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.