A mixture distribution approach for assessing genetic impact from twin study.

It is challenging to evaluate the genetic impacts on a biologic feature and separate them from environmental impacts. This is usually achieved through twin studies by assessing the collective genetic impact defined by the differential correlation in monozygotic twins vs dizygotic twins. Since the underlying order in a twin, determined by latent genetic factors, is unknown, the observed twin data are unordered. Conventional methods for correlation are not appropriate. To handle the missing order, we model twin data by a mixture bivariate distribution and estimate under two likelihood functions: the likelihood over the monozygotic and dizygotic twins separately, and the likelihood over the two twin types combined. Both likelihood estimators are consistent. More importantly, the combined likelihood overcomes the drawback of mixture distribution estimation, namely, the slow convergence. It yields correlation coefficient estimator of root-n consistency and allows effective statistical inference on the collective genetic impact. The method is demonstrated by a twin study on immune traits.