Comparing the Structural Components Variance Estimator and U-Statistics Variance Estimator When Assessing the Difference Between Correlated AUCs with Finite Samples

COMPARING THE STRUCTURAL COMPONENTS VARIANCE ESTIMATOR AND USTATISTICS VARIANCE ESTIMATOR WHEN ASSESSING THE DIFERENCE BETWEEN CORRELATED AUCs WITH FINITE SAMPLES By Anna Leigh Bosse, M.S. A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science at Virginia Commonwealth University. Virginia Commonwealth University, 2017 Major Director: Dr. Le Kang, Associate Professor, Department of Biostatistics Introduction: The structural components variance estimator proposed by DeLong et al. (1988) is a popular approach used when comparing two correlated AUCs. However, this variance estimator is biased and could be problematic with small sample sizes. Methods: A U-statistics based variance estimator approach is presented and compared with the structural components variance estimator through a large-scale simulation study under different finite-sample size configurations. Results: The U-statistics variance estimator was unbiased for the true variance of the difference between correlated AUCs regardless of the sample size and had lower RMSE than the structural components variance estimator, providing better type 1 error control and larger power. The structural components variance estimator provided increasingly biased variance estimates as the correlation between biomarkers increased. Discussion: When comparing two correlated AUCs, it is recommended that the U-Statistics variance estimator be used whenever possible, especially for finite sample sizes and highly correlated biomarkers.