Semi-parametric estimation of age-time specific infection incidence from serial prevalence data

Many infections cause lasting detectable immune responses, whose prevalence can be estimated from cross-sectional surveys. However, such surveys do not provide direct information on the incidence of infection. We address the issue of estimating age and time specific incidence from a series of prevalence surveys under the assumption that incidence changes exponentially with time, but make no assumption about the age specific incidence. We show that these assumptions lead to a proportional hazards model and estimate its parameters using semi parametric maximum likelihood methods. The method is applied to tuberculin surveys in The Netherlands to explore age dependence of the risk of tuberculous infection in the presence of a strong secular decline in this risk.