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Receiver operating characteristic (ROC) curve is an effective and widely used method for evaluating the discriminating power of a diagnostic test or statistical model. As a useful statistical method, a wealth of literature about its theories and computation methods has been established. The research on ROC curves, however, has focused mainly on cross-sectional design. Very little research on estimating ROC curves and their summary statistics, especially significance testing, has been conducted for repeated measures design. Due to the complexity of estimating the standard error of a ROC curve, there is no currently established statistical method for testing the significance of ROC curves under a repeated measures design. In this paper, we estimate the area of a ROC curve under a repeated measures design through generalized linear mixed model (GLMM) using the predicted probability of a disease or positivity of a condition and propose a bootstrap method to estimate the standard error of the area under a ROC curve for such designs. Statistical significance testing of the area under a ROC curve is then conducted using the bootstrapped standard error. The validity of bootstrap approach and the statistical testing of the area under the ROC curve was validated through simulation analyses. A special statistical software written in SAS/IML/MACRO v8 was also created for implementing the bootstrapping algorithm, conducting the calculations and statistical testing.

Testing Statistical Significance of the Area under a Receiving Operating Characteristics Curve for Repeated Measures Design with Bootstrapping