Likelihood-based concordance tests for analysis of ascertained twin pair multinomial data

The classic twin model design has a wide application in human genetics. Under the assumption that nongenetic effects are shared to the same degree by monozygotic (MZ) and dizygotic (DZ) twin pairs, a test of the equality of casewise concordances between MZ and DZ twins provides a clue to the influence of genetic and environmental factors on a disease. The casewise concordance is the conditional probability that given that one member of a twin pair is affected, the other is also affected. When disease prevalence is low or cost-effectiveness is considered, collection of twin pairs by ascertainment for performing casewise concordance analysis is required. In this article, by defining an overall casewise concordance parameter, several likelihood-based tests, such as likelihood ratio test LR, score test Score, the usual Wald test Wald and an alternative Wald test WaldA are investigated for a test of the equality of concordances between ascertained MZ and DZ twin pairs under multinomial models. Simulation studies were conducted for data with small sample sizes. The results show that the type I error rates and power of LR and Score are stable only when the overall casewise concordances are not extremely small or large. The Wald has higher power performance in most cases but would slightly inflate type I error rates; the WaldA is the most robust and recommended approach.