Jérôme R. Simons, Yuntao Chen, Eric Brunner, Eric French
arXiv 9 Sep 2025 · Statistics — Applications
arXiv:2509.07874 · PDF · DOI · OpenAlex · Extracted main text
This paper estimates the stochastic process of how dementia incidence evolves over time. We proceed in two steps: first, we estimate a time trend for dementia using a multi-state Cox model. The multi-state model addresses problems of both interval censoring arising from infrequent measurement and also measurement error in dementia. Second, we feed the estimated mean and variance of the time trend into a Kalman filter to infer the population level dementia process. Using data from the English Longitudinal Study of Aging (ELSA), we find that dementia incidence is no longer declining in England. Furthermore, our forecast is that future incidence remains constant, although there is considerable uncertainty in this forecast. Our two-step estimation procedure has significant computational advantages by combining a multi-state model with a time series method. To account for the short sample that is available for dementia, we derive expressions for the Kalman filter's convergence speed, size, and power to detect changes and conclude our estimator performs well even in short samples.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chen, Yuntao, Bandosz, Piotr, Stoye, George, Liu, Yuyang, Wu, Yanjua… (2023) Dementia incidence trend in England and Wales, 2002–19, and projection for dementia burden to 2040: analysis of data from the En… self | 1.000 | 9 | 4 | 100% |
| 2 | Ahmadi-Abhari, Sara, Guzman-Castillo, Maria, Bandosz, Piotr, Shipley… (2017) Temporal trend in dementia incidence since 2002 and projections for prevalence in England and Wales to 2040: modelling study | 0.843 | 5 | 3 | 60% |
| 3 | Jackson, Christopher H (2011) Multi-state models for panel data: the msm package for R | 0.737 | 3 | 2 | 100% |
| 4 | Harvey, Andrew C (1990) Forecasting, Structural Time Series Models and the Kalman Filter | 0.644 | 3 | 2 | 67% |
| 5 | Banks, James, French, Eric, McCauley, Jeremy (2025) The costs of long term care for those with cognitive impairments in England self | 0.511 | 2 | 2 | 50% |
| 6 | Cox, DR, Miller, HD (1965) The Theory of Stochastic Processes, Chapman and Hall | 0.511 | 2 | 2 | 50% |
| 7 | Busetti, Fabio, Harvey, Andrew C (2007) Testing for trend | 0.511 | 2 | 2 | 50% |
| 8 | Wolters, Frank J, Chibnik, Lori B, Waziry, Reem, Anderson, Roy, Berr… (2020) Twenty-seven-year time trends in dementia incidence in Europe and the United States: The Alzheimer Cohorts Consortium | 0.511 | 2 | 1 | 100% |
| 9 | Bougerol, Philippe (1993) Kalman Filtering with Random Coefficients and Contractions | 0.481 | 6 | 2 | 17% |
| 10 | Bhadra, Anindya, Ionides, Edward L., Laneri, Karina, Pascual, Merced… (2011) Malaria in Northwest India: Data Analysis via Partially Observed Stochastic Differential Equation Models Driven by Lévy Noise | 0.405 | 1 | 1 | 100% |
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