Computing Sample Size for Receiver Operating Characteristic Studies

RATIONALE AND OBJECTIVES: Hanley and McNeil (1982) proposed a nonparametric method for computing the standard error of the area under the receiver operating characteristic (ROC) curve. The method has been important in planning the minimum sample size for ROC studies. However, the validity of this method for rating data with various standard deviation ratios has not been investigated. METHODS: A simulation study was conducted to compare the empirical standard error of the area under the curve with Hanley and McNeil's estimate over a range of parameters. An alternative method of computing the standard error based on a binormal distribution is proposed. RESULTS: The method of Hanley and McNeil can lead to underestimation of the minimum sample size. The proposed method provides more appropriate estimates of sample size. CONCLUSIONS: When determining sample size for a study of the area under the ROC curve where rating data are used, the standard error estimator based on the binormal distribution should be used.