Bayesian inference on protective antibody levels using case-control data

In the study of immune responses to infectious pathogens, the minimum prote ctive antibody concentration (MPAC) is a quantity of great interest. We use case-control data to estimate the posterior distribution of the conditiona l risk of disease given a lower bound on antibody concentration in an at-ri sk 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 ver y simple Gibbs sampling procedure that permits inference on the risk of dis ease given antibody level is presented. In problems involving small numbers of patients, the procedure is shown to have favorable accuracy and robustn ess 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 epidemiolo gical data.