A Non-parametric Method for the Reconstruction of Age- and Time-Dependent Incidence from the Prevalence Data of Irreversible Diseases with Differential Mortality

A method is proposed for reconstructing the time and age dependence of incidence rates from successive age-prevalence cross sections taken from the sentinel surveys of irreversible diseases when there is an important difference in mortality between the infected and susceptible subpopulations. The prevalence information at different time–age points is used to generate a surface; the time–age variations along the life line profiles of this surface and the difference in mortality rates are used to reconstruct the time and age dependence of the incidence rate. Past attempts were based on specified parametric forms for the incidence or on the hypothesis of time-invariant forms for the age–prevalence cross sections. The proposed method makes no such assumptions and is thus capable of coping with rapidly evolving prevalence situations. In the simulations carried out, it is found to be resilient to important random noise components added to a prescribed incidence rate input. The method is also tested on a real data set of successive HIV age–prevalence cross sections from Burundi coupled to differential mortality data on HIV+ and HIV− individuals. The often-made assumption that the incidence rate can be written as the product of a calendar time component and an age component is also examined. In this case, a pooling procedure is proposed to estimate the time and the age profiles of the incidence rate using the reconstructed incidence rates at all time–age points.