A multistate cure model is a statistical framework used to analyze and represent the transitions individuals undergo between different states over time, accounting for the possibility of being cured by initial treatment. This model is particularly useful in pediatric oncology where a proportion of the patient population achieves cure through treatment and therefore will never experience certain events. Despite its importance, no universal consensus exists on the structure of multistate cure models. Our study provides a novel framework for defining such models through a set of non-cure states. We develops a generalized algorithm based on the extended long data format, an extension of the traditional long data format, where a transition can be divided into two rows, each with a weight assigned reflecting the posterior probability of its cure status. The multistate cure model is built upon the current framework of multistate model and mixture cure model. The proposed algorithm makes use of the Expectation-Maximization (EM) algorithm and weighted likelihood representation such that it is easy to implement with standard packages. Additionally, it facilitates dynamic prediction. The algorithm is applied on data from the European Society for Blood and Marrow Transplantation (EBMT). Standard errors of the estimated parameters in the EM algorithm are obtained via a non-parametric bootstrap procedure, while the method involving the calculation of the second-derivative matrix of the observed log-likelihood is also presented.

翻译：多状态治愈模型是一种用于分析和表示个体在不同状态间随时间转移的统计框架，该框架考虑了初始治疗可能实现治愈的情况。该模型在儿科肿瘤学中尤为有用，因为部分患者群体通过治疗获得治愈，从而永远不会经历某些特定事件。尽管其重要性显著，但目前对于多状态治愈模型的结构尚未形成普遍共识。本研究提出了一种通过一组非治愈状态来定义此类模型的新框架。我们基于扩展长数据格式开发了一种通用算法，该格式是传统长数据格式的扩展，其中一次转移可被拆分为两行数据，每行分配一个反映其治愈状态后验概率的权重。多状态治愈模型建立在当前多状态模型和混合治愈模型的框架基础上。所提出的算法利用期望最大化（EM）算法和加权似然表示，使其易于通过标准软件包实现。此外，该方法有助于动态预测。该算法已应用于欧洲血液与骨髓移植学会（EBMT）的数据。EM算法中估计参数的标准误通过非参数自助法获得，同时本文也介绍了涉及观测对数似然二阶导数矩阵计算的方法。