Estimating the Probability of Clonal Relatedness of Pairs of Tumors in Cancer Patients

Next generation sequencing panels are being used increasingly in cancer research to study tumor evolution. A specific statistical challenge is to compare the mutational profiles in different tumors from a patient to determine the strength of evidence that the tumors are clonally related, i.e. derived from a single, founder clonal cell. The presence of identical mutations in each tumor provides evidence of clonal relatedness, although the strength of evidence from a match is related to how commonly the mutation is seen in the tumor type under investigation. This evidence must be weighed against the evidence in favor of independent tumors from non-matching mutations. In this article we frame this challenge in the context of diagnosis using a novel random effects model. In this way, by analyzing a set of tumor pairs, we can estimate the proportion of cases that are clonally related in the sample as well as the individual diagnostic probabilities for each case. The method is illustrated using data from a study to determine the clonal relationship of lobular carcinoma in situ with subsequent invasive breast cancers where each tumor in the pair was subjected to whole exome sequencing. The statistical properties of the method are evaluated using simulations, demonstrating that the key model parameters are estimated with only modest bias in small samples.