A method to estimate demographic intensities via cumulative incidence rates

In many situations it is impossible to calculate the occurrence/exposure rates which are so important for analysis in demography, epidemiology, and other fields, because the only information available for each age group is the occurrences and total exposure, but not the distribution of the latter over the various separate statuses. The literature contains a method to estimate the occurrence/ exposure rates from cumulative incidence rates for closed cohorts in some simple situations of this kind. The purpose of this paper is to justify the method by a probabilistic argument, to generalize it to cover a much broader set of cases, described as time-continuous Markov chains, and to illustrate it with some new sets of data. The method is originally based on an assumption of nondifferential mortality, but our findings suggest that it is strongly robust against deviations from this assumption. We also comment upon the effect of migration.