Multi-state, multi-time, multi-level analysis of health-related demographic events: Statistical aspects and applications
Final Report Abstract
Progress has been made in moderately advanced topics of event history analysis (EHA). Mainly, but not only, has understanding improved on the fields of missing data, which is immanent in event histories, and for misspecification. Efficient methods have been applied to the EHA-models subject to constraints and to adjacent models. Consistency and asymptotic Gaussianity had been proven mostly traditionally, and avoiding so far the counting process approach. In one situation, an EM-Algorithm had to be developed for a better algorithmic performance. (1) Knowledge on how to analyze leftcensored duration has being extended to a second time axis, namely the cohort information, and to right-censoring. (2) After insight on the pur demography of dementia, now increasingly the genesis, e.g. by considering transitions from depression or diabetes into dementia, have become assessable. (3) Knowledge of how to work with truncated durations has been extended to include covariates. (4) We have constructed, analyzed and applied new statistical testing procedures for boundary regression. (5) New insight has been reached for working with non-Markovian durations in toy models. The new models and improved methods have mainly been applied to the rich AOK-database and have confirmed state-of-the-art results on demographic trends. The interaction between demographers, applied and theoretical statisticians was fruitful with the main challenge to bridge the different trade-off’s in pace and precision between the disciplines. Furthermore, the difference between a random sample - as ideal situation of mathematical statistics - and observational data - as typical situation in demography - needed to be overcome by explicit models of heterogeneity and dependence. The cross-sectional thinking in statistics (and microeconometrics) needed to be amended by the longitudinal approach of macro-econometrics to result in the panel data situation given by the (micro-)demographic questions. Some aspects of statistics, namely the unease with parametric approaches, have not been able to resolve completely, also as a consequence of the fast pace in demographic epidemiology and due to time constraints of the project. But initial tools, such as density estimation, are now approaching the application by integrating missing information. A general value was to see that methodological needs that arise in demographic questions also arise in many other fields. Several data sets of adjacent areas like finance and economics have been analyzed. Overall results were in part resolved by the public, for instance on idw-online.de (6.8.2019), in the regional newspaper “Ostseezeitung” (8.11.2018), on abitur-und-studium.de (6.2.2017) or on wirtschaftskurier.de (17.6.2019).
Publications
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(2019) Estimating the probability of a non-Markovian rating transition from partially unobserved histories, Journal of Risk Management in Financial Institutions 12, 256–267
Weißbach, R. and F. Schmal
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(2020) Consistency for the negative binomial regression with fixed covariate, Metrika 83, 627-641
Weißbach, R. and L. Radloff
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(2020) Left-censored dementia incidences in estimating cohort effects. Lifetime Data Analysis
Weißbach, R., Kim, Y.-D., Dörre, A., Fink, A. and G. Doblhammer
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(2020) Likelihood-based analysis of doublytruncated data under the location-scale and AFT model, Computational Statistics
Dörre, A., Huang, C.-Y., Tseng, Y.-K. and T. Emura
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(2020) Nonparametric density estimation for intentionally corrupted functional data. Statistica Sinica
Delaigle, A. and A. Meister
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(2020) Rate-optimal nonparametric estimation for random coefficient regression models, Bernoulli 26, 2790–2814
Holzmann, H. and A. Meister
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(2020) The temporal association between incident late-life depression and incident dementia, Acta Psychiatrica Scandinavia
Heser, K., Fink, A., Reinke, C., Wagner, M. and G. Doblhammer
