Testing clonal relatedness of tumors using array comparative genomic hybridization: a statistical challenge.

In recent years several investigative groups have sought to use array technologies that characterize somatic alterations in tumors, such as array comparative genomic hybridization (ACGH), to classify pairs of tumors from the same patients as either independent primary cancers or metastases. A wide variety of strategies have been proposed. Several groups have endeavored to use hierarchical clustering for this purpose. This technique was popularized in genomics as a means of finding clusters of patients with similar gene expression patterns with a view to finding subcategories of tumors with distinct clinical characteristics. Unfortunately, this method is not well suited to the problem of classifying individual pairs of tumors as either clonal or independent. In this article we show why hierarchical clustering is unsuitable for this purpose, and why this method has the paradoxical property of producing a declining probability that clonal tumor pairs will be correctly identified as more information is accrued (i.e., more patients). We discuss alternative strategies that have been proposed, which are based on more conventional conceptual formulations for statistical testing and diagnosis, and point to the remaining challenges in constructing valid and robust techniques for this problem.