Statistical modelling for complex longitudinal multi-state data

拟议研究计划的主要目标是改进和发展事件历史分析方法，以分析复杂调查的纵向数据。 事件历史分析和复杂调查是统计学中相互独立发展的两个领域。事件历史分析的起源在于用于估计生存时间的生存分析模型；而复杂调查数据的起源在于抽样设计，它允许人们通过过度抽样和不足抽样来降低成本。虽然复杂的多阶段抽样有很多好处，但主要的缺点是使调查数据的分析变得复杂。事件历史分析中的模型，顾名思义，考虑了个人的协变量历史，并专门为分析纵向数据而开发。这些模型还解决了不完整数据的类型，如正确审查，这可能是由于调查中失去后续行动的个人的自然减员或调查小组结束时发生的。也可以解决在复杂的纵向数据中发生的偏差，称为左截断。例如，当失业咒语因面板的启动而被切断，因此是不完整的时，就会发生左截断。 例如，来自事件历史分析的有限方法已经被用于分析失业时期。通常情况下，不完整的数据，例如左侧截断的法术，会被丢弃，而剩余的法术则通过使用共享脆弱模型在法术之间引入对同一个体的依赖来分析。多状态模型提供了卓越的参数化。对于失业持续时间，最简单的多状态模型将允许一个人在两个状态之间跳跃：就业和失业。失业时期也被称为失业状态下的逗留时间。 我的建议是开发多状态模型来解释面板调查数据的共同特征，例如，许多人的逗留时间信息不完整。这种方法的一个主要优点是，参数化捕获了种群中动态过程的可能基本元素。此外，通过开发将丢失数据的人包括在内的可能性和优化它们的方法来处理丢失逗留时间信息等特征，将显著改进从这些复杂的纵向调查中得出的推断。

The primary objective of the proposed research program is the refinement and development of methodologies in event history analysis for the analysis of longitudinal data from complex surveys. Event history analysis and the field of complex surveys are two areas in statistics which have developed independently of one another. The origins of event history analysis lies in survival analysis models used to estimate survival times; whereas the origins of complex survey data lie in sampling designs which allow one to lower costs by over sampling and under sampling particular sub-populations. Although there are many benefits to complex multistage sampling, the main disadvantage is that is complicates the analysis of survey data. Models in event history analysis, as the name suggests, account for the covariate histories of individuals and are specifically developed for the analysis of longitudinal data. These models also address types of incomplete data such as right censoring which can occur either from the attrition of individuals as people are lost to follow up in the survey or by the end of a survey panel. A bias which occurs in complex longitudinal data known as left truncation can also be addressed. Left truncation occurs when for example an unemployment spell is cut off by the start of a panel and is therefore incomplete. Limited methods from event history analysis have already been used to analyze unemployment spells for example. Typically incomplete data, such as left truncated spells, are discarded and the remaining spells are analyzed by introducing a dependency between spells on the same individual using a shared frailty model. Multi-state models offer a superior parametrization. For unemployment durations, the simplest multi-state model will allow one to jump between two states: employed and unemployed. An unemployment spell is also known as a sojourn time in the unemployment state. My proposal is to develop multi-state models to account for common features of panel survey data, such as, incomplete sojourn time information for many individuals. A primary advantage of this approach is that the parametrization captures may essential elements of a dynamic process in a population. Furthermore, addressing features such as missing sojourn time information by developing likelihoods to include people with missing data and methods to optimize them will significantly improve inference from these complex longitudinal surveys.