A likelihood-ratio test of twin zygosity using molecular genetic markers

The importance of using multiple polymorphic genetic markers to determine unambiguously whether a twin pair is monozygotic (MZ) or dizygotic (DZ) has long been recognized. Concordance among a set of markers is used as evidence of monozygosity, as it would be improbable for DZ twins to be concordant at a large number of polymorphic loci. Several sources give a formula for the probability of two DZ twins sharing the same genotype at a locus, assuming knowledge of allele frequencies but not of either twin's genotype; this probability can be used to determine whether a set of markers will reliably distinguish between MZ and DZ status in a randomly selected twin pair. If the shared genotype is known, however, the likelihood-ratio test (LRT) of the null hypothesis of dizygosity against the alternative hypothesis of monozygosity takes into account the observed genotype and, by the Neyman-Pearson lemma, is the most powerful test of its size. The LRT is equivalent to conditioning on the genotype of one of the twins, and computing the probability, assuming DZ status, of the other twin sharing that genotype. The resulting p values are frequently lower than those produced by the unconditional probability, especially if rare alleles are observed. The unconditional probability can be recapitulated from conditional probabilities by averaging across all of the conditioned sibling's possible genotypes. To illustrate properties of the LRT applied to multiple markers, the probability distribution of the LRT p value is computed from allele frequencies of twelve unlinked markers published in Elbaz et al. (2006) and compared with the p value computed from unconditional probabilities.