In biomedical research dealing with biomarker data, “Naïve pooling” is a common practice for combing data, and subsequently, based on pooled data, estimated diagnostic measures such as AUC are presented to assess the diagnostic ability of biomarkers. This talk will point out several severe hidden problems induced by such practice and present a new ROC framework under tree or umbrella ordering (denoted as TROC) for such data. Compared to the traditional AUC based on the pooled data, the area under TROC curve (denoted as TAUC) is a more appropriate diagnostic measure. Furthermore, issues such as optimal threshold selection will be addressed and the resulting diagnostic accuracy will be compared between naïve pooling and umbrella ordering. In the end, a published lung cancer data set will be analyzed.