Stationarity in a prevalent cohort study with follow-up

In a prevalent cohort study with follow-up, the incidence process is not directly observed since only the onset times of prevalent cases can be ascer-tained. Several important consequences follow if one can establish station-arity of the incidence process: (1)The useful epidemiological relationship between prevalence, incidence, and mean duration holds, (2)There is im-proved efficiency when estimating the underlying survivor function from a prevalent cohort study with follow-up, (3)The constancy of the incidence rate is established, and (4)The constant incidence rate can be estimated using data from a prevalent cohort study. We propose a formal test for stationarity using data from a prevalent cohort study with follow-up, and establish new characterizations of station-arity, and of useful types of departure from stationarity. A dual to the problem of establishing stationarity by comparing the backward and forward recurrence times is addressed. Assuming stationar-ity of the underlying incidence process, we use the backward and forward recurrence times to verify whether the underlying survival distribution is independent of the date of onset. In doing so, we characterize specific types of dependence of the underlying survival distribution on calendar time. If the data are consistent with stationarity of the incidence rate, then a natural next step is to estimate the (constant) incidence rate. We derive the nonparametric maximum likelihood estimator of the constant incidence rate, prove that the estimator is weakly consistent, and show how one may construct an asymptotic confidence interval for the incidence rate. One main advantage of our procedure is that it only requires the completion of a single prevalent cohort study with follow-up. i We apply our test for stationarity to data obtained as part of the Canadian Study of Health and Aging to verify that the incidence rate of dementia amongst the elderly in Canada has remained constant. Upon concluding that this constancy is plausible, we estimate the incidence rate. i