Linking the seroresponse to infection to within-host heterogeneity in antibody production

A recently published model for the serum antibody response to infection appeared well suited for use in statistical analyses of longitudinal serological data. The published model assumed exponential decay with fixed rates for pathogen and serum antibody kinetics, ignoring any within-host heterogeneity in the seroresponse. A bi-exponential model shows that there is rapid initial decay followed by a prolonged period of persistent low serum antibody concentrations. We propose a small modification of the decay model that greatly increases its flexibility by allowing for non-exponential antibody decay. The modified model produces power functions that may be interpreted as a mixture of exponential decay curves, with a mixing distribution representing the relative contribution of many centres of antibody production to the serum antibody concentration. Fitting the power function decay model to observed longitudinal data for pertussis shows improved goodness of fit compared to the exponential decay model, with estimates for the shape parameter (r=2.2; 95% CI (1.7-2.8)) that differ from exponential shape (r=1). The power function decay model predicts more persistent antibody concentrations in the long term (symptomatic threshold reached >30 years after infection) which, when used in biomarker studies, will lead to lower estimates of seroconversion rates compared to exponential antibody decay.