Multi-state, multi-time, multi-level analysis of health-related demographic events: Statistical aspects and applications

人口分析在很大程度上依赖于基于人口的（纵向）研究的观察结果和过程产生的大量数据，如健康索赔数据和人口登记册。在这一建议中，我们处理的多个方面的多状态，多时间和多层次的性质的观察人口数据。扩展生存分析，健康事件意味着多个状态，保持在时间的过程中的统计单位的可观察性。然而，类似地，错误测量、双重删失和/或截断导致至事件时间的缺失测量。EM算法作为一种当代的方法，已经被证明是有用的人口统计数据的分析，特别是危险估计，当历史是不完整的。我们对人口统计学的具体贡献将是揭示预期寿命的增加是否会导致相对更多的健康年数。具体来说，我们专注于痴呆症，这是老年人最常见和最昂贵的疾病之一。我们将借鉴为分析具有类似数据生成的疾病（即癌症、蛀牙和艾滋病毒）的特定事件历史而设计的方法。作为多时间轴的一个方面，我们将在个人层面上估计最大年龄和痴呆症诊断的最大年龄增加了多少。对于（无痴呆）寿命的分布，我们将确定正确的终点，以及它与时间的函数关系，采用非参数前沿估计的最新方法。人口数据通常具有依赖性，无论是纵向的还是横向的。我们将通过研究相关模型（如马尔可夫性质）和采用抽样技术（如聚类抽样）来认识它对标准误差的膨胀效应。

Demographic analysis relies heavily on observations from population-based (longitudinal) studies and large process-generated data such as health-claims data and population registers. In this proposal, we deal with aspects of the multi-state, multi-time and multi-level nature of observational demographic data. Extending survival analysis, health events imply multiple states that preserve the observability of the statistical unit in the course of time. However similarly, erroneous measurements, double censoring and/or truncation result in missing measurements of the time-to-event. As a contemporary method, the EM algorithm has already proved useful for the analysis of demographic data, and especially for hazard estimation, when histories are incomplete. Our specific contribution to demography will be to reveal whether increasing life expectancy results in comparatively more years in good or poor health. Specifically, we focus on dementia, which is among the most common and most expensive diseases in old age. We will draw on methodology designed for the analysis of event histories specific for diseases with similar data generation, namely cancer, tooth decay and HIV. As an aspect of multiple-time axes, we will estimate, at the individual level, to what extent the maximum age and the maximum age-at-dementia diagnosis have increased. For the distribution of the (dementia-free) life duration, we will determine the right endpoint, and its functional relation to time, with recent methods from nonparametric frontier estimation. Demographic data are usually equipped with dependencies, be it longitudinal or in the cross-section. We will acknowledge its inflationary effect on the standard error by studying dependency models, like the Markovian property, and by employing methods from sampling techniques, like cluster-sampling.