Constructing the best linear combination of diagnostic markers via sequential sampling

We study the best linear combination of markers in terms of the area under the receiver operating characteristic curve, since no single marker is perfect for classification purposes. The sequential fixed-width confidence interval estimate method is applied. We show that the proposed procedure is efficient in terms of the total sample size, with an optimal ratio of cases to controls, and is asymptotically consistent. The performance of our method is illustrated by synthesized data and a real example.