Complete observation of event histories is often impossible due to sampling effects such as right-censoring and left-truncation, but also due to reporting delays and incomplete event adjudication. This is for example the case during interim stages of clinical trials and for health insurance claims. In this paper, we develop a parametric method that takes the aforementioned effects into account, treating the latter two as partially exogenous. The method, which takes the form of a two-step M-estimation procedure, is applicable to multistate models in general, including competing risks and recurrent event models. The effect of reporting delays is derived via thinning, extending existing results for Poisson models. To address incomplete event adjudication, we propose an imputed likelihood approach which, compared to existing methods, has the advantage of allowing for dependencies between the event history and adjudication processes as well as allowing for unreported events and multiple event types. We establish consistency and asymptotic normality under standard identifiability, integrability, and smoothness conditions, and we demonstrate the validity of the percentile bootstrap. Finally, a simulation study shows favorable finite sample performance of our method compared to other alternatives, while an application to disability insurance data illustrates its practical potential.

翻译：由于右删失和左截断等抽样效应，以及报告延迟和不完全事件裁定，事件历史的完整观测通常难以实现。例如，在临床试验的中期阶段和健康保险理赔中常出现此类情况。本文提出一种参数化方法，将前述效应纳入考量，并将后两种效应视为部分外生变量。该方法采用两步M估计过程的形式，可应用于一般多状态模型，包括竞争风险模型和复发事件模型。报告延迟的影响通过稀疏化推导得出，扩展了泊松模型的现有结论。针对不完全事件裁定问题，我们提出一种基于插补的似然方法，相较于现有方法，其优势在于允许事件历史与裁定过程之间存在依赖关系，且能处理未报告事件及多种事件类型。我们在标准的可识别性、可积性和光滑性条件下建立了相合性和渐近正态性，并验证了百分位自助法的有效性。最后，模拟研究显示本方法相较于其他替代方法在有限样本下表现更优，而基于伤残保险数据的应用案例则展示了其实用潜力。