Penalized estimation of frailty‐based illness–death models for semi‐competing risks

Semi‐competing risks refer to the time‐to‐event 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, including studies of preeclampsia, a condition that may arise during pregnancy and for which delivery is a terminal event. 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. Moreover, in such settings 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 statistical error rate 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.