On the non‐inferiority of a diagnostic test based on paired observations

Non-inferiority of a diagnostic test to the standard or the optimum test is a common issue in medical research. Often we want to determine if a new diagnostic test is as good as the standard reference test. Sometimes we are interested in an inexpensive test that may have an acceptably inferior sensitivity or specificity. While hypothesis testing procedures and sample size formulae for the equivalence of sensitivity or specificity alone have been proposed, very few studies have discussed simultaneous comparisons of both parameters. In this paper, we present three different testing procedures and sample size formulae for simultaneous comparison of sensitivity and specificity based on paired observations and with known disease status. These statistical procedures are then used to compare two classification rules that identify women for future osteoporotic fracture. Simulation experiments demonstrate that the new tests and sample size formulae give the appropriate type I and II error rates. Differences between our approach and the approach of Lui and Cumberland are discussed.