In many demographic analyses, such as the assessment of environmental cancer risks, one may be interested not only in the age-by-state distribution of the population but also in the distribution of the population by time spent in a given state. States can represent geographic areas, marital statuses, labor force participation, or states of epidemiologic exposure. Recursive formulas for the calculation of the distribution of the population according to exposure time are derived under time-invariant state transition rates. Although populations can have identical growth rates and identical age-by-state distributions, they can have very different distributions by exposure time. An application to the analysis of carcinogenic exposure states is given, using data from Finland. The effect of population heterogeneity on the estimated exposure time distributions is studied.

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