Our goal in this work has been to develop a formal statistical procedure to make the differential diagnosis of metastases from second independent primaries on the basis of somatic allelic changes obtained from array copy number data. This is difficult for many reasons. The first, and possibly the most difficult step, is to organize the voluminous data into a conceptual framework that facilitates formal statistical analysis. Because of the richness and complexity of the data, this process is necessarily somewhat ad hoc, following a growing tradition in statistical genomics [32
]. Our belief is that the pivotal information for establishing the clonal origin of pairs of tumors lies in the precise comparison of the locations of specific allelic gains and losses that are potentially clonal events. These comparisons are then combined with the gross correlation patterns of losses and gains across all chromosome arms to determine an overall diagnosis for the patient. The data analyses of our various examples using this methodology suggest that the method can provide conclusive diagnoses for individual patients where the DNA is of high quality and the clonality signals are strong. Our simulation study suggests also that the statistical properties of the method compare favorably with simpler classification measures that have been proposed by other investigators.
The complexity of the data means that any proposed method, including our own, necessarily has limitations due to the analytic and modeling trade-offs required. A particularly difficult feature of the problem is the fact that the two alternative diagnoses that we are trying to distinguish are structured very differently. Under the hypothesis that the two tumors are independent the somatic mutational patterns are presumed to have arisen independently. However, we know that different genetic loci experience mutations with different frequencies in cancers, and so the method requires knowledge of these “marginal” mutation probabilities to effectively filter out the induced correlation that will necessarily occur in the mutational profiles of biologically independent tumors. Our knowledge at present of these marginal probabilities is limited, and we chose to estimate them from the relatively small data sets at our disposal. Under the hypothesis that the tumors share a clonal origin, tumors must contain allelic gains or losses that occurred in the original “clonal” cell that led to the cancers. However, even tumors of clonal origin may, and usually do, harbor numerous other non-clonal mutations. Consequently, we recognize that a change on one tumor that is not observed on the other should be evidence against the clonal hypothesis. We have approached this issue by constructing a likelihood in which the relative frequency of clonal mutations in tumors that are clonal is assumed to be known (c), but in practice we have very limited knowledge of this parameter. The initial term in the likelihood captures the broad correlation of gains and losses across the chromosome arms. In other words, an allelic gain on one tumor that is not replicated on the other tumor will contribute to a negative correlation, and that in turn provides evidence against the clonal hypothesis.
Application of the method to our various examples demonstrates that it has the potential to provide convincing evidence that some tumor pairs are of clonal origin. However, the method has some arbitrary features. First, the method requires an initial segmentation analysis to identify the allelic gains and losses. This is influenced strongly by both the segmentation method used and by the parameters of this analysis, namely the significance level for detecting an allelic change, and the MAD criterion for ensuring that the signal detected is sufficiently strong. Segmentation methodology is an evolving area of research beyond the scope of this article, and higher resolution arrays can lead to increased sensitivity to array artifacts [33
]. In practice, some judgment may need to be exercised when using segmentation to find the level of resolution that seems to be the most credible for identifying copy number changes in the data set under investigation. Second, we have restricted the entire testing strategy to the assumption that each chromosome arm possesses at most one allelic gain or loss. In practice, multiple changes may be observed within a single chromosome arm. If these more complex patterns match closely the evidence favoring clonality can be enhanced. Indeed we see such a pattern in . This is from chromosome 5q on patient #13 in the Bollet et al. [24
] data, a patient with strong overall evidence for clonality. The method could possibly benefit from further refinement to accommodate complex changes of this nature, although we acknowledge that it is not straightforward to generalize our approach to accommodate these complex changes. Our impression is that when the tumors are truly clonal, comparison of the observed single most prominent change on each chromosome arm will usually provide considerable strength of evidence. Our empirical results show that many of the tumor pairs that we analyze are diagnosed as clonal very convincingly.
Example of a closely matching complex change, from 5q on patient #13 in Bollet et al. (2008).
Other authors have suggested alternative strategies for tackling the problem. We compared our results with two recently proposed methods, both based on the creation of arbitrarily constructed scoring schemes as the diagnostic classifier. Waldman’s similarity score is a measure that essentially captures the broad correlation of allelic changes with the chromosome arm as the unit of analysis. This is similar in spirit to our construction of the first portion of the likelihood. Bollet’s partial identity score, which counts the number of places where the endpoints of allelic changes match exactly on the two tumors is similar in spirit to our construction of the second portion of the likelihood. Our comparisons of these methods suggest that use of the partial identity score has similar diagnostic properties to our likelihood ratio approach, but that use of Waldman’s similarity score lacks power. Our simulations suggest that a method (such as Bollet’s) that relies on exact matches of allelic changes is unlikely to have good properties when the arrays are “noisy”. Our method is also self-contained, in that one can use it to analyze data from a single patient without an available dataset of other patients to provide a benchmark for the score, as is required by the other proposed methods. Conversely, we do need information with which to estimate the marginal probabilities of allelic changes on each chromosome arm. It is important to note that all of the methods are dependent on the selection of segmentation algorithm, and that we need to be able to filter out small germ-line copy number variants. We have accomplished this by local averaging, but one could attempt to identify and exclude these based on prior knowledge, as Bollet et al. have done.
We have focused on the statistical issues, but there are numerous practical aspects of molecular testing that can influence the data and the resulting analyses. To accomplish array copy number testing, tumor cells must be isolated for analysis. The specimen may be substantially contaminated with normal stromal or interstitial cells, and this can radically reduce the detectable signal from any allelic change. The “quality” of the data can also be affected by whether the tumor samples are fresh frozen or obtained from formalin fixed paraffin-embedded archival material. This “quality” is reflected in the clarity of the signals that identify allelic changes. In poor quality data it is both harder to detect the changes, and also the endpoints of the changes are estimated with much greater variability. As indicated above, our analytic strategy depends on several “tuning” parameters. It also depends on further arbitrary choices, such as how to classify changes as gains versus losses, as indicated in our discussion of , and on the extent to which we elect to reduce the total number of markers by averaging adjacent markers. We need further research to determine how to select these parameters to optimize the method, recognizing that the choices may be dependent at the outset on the overall degree of noise in the data. We view this entire methodology as a suggested framework for the task of differential diagnosis of metastases and second primaries, and recognize that additional work is needed to refine the methodological details.