Previous approaches to modelling interval-censored data have often relied on assumptions of homogeneity in the sense that the censoring mechanism, the underlying distribution of occurrence times, or both, are assumed to be time-invariant. In this work, we introduce a model which allows for non-homogeneous behaviour in both cases. In particular, we outline a censoring mechanism based on semi-Markov processes in which interval generation is assumed to be time-dependent and we propose a Markov point process model for the underlying occurrence time distribution. We prove the existence of this process and derive the conditional distribution of the occurrence times given the intervals. We provide a framework within which the process can be accurately modelled, and subsequently compare our model to homogeneous approaches by way of a parametric example.

翻译：针对区间删失数据的建模方法先前常依赖于齐次性假设，即删失机制、事件发生时间的潜在分布或两者均被假定为时间不变。本研究提出一种允许两者均具有非齐次行为的模型。具体而言，我们基于半马尔可夫过程构建了一种删失机制，其中区间生成被视为时间依赖的，并为潜在事件发生时间分布提出了一个马尔可夫点过程模型。我们证明了该过程的存在性，并推导了给定区间条件下事件发生时间的条件分布。我们提供了一套可精确建模该过程的框架，随后通过参数化实例将本模型与齐次方法进行了比较。