Demographic Incidence Rates and Estimation of Intensities with Incomplete Information

Demographic Incidence Rates and Estimation of Intensities with Incomplete Information

Many population processes in demography, epidemiology and other fields can be represented by a time-continuous Markov chain model with a finite state space. If we have complete information on the life history of a cohort, the intensities of the Markov model may be estimated by the occurrence/exposur...

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Veröffentlicht in:The Annals of Statistics. - Institute of Mathematical Statistics. - 13(1985), 2, Seite 564-582
1. Verfasser: Borgan, Ornulf (VerfasserIn)
Weitere Verfasser: Ramlau-Hansen, Henrik
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1985
Zugriff auf das übergeordnete Werk:The Annals of Statistics
Schlagworte:Asymptotic theory cohort analysis counting processes cumulative incidence rates martingales occurrence/exposure rates time-continuous Markov chains Mathematics Behavioral sciences Social sciences
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520 |a Many population processes in demography, epidemiology and other fields can be represented by a time-continuous Markov chain model with a finite state space. If we have complete information on the life history of a cohort, the intensities of the Markov model may be estimated by the occurrence/exposure rates or by nonparametric techniques. In many situations, however, we have only incomplete information. In this paper we consider the special, but important, case where the occurrences and the total exposure are known, but not the distribution of the latter over the various separate statuses. Methods for handling such data, so-called demographic incidence rates, and methods for estimating the intensities from this kind of data, are known in the literature. However, their statistical properties are only vaguely known. The present paper gives a thorough presentation of the theory of these methods, and provide rigorous proofs of their statistical properties using stochastic process theory. 
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