The Annals of Statistics

Demographic Incidence Rates and Estimation of Intensities with Incomplete Information

Ornulf Borgan and Henrik Ramlau-Hansen

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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.

Article information

Ann. Statist., Volume 13, Number 2 (1985), 564-582.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62M05: Markov processes: estimation
Secondary: 62P99: None of the above, but in this section

Asymptotic theory cohort analysis counting processes cumulative incidence rates martingales occurrence/exposure rates time-continuous Markov chains


Borgan, Ornulf; Ramlau-Hansen, Henrik. Demographic Incidence Rates and Estimation of Intensities with Incomplete Information. Ann. Statist. 13 (1985), no. 2, 564--582. doi:10.1214/aos/1176349539.

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