Handling incomplete observations with supplementary information in event history data analysis

不完整的观察在许多情况下都会出现。例如，丢失、删除和截断数据；如果我们将不完整的观测更广泛地视为可用数据缺乏所需信息，则诸如测量误差和潜在变量之类的问题可能被视为特例。各种类型的不完全数据推动了事件历史数据分析的许多主要方法论的进步。在现实中，导致一组特定的不完整观测的不完整机制通常是未知的和随机的，很少有科学价值。为了适当地解释这一点，以努力得出有效和所需的推论，分析不完整数据的统计方法需要对机制做出强有力的假设，例如随机缺失和非信息性审查，和/或对机制分布的估计。然而，这些假设不能用目前不完整的数据在总体上得到验证，而且经常被批评为在实践中不可信。此外，估计机制的分布往往会使主要推断复杂化。我们的目标是发展不完全数据分析的新理论和新方法。我们提出了一种新的不完全观测公式，它扩展了粗化的概念，并加入了截断。注意，可能是关于基本分布或不完整机制的知识和/或数据形式的补充信息，往往很容易从同一项研究或不同的信息来源通过设计获得或很容易收集。我们探索补充信息的有用性，并开发治疗方法来解决在确定不完备性机制、提高推理效率和降低流行病学、营销和可靠性方面来自真实数据集的计算强度方面的特殊挑战。我们专注于事件历史分析，但方法有更广泛的应用；本研究计划通过在纵向和空间分析方面的扩展来举例说明。研究成果将为这一理论提供新的启示，为处理不完整数据提供可行的替代方法，并有助于推动实践。

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.