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We consider profile-likelihood inference based on the multinomial distribution for assessing the accuracy of a diagnostic test. The methods apply to ordinal rating data when accuracy is assessed using the area under the receiver operating characteristic (ROC) curve. Simulation results suggest that the derived confidence intervals have acceptable coverage probabilities, even when sample sizes are small and the diagnostic tests have high accuracies. The methods extend to stratified settings and situations in which the ratings are correlated. We illustrate the methods using data from a clinical trial on the detection of ovarian cancer.

This paper develops an empirical likelihood approach to testing for the presence of stochastic ordering among univariate distributions based on independent random samples from each distribution. The proposed test statistic is formed by integrating a localized empirical likelihood statistic with respect to the empirical distribution of the pooled sample. The asymptotic null distribution of this test statistic is found to have a simple distribution-free representation in terms of standard Brownian bridge processes. The approach is used to compare the lengths of rule of Roman Emperors over various historical periods, including the "decline and fall" phase of the empire. In a simulation study, the power of the proposed test is found to improve substantially upon that of a competing test due to El Barmi and Mukerjee.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ393 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm