Sequential estimate of partial area under ROC curve with and optimal ratio of cases to controls

Abstract: Due to new technologies, potential variables are collected in a more efficient manner than before. Thus, how to sift effective variable from an abundance of newly discovered markers is an important issue. To this end, an adaptive sequential method is proposed for estimating the diagnostic power based on the partial area under the receiving operating characteristic curve of variables. However, the estimating accuracy of these performance criteria are usually affected by the sample sizes of two groups, say case and control. Thus, we need to decide which group to sample from as that in a two-armed bandit problem. Sequential confidence interval estimation methods are used to control the accuracy of the estimates. Both two-sided fixed-width and one-sided confidence intervals are considered. The proposed methods are proved to be optimal, since they not only guarantee the accuracy of the performance estimates, but also maintain the ratio of cases to controls converging to their corresponding optima in terms of minimization of the variance of the estimate. When the availabilities of two classes are imbalanced or the costs of sampling them are seriously unequal, our method can include suchlike information as a part of its criteria. [Copyright &y& Elsevier]