We propose a new likelihood-based approach for estimation, inference and variable selection for parametric cure regression models in time-to-event analysis under random right-censoring. In this context, it often happens that some subjects are “cured”, i.e., they will never experience the event of interest. Then, the sample of censored observations is an unlabeled mixture of cured and “susceptible” subjects. Using inverse probability censoring weighting (IPCW), we propose a likelihood-based estimation procedure for the cure regression model without making assumptions about the distribution of survival times for the susceptible subjects. The IPCW approach does require a preliminary estimate of the censoring distribution, for which general parametric, semi- or nonparametric approaches can be used. The incorporation of a penalty term in our estimation procedure is straightforward; in particular, we propose \(\ell _1\)-type penalties for variable selection. Our theoretical results are derived under mild assumptions. Simulation experiments and real data analysis illustrate the effectiveness of the new approach.

我们提出了一种新的基于可能性的方法，用于在随机右删失下的事件分析中对参数治愈回归模型进行估计，推断和变量选择。在这种情况下，经常会发生某些对象被“治愈”的情况，即他们永远不会经历感兴趣的事件。然后，被检查的观察样本是治愈和“易感”受试者的未标记混合物。使用逆概率审查加权（IPCW），我们为治愈回归模型提出了一种基于似然性的估计程序，而无需对易感受试者的生存时间分布进行假设。IPCW方法确实需要对检查分布进行初步估计，可以使用一般的参数，半参数或非参数方法。在我们的估算程序中加入惩罚项很简单；我们特别建议\（\ ell _1 \） -选择变量的惩罚。我们的理论结果是在温和的假设下得出的。仿真实验和真实数据分析证明了这种新方法的有效性。