Optimal sampling ratios in comparative diagnostic trials

A subjective sampling ratio between the case and the control groups is not always an efficient choice to maximize the power or to minimize the total required sample size in comparative diagnostic trials. We derive explicit expressions for an optimal sampling ratio based on a common variance structure shared by several existing summary statistics of the receiver operating characteristic curve. We propose a two-stage procedure to estimate adaptively the optimal ratio without pilot data. We investigate the properties of the proposed method through theoretical proofs, extensive simulation studies and a real example in cancer diagnostic studies.