Prediction Accuracy of a Sample-size Estimation Method for ROC Studies

Abstract

Sample-size estimation is an important consideration when planning a receiver operating characteristic (ROC) study. The aim of this work was to assess the prediction accuracy of a sample-size estimation method using the Monte Carlo simulation method. Two ROC ratings simulators characterized by low reader and high case variabilities (LH) and high reader and low case variabilities (HL) were used to generate pilot data sets in two modalities. Dorfman-Berbaum-Metz multiple-reader multiple-case (DBM-MRMC) analysis of the ratings yielded estimates of the modality-reader, modality-case, and error variances. These were input to the Hillis-Berbaum (HB) sample-size estimation method, which predicted the number of cases needed to achieve 80% power for 10 readers and an effect size of 0.06 in the pivotal study. Predictions that generalized to readers and cases (random-all), to cases only (random-cases), and to readers only (random-readers) were generated. A prediction-accuracy index defined as the probability that any single prediction yields true power in the 75%-90% range was used to assess the HB method. For random-case generalization, the HB-method prediction-accuracy was reasonable, approximately 50% for five readers and 100 cases in the pilot study. Prediction-accuracy was generally higher under LH conditions than under HL conditions. Under ideal conditions (many readers in the pilot study) the DBM-MRMC-based HB method overestimated the number of cases. The overestimates could be explained by the larger modality-reader variance estimates when reader variability was large (HL). The largest benefit of increasing the number of readers in the pilot study was realized for LH, where 15 readers were enough to yield prediction accuracy >50% under all generalization conditions, but the benefit was lesser for HL where prediction accuracy was approximately 36% for 15 readers under random-all and random-reader conditions. The HB method tends to overestimate the number of cases. Random-case generalization had reasonable prediction accuracy. Provided about 15 readers were used in the pilot study the method performed reasonably under all conditions for LH. When reader variability was large, the prediction-accuracy for random-all and random-reader generalizations was compromised. Study designers may wish to compare the HB predictions to those of other methods and to sample-sizes used in previous similar studies.