Model Selection Based on FDR-Thresholding Optimizing the Area under the ROC-Curve

We evaluate variable selection by multiple tests controlling the false discovery rate (FDR) to build a linear score for prediction of clinical outcome in high-dimensional data. Quality of prediction is assessed by the receiver operating characteristic curve (ROC) for prediction in independent patients. Thus we try to combine both goals: prediction and controlled structure estimation. We show that the FDR-threshold which provides the ROC-curve with the largest area under the curve (AUC) varies largely over the different parameter constellations not known in advance. Hence, we investigated a new cross validation procedure based on the maximum rank correlation estimator to determine the optimal selection threshold. This procedure (i) allows choosing an appropriate selection criterion, (ii) provides an estimate of the FDR close to the true FDR and (iii) is simple and computationally feasible for rather moderate to small sample sizes. Low estimates of the cross validated AUC (the estimates generally being positively biased) and large estimates of the cross validated FDR may indicate a lack of sufficiently prognostic variables and/or too small sample sizes. The method is applied to an oncology dataset.