New methods for analyzing serological data with applications to influenza surveillance
For decades, the hemagglutination-inhibition (HI) assay has been used in epidemiological and basic biological studies of influenza viruses. The mechanistic basis of the assay results (called titers) is not well understood. The first part of this document describes a biophysical model of HI that illuminates the mechanistic basis of and provides the theoretical motivation for new ways of interpreting titers. The biophysical model is applicable to other serological assays; this fact is illustrated using the neutralization assay. The second part of the document describes some new ways of interpreting titers, which involve, among other methods, singular value decomposition and probabilistic multidimensional scaling. The third part of the document discusses biological and mathematical issues related to the determination of the effective dimensionality of titers, and describes an algorithm for recovering unavailable titers.