On the covariance between parameter estimates in models of twin data

We study the covariance between estimates of additive genetic variance and either dominance genetic variance or common environmental variance in likelihood-based twin analyses. The central tools used in these investigations are the asymptotic covariances of variance component estimates, which we present for several commonly used twin models. We first illustrate the use of the asymptotic covariance terms for determining the optimal ratio of monozygotic to dizygotic group sample sizes for a twin study. We then focus attention on the asymptotic correlations between estimates of additive genetic variance, and either dominance genetic variance or common environmental variance, and their use in understanding when parameters are efficiently estimable from twin data. The results of this investigation are confirmed by simulation studies, and highlight inherent limitations of the twin model, in the sense that having only twin data limits the ability to detect individual variance components. Finally, remarks on possible alternative statistical methods are given, and results are presented to illustrate the improvements in efficiency that are possible with additional family data. In particular, the results provide insight into the limitations of inference from twin data.