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

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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.