T. Ng, CBER, FDA, Rockville, MD
The frequentist describes the data (or outcomes) conditioned on the unknown parameters while the Bayesian describes the parameters conditioned on the observed data. The two approaches are shown to be complementing each other in two applications, namely, (i) diagnostic test kit, and (ii) hypothesis testing.
The performance of a diagnostics test kit is evaluated based on the sensitivity and specificity, which describe the test results given the disease status of an individual. So, it is the frequentist approach. On the other hand, the positive predictive value and negative predictive value answers very practical questions given that the test result is positive and negative, respectively. So, it is the Bayesian approach.
In hypothesis testing, the frequentist approach controls the error rate of rejecting the null hypothesis given the null hypothesis is true, that is the traditional type I error rate. The Bayesian counterpart of the type I error rate is the false discovery rate, that is, the expected proportion of falsely rejected hypotheses as defined by Benjamini and Hochberg (1995). Recently, Ng (2006) argues that simultaneous testing for noninferiority and superiority increases the false discovery rate for superiority although the type I error rate is controlled.