Power and validity of methods to identify variability genes

A variability gene model [Magnus et al., Clin Genet 19:67-70, 1981] hypothesizes that environmental influences on the expression of additive genes for a quantitative trait such as cholesterol are under the control of alleles at a separate nonadditive locus. They suggest identifying such genes using an analysis of variance to compare absolute intrapair monozygotic twin trait differences between the genotypes of the postulated variability locus. However, quantitative traits such as cholesterol often have skewed distributions with a long right tail; what are the effects of such non-normality on the procedure suggested by Magnus et al. [1981]? We show that their method is a special case of the Levene tests, robust tests for variability differences. We introduce a statistical model representing sources of variability in twin pair differences and demonstrate with simulation studies that although the Levene tests have robust Type I error, power is enhanced when nonnormal data are transformed before analysis, and the apparent presence and degree of variability differences are dependent on the scale of analysis. These findings indicate the importance of appropriate transformation of the trait before analysis. Analysis of a well-characterized twin data set illustrates these conclusions.