Checking stationarity of the incidence rate using prevalent cohort survival data

When survival data are collected as part of a prevalent cohort study with follow-up, the recruited cases have already experienced their initiating event, say onset of a disease, and consequently the incidence process is only partially observed. Nevertheless, there are good reasons for interest in certain features of the underlying incidence process, for example whether or not it is stationary. Indeed, the well known relationship between incidence and prevalence, often used by epidemiologists, requires stationarity of the incidence rate for its validity. Also, the statistician can exploit stationarity of the incidence process by improving the efficiency of estimators in a prevalent cohort survival analysis. In addition, whether the incident rate is stationary is often in itself of central importance to medical and other researchers. We present here a necessary and sufficient condition for stationarity of the underlying incidence process, which uses only survival observations, possibly right censored, from a prevalent cohort study with follow-up. This leads to a simple graphical means of checking for the stationarity of the underlying incidence times by comparing the plots of two Kaplan-Meier estimates that are based on partially observed incidence times and follow-up survival data. We use our method to discuss the incidence rate of dementia in Canada between 1971 and 1991.