Illustration of fitted a:b model for the 15 datasets. Threshold values and 95% CIs for τ are superposed on the observed data showing the infection rates by titer value. The numbers above each bar show the number of cases of disease and the number of subjects at each binned assay value. Thresholds illustrated are those obtained by profile likelihood estimation. P-values refer to the modified likelihood ratio test with small values indicating statistical significance. GoF refers to the p-value of the goodness-of-fit test with small values implying a poor fit of the model to the data. RR is relative risk of infection above and below the threshold.