Modelling forces of infection by using monotone local polynomials

On the basis of serological data from prevalence studies of rubella, mumps and hepatitis A, the paper describes a flexible local maximum likelihood method for the estimation of the rate at which susceptible individuals acquire infection at different ages. In contrast with parametric models that have been used before in the literature, the local polynomial likelihood method allows this age-dependent force of infection to be modelled without making any assumptions about the parametric structure. Moreover, this method allows for simultaneous nonparametric estimation of age-specific incidence and prevalence. Unconstrained models may lead to negative estimates for the force of infection at certain ages. To overcome this problem and to guarantee maximal flexibility, the local smoother can be constrained to be monotone. It turns out that different parametric and nonparametric estimates of the force of infection can exhibit considerably different qualitative features like location and the number of maxima, emphasizing the importance of a well-chosen flexible statistical model.