Download Estimation of the Force of Infection from Current Status Data Using

Estimation of the Force of Infection from Current Status Data Using
Generalized Linear Mixed Models
Harriet Namata*, Ziv Shkedy, Christel Faes, Marc Aerts and Geert
Molenberghs
Universiteit Hasselt, Campus Diepenbeek, Center for
Statistics, Biostatistics, Agoralaan, B 3590 Diepenbeek, Belgium
Email: [email protected]
Philippe Beutels and Pierre Van Damme
University of Antwerp, Epidemiology and Community Medicine, Center for Evaluation of
Vaccination, B2610 Antwerp, Belgium
Abstract
Based on seroprevalence data from rubella, mumps and varicella, we show how the force
of infection, the age-specific rate at which susceptible individuals contract infection, can
be estimated using generalized linear mixed models (McCulloch and Searle 2001).
Modelling the dependency of the cumulative probability of being infected before a given
age by penalized splines, which involve fixed and random effects, allows us to use
generalized linear mixed models techniques to estimate both the cumulative probability
and the force of infection as a function of age. Moreover, these models permit an
automatic selection of the smoothing parameter. The smoothness of the estimated force
of infection is influenced by the number of knots and the degree of the penalized spline.
Simulations with different number of knots and polynomial spline bases of different
degrees suggest, for estimating the force of infection from serological data, the use of a
quadratic penalized spline based on about 10 knots.
Keywords:
Prevalence data; Penalized splines; Generalized linear mixed models; Smoothing
parameter; Force of infection.