Precision and bias of a normal finite mixture distribution model to analyze twin data when zygosity is unknown: simulations and application to IQ phenotypes on a large sample of twin pairs.

The classification of twin pairs based on zygosity into monozygotic (MZ) or dizygotic (DZ) twins is the basis of most twin analyses. When zygosity information is unavailable, a normal finite mixture distribution (mixture distribution) model can be used to estimate components of variation for continuous traits. The main assumption of this model is that the observed phenotypes on a twin pair are bivariately normally distributed. Any deviation from normality, in particular kurtosis, could produce biased estimates. Using computer simulations and analyses of a wide range of phenotypes from the U.K. Twins' Early Developments Study (TEDS), where zygosity is known, properties of the mixture distribution model were assessed. Simulation results showed that, if normality assumptions were satisfied and the sample size was large (e.g., 2,000 pairs), then the variance component estimates from the mixture distribution model were unbiased and the standard deviation of the difference between heritability estimates from known and unknown zygosity in the range of 0.02-0.20. Unexpectedly, the estimates of heritability of 10 variables from TEDS using the mixture distribution model were consistently larger than those from the conventional (known zygosity) model. This discrepancy was due to violation of the bivariate normality assumption. A leptokurtic distribution of pair difference was observed for all traits (except non-verbal ability scores of MZ twins), even when the univariate distribution of the trait was close to normality. From an independent sample of Australian twins, the heritability estimates for IQ variables were also larger for the mixture distribution model in six out of eight traits, consistent with the observed kurtosis of pair difference. While the known zygosity model is quite robust to the violation of the bivariate normality assumption, this novel finding of widespread kurtosis of the pair difference may suggest that this assumption for analysis of quantitative trait in twin studies may be incorrect and needs revisiting. A possible explanation of widespread kurtosis within zygosity groups is heterogeneity of variance, which could be caused by genetic or environmental factors. For the mixture distribution model, violation of the bivariate normality assumption will produce biased estimates.