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以人口为基础的(纵向)研究的观察结果，以及健康报销数据和人口登记册等大量程序生成的数据。在这项建议中，我们处理多状态、多时间和多层次的观测人口统计数据的各个方面。扩展生存分析，健康事件意味着在一段时间内保持统计单位的可观察性的多个状态。然而，类似地，错误的测量、双重审查和/或截断会导致事件间隔时间的测量丢失。作为一种当代的方法，EM算法已经被证明对人口统计数据的分析很有用，特别是在历史不完整的情况下进行危险评估。我们对人口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长的健康状况。具体地说，我们关注痴呆症，这是老年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的特定事件历史而设计的方法，即癌症、龋齿和艾滋病毒。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最大痴呆症诊断年龄增加到什么程度。对于(无痴呆)寿命的分布，我们将使用非参数前沿估计的最新方法来确定正确的终点及其与时间的函数关系。人口统计数据通常带有相关性，无论是纵向的还是横截面的。我们将通过研究依赖模型，如马尔科夫性质，并通过使用抽样技术的方法，如集群抽样，来认识到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.