Forecasting dementia incidence

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.