In a recent article Begg et al. (2007) proposed a statistical test to determine whether or not a diagnosed second primary tumor is biologically independent of the original primary tumor, by comparing patterns of allelic losses at candidate genetic loci. The proposed Concordant Mutations Test is a conditional test, an adaptation of Fisher’s Exact Test, that requires no knowledge of the marginal mutation probabilities. The test was shown to have generally good properties, but is susceptible to anti-conservative bias if there is wide variation in mutation probabilities between loci, or if the individual mutation probabilities of the parental alleles for individual patients differ substantially from each other. In this article, a likelihood ratio test is derived in an effort to address these validity issues. This test requires pre-specification of the marginal mutation probabilities at each locus, parameters for which some information will typically be available in the literature. In simulations this test is shown to be valid, but to be considerably less efficient than the Concordant Mutations Test for sample sizes (numbers of informative loci) typical of this problem. Much of the efficiency deficit can be recovered, however, by restricting the allelic imbalance parameter estimate to a pre-specified range, assuming that this parameter is in the pre-specified range.

Keywords: Clonality, concordant mutations test, likelihood ratio test