsia has onset. To address this gap we propose a novel penalized estimation framework for frailty-based illness-death multi-state modeling of semi-competing risks. Our approach combines non-convex and structured fusion penalization, inducing global sparsity as well as parsimony across submodels. We perform estimation and model selection via a pathwise routine for non-convex optimization, and prove the first statistical error bound results in this setting. We present a simulation study investigating estimation error and model selection performance, and a comprehensive application of the method to joint risk modeling of preeclampsia and timing of delivery using pregnancy data from an electronic health record.

翻译：半竞争风险是指生存分析中的一种情形，其中非终点事件的发生受限于终点事件是否发生，但反之则不然。半竞争风险广泛存在于临床场景中，一个典型的新例是妊娠期子痫前期——该疾病仅能在分娩这一“终点”事件发生前出现。考虑半竞争风险的模型能够研究协变量与结局联合时间之间的关系，但高维场景下针对半竞争风险的模型选择与预测方法仍付之阙如。研究者通常仅分析单一或复合结局，这导致宝贵信息的丢失并限制了临床实用性——在产科领域，这意味着子痫前期发作后分娩时机的关键洞察被忽视。为填补这一空白，我们提出了一种基于脆弱性的疾病-死亡多状态建模半竞争风险的惩罚估计新框架。该方法融合非凸惩罚与结构化融合惩罚，可在全局稀疏性与子模型间简约性之间取得平衡。我们通过非凸优化的路径算法实现估计与模型选择，并首次推导出该场景下的统计误差界。通过模拟研究评估估计误差与模型选择性能后，我们将该方法系统应用于基于电子健康档案妊娠数据的子痫前期与分娩时机联合风险建模。