Handling incomplete observations with supplementary information in event history data analysis

在许多情况下都会出现不完整的观察结果。例子包括丢失、删减和截断的数据；测量误差和潜在变量等问题可能被视为特殊情况，如果我们更普遍地认为不完全观察意味着可用数据缺乏所需的信息。各种类型的不完整数据推动了事件历史数据分析中许多主要方法的进步。在现实中，引起一组特定的不完整观察的不完备机制通常是未知的和随机的，很少有科学意义。为了在努力得出有效和期望的推论中适当地解释它，分析不完整数据的统计方法需要对机制进行强有力的假设，例如在随机和非信息审查中缺失，和/或对机制分布的估计。然而，这些假设通常无法用目前不完整的数据来验证，并且在实践中经常被批评为不可信。此外，估计机制的分布往往使初步推断复杂化。我们的目标是为不完全数据分析发展新的理论和方法。我们提出了一个不完全观测的新公式，它扩展了粗化的概念并包含了截断。请注意，附加信息可能是关于潜在分布或不完整性机制的知识和/或数据形式，这些信息通常很容易获得，或者很容易通过设计从同一研究或不同的信息源中收集。我们探索补充信息的有用性，并开发处理方法，以解决识别不完备性机制，提高推理效率和减少流行病学，市场营销和可靠性中真实数据集产生的计算强度的特定挑战。我们专注于事件历史分析，但方法有更广泛的应用；这个研究项目通过纵向和空间分析的扩展来例证它。研究成果将为理论提供新的启示，为处理不完整数据提供可行的替代方法，并有助于推进实践。

Incomplete observations arise in numerous settings. Examples include missing, censored, and truncated data; problems such as measurement errors and latent variables may be viewed as special cases, if we take incomplete observations more generally to mean that the available data lack desired information. Various types of incomplete data motivated many major methodology advances in event history data analysis. In reality, the incompleteness mechanism that gives rise to a particular set of incomplete observations is usually unknown and random, and rarely of scientific interest. To account for it properly in an effort to draw valid and desired inferences, statistical methods for analyzing incomplete data require strong assumptions on the mechanism, such as missing at random and non-informative censoring, and/or estimation of the mechanism's distribution. However, the assumptions cannot be verified in general with the current incomplete data, and are regularly criticized as implausible in practice. Plus, estimating the distribution of the mechanism often complicates the primary inference. Our objective is the development of new theory and methods for incomplete data analysis. We propose a novel formulation for incomplete observations, which extends the notion of coarsening and incorporates truncation. Notice that additional information, which may be in the form of knowledge and/or data on the underlying distribution or the incompleteness mechanism, is often readily available or easily collected by design from the same study or from different information sources. We explore the usefulness of supplementary information, and develop treatments to address particular challenges in identifying the incompleteness mechanism, improving inference efficiency and reducing computational intensity arising from real data sets in epidemiology, marketing and reliability. We focus on event history analysis but the methodologies have broader applications; this research program exemplifies it by extensions in longitudinal and spatial analysis. The research outcomes will shed new light on the theory, provide feasible alternative approaches to handling incomplete data, and help to advance the practice.