Identifying combinations of cancer markers for further study as triggers of early intervention

In many long-term clinical trials or cohort studies, investigators repeatedly collect and store tissue or serum specimens and later test specimens from cancer cases and a random sample of controls for potential markers for cancer. An important question is what combination, if any, of the molecular markers should be studied in a future trial as a trigger for early intervention. To answer this question, we summarized the performance of various combinations using Receiver Operating Characteristic (ROC) curves, which plot true versus false positive rates. To construct the ROC curves, we proposed a new class of nonparametric algorithms which extends the ROC paradigm to multiple tests. We fit various combinations of markers to a training sample and evaluated the performance in a test sample using a target region based on a utility function. We applied the methodology to the following markers for prostate cancer, the last value of total prostate-specific antigen (PSA), the last ratio of total to free PSA, the last slope of total PSA, and the last slope of the ratio. In the test sample, the ROC curve for last total PSA was slightly closer to the target region than the ROC curve for a combination of four markers. In a separate validation sample, the ROC curve for last total PSA intersected the target region in 77% of bootstrap replications, indicating some promise for further study. We also discussed sample size calculations.