Models to Use Receiver Operating Characteristic Curve to Evaluate Surrogacy of Biomarkers in Clinical Trials

• Activity Number: 647
• Type: Topic Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Government Statistics
• Author(s): Ying Lu*+
• Companies: Palo Alto VA CSP Coordinating Center/Stanford
• Keywords: Receiver Operating Characteristic Curves (ROC) ; Area under ROC curves ; Surrogate Endpoint ; Sample Size ; Clinical Trials ; Survival Endpoints

Abstract

Surrogate markers can improve clinical trial efficiency by answering research questions in a shorter time than the diseases-specific endpoints. As the predictive accuracy measured by area under the receiver operating characteristic (ROC) curves (AUC) is often evaluated during the validation of biomarkers, this paper discusses models to use the AUC of ROC curves to evaluate surrogacy of biomarkers in clinical trials. Both single arm design for phase II cancer trials and parallel design for phase III trials are discussed. We assume that patient population consists of a mixture of responders and non-responders. Effective treatment increases the proportion of responders. AUC of ROC is a decreased function of prediction time. Sample size formulas link the proportion of responders and AUC of ROC curves. The ratio of required sample sizes for the clinical and marker endpoints under the same design parameters is used to measure the surrogacy. Surrogacy depends on the rate of change in AUC and the range of AUC. A location shift of a biomarker for non-responders due to treatment indicates an inappropriate surrogate marker for the treatment. I discuss some application examples.