A method for estimating the transmissibility of influenza using serial cross-sectional seroepidemiological data

Seroepidemiological surveillance data has been demonstrated to be useful for estimating the cumulative incidence of influenza, and measures the difference between pre- and post-epidemic seropositive fractions. Despite this, such studies relied on a chosen cut-off value for seropositivity. The aim of the present study is to develop a method to analyze distributions of serial cross-sectional seroepidemiological surveillance datasets using an epidemiological model so that the transmission potential can be estimated without imposing a cut-off value.

A mathematical model of influenza transmission with a discrete antibody titer level was constructed. The final size equation for pre- and post-epidemic titer levels was derived. Subsequently, using the estimated distribution of the dilution increase caused by infection and the measurement error distribution, the model parameters were optimized using the maximum likelihood method. A bootstrap-based confidence interval calculation and sensitivity analysis were also performed.

Without imposing a cut-off value, the cumulative incidence was quantified, thereby yielding an estimate of the basic reproduction number. For the purpose of exposition, the proposed method was applied to influenza A/Victoria/3/75(H3N2) data, and serological data between 1975 and 1976 were compared. The estimated reproduction number was greater than that using the cut-off value of the hemagglutination inhibition level with titer level 20 (dilution 1:20) or above to define positives.

The proposed method without a cut-off value offers an unbiased approach to estimating the cumulative incidence along with the reproduction number. If a cut-off value is required, the results imply that titer level 20 or above may better represent a reasonable cut-off value for calculating the incidence, but it could underestimate the basic reproduction number.