• fractional polynomials
• generalized linear models
• nonlinear least squares models
• confidence intervals for a binomial proportion
• force of infection
• seroprevalence
• serological survey

The force of infection is a fundamental epidemiological parameter of infectious diseases. For many infectious diseases it is assumed that the force of infection is age-dependant. Although the force of infection can be estimated directly from a follow up study, it is much more common to have cross-sectional seroprevalence data from which the seroprevalence and the force of infection can be estimated. Here we propose to model the seroprevalence with three different parametric models: a nonlinear least squares model proposed by Farrington (1990); a logistic model, estimated using the generalized linear models; two fractional polynomial models of different order. We illustrate the methods on three seroprevalence samples, taken by the literature, regarding the following infectious diseases: mumps, rubella and parvovirus. Besides, in order to determine the optimal sample size for a serological survey, we show the serious problems of the standard confidence interval for a binomial proportion and we introduce some alternative confidence intervals proposed by the literature.