Modeling Forces of Infection Using Monotone Local Polynomials

Based on serological data from prevalence studies of rubella, mumps and hepatitis A, this 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 to parametric models used before in the literature, the local polynomial likelihood method allows one to model this age-dependent force of infection 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 considerable different qualitative features like location and number of maxima, emphasizing the importance of a well-chosen flexible statistical model.