Bayesian inference on protective antibody levels using case-control data

In the study of immune responses to infectious pathogens, the minimum protective antibody concentration (MPAC) is a quantity of great interest. We use case-control data to estimate the posterior distribution of the conditional risk of disease given a lower bound on antibody concentration in an at-risk subject. The concentration bound beyond which there is high credibility that infection risk is zero or nearly so is a candidate for the MPAC. A very simple Gibbs sampling procedure that permits inference on the risk of disease given antibody level is presented. In problems involving small numbers of patients, the procedure is shown to have favorable accuracy and robustness to choice/misspecification of priors. Frequentist evaluation indicates good coverage probabilities of credibility intervals for antibody-dependent risk, and rules for estimation of the MPAC are illustrated with epidemiological data.