Mortality and Aging in a Heterogeneous Population: A Stochastic Process Model with Observed and Unobserved Variables

Yashin, A.I., Manton, K.G., & Vaupel, J.W. (1983). Mortality and Aging in a Heterogeneous Population: A Stochastic Process Model with Observed and Unobserved Variables. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-83-081

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Abstract

A number of multivariate stochastic process models have been developed to represent human physiological aging and mortality. In this paper, we extend those efforts by considering the effects of unobserved state variables on the age trajectory of physiological parameters. This is accomplished by deriving the Kolmogorov-Fokker-Planck equations for the distribution of the state variables conditionally on the process of the observed state variables. Proofs are given that this form of the process will preserve the Gaussian properties of the distribution. Strategies for estimating the parameters of the distribution of the unobserved variable are suggested based on an extension of the theory of Kalman filters to include systematic mortality selection. Implications of individual differences on the trajectories of the unobserved process for observed aging changes are discussed as well as the consequences of such modeling for dealing with other types of processes in heterogeneous populations.

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