We consider survival data in the presence of a cure fraction, meaning that some subjects will never experience the event of interest. We assume a mixture cure model consisting of two sub-models: one for the probability of being uncured (incidence) and one for the survival of the uncured subjects (latency). Various approaches, ranging from parametric to nonparametric, have been used to model the effect of covariates on the incidence, with the logistic model being the most common one. We propose a monotone single-index model for the incidence and introduce a new estimation method that is based on the profile maximum likelihood approach and techniques from isotonic regression. The monotone single-index structure relaxes the parametric logistic assumption while maintaining interpretability of the regression coefficients. We investigate the consistency of the proposed estimator and show through a simulation study that, when the monotonicity assumption is satisfied, it performs better compared to the non-constrained single-index/Cox mixture cure model. To illustrate its practical use, we use the new method to study melanoma cancer survival data.

翻译：我们考虑存在治愈比例的生存数据，即部分受试者永远不会经历目标事件。采用由两个子模型构成的混合治愈模型：一个用于预测未治愈概率（发病率），另一个用于描述未治愈患者的生存期（潜伏期）。从参数化到非参数化的多种方法已被用于建模协变量对发病率的影响，其中逻辑模型最为常见。本文提出发病率的单调单指标模型，并基于剖面极大似然方法和保序回归技术建立新估计方法。单调单指标结构在保持回归系数可解释性的同时放松了参数逻辑假设。我们研究了所提估计量的一致性，并通过模拟研究表明：当单调性假设成立时，该模型相较于无约束的单指标/Cox混合治愈模型表现更优。为说明其实用价值，我们采用新方法分析黑色素瘤癌症生存数据。