Predicting Hearing Threshold in Nonresponsive Subjects Using a Log-Normal Bayesian Linear Model in the Presence of Left-Censored Covariates

We provide a nontrivial example illustrating analysis of a Bayesian clinical trial. Many of the issues discussed in the article are emphasized in a recent Food and Drug Administration (FDA) guidance on use of Bayesian statistics in medical device clinical trials. Here we present a fully Bayesian data analysis for predicting hearing thresholds in subjects who cannot respond to usual hearing tests. The article begins with simple concepts such as simple linear regression and proceeds into more complex issues such as censoring in the dependent and independent variables. Throughout, we emphasize the substantive interpretation of the analysis. Of particular interest is interval estimation, predictive probability for outcomes in future patients, missing data, model checking, and the assessment of frequentist properties of the Bayesian method.