Interval censored data commonly arise in medical studies when the event time of interest is only known to lie within an interval. In the presence of a cure subgroup, conventional mixture cure models typically assume a logistic model for the uncure probability and a proportional hazards model for the susceptible subjects. However, in practice, the assumptions of parametric form for the uncure probability and the proportional hazards model for the susceptible may not always be satisfied. In this paper, we propose a class of flexible single-index semiparametric transformation cure models for interval-censored data, where a single-index model and a semiparametric transformation model are utilized for the uncured and conditional survival probability, respectively, encompassing both the proportional hazards cure and proportional odds cure models as specific cases. We approximate the single-index function and cumulative baseline hazard functions via the kernel technique and splines, respectively, and develop a computationally feasible expectation-maximisation (EM) algorithm, facilitated by a four-layer gamma-frailty Poisson data augmentation. Simulation studies demonstrate the satisfactory performance of our proposed method, compared to the spline-based approach and the classical logistic-based mixture cure models. The application of the proposed methodology is illustrated using the Alzheimers dataset.

翻译：区间删失数据在医学研究中普遍存在，此时感兴趣的事件发生时间仅知其落于某个区间内。当存在治愈亚组时，传统的混合治愈模型通常对未治愈概率采用逻辑斯蒂模型，而对易感个体采用比例风险模型。然而在实践中，未治愈概率的参数形式假设以及易感个体的比例风险模型假设未必总能满足。本文针对区间删失数据提出一类灵活的单指标半参数变换治愈模型，其中分别采用单指标模型和半参数变换模型刻画未治愈概率与条件生存概率，该框架将比例风险治愈模型和比例优势治愈模型均包含为特例。我们分别通过核技巧与样条函数逼近单指标函数和累积基准风险函数，并构建了计算可行的期望最大化算法，该算法通过四层伽马脆弱泊松数据增广技术实现。模拟研究表明，与基于样条的方法及经典逻辑斯蒂混合治愈模型相比，所提方法具有令人满意的性能。本文通过阿尔茨海默病数据集展示了所提方法的应用。