Data analysis was based on quantitative genetic modeling
22 23 using the Mx program.
24 In short, the technique is based on the comparison of the covariances (or correlations) within MZ and DZ twin pairs. Familial aggregation of a trait or disease suggests that genetic factors may be involved in etiology, but it does not exclude the possibility of shared environmental factors. Twin modeling assumes that MZ and DZ twin pairs share the same common (family) environment—the “equal environment” assumption—which has been tested and largely found to be true.
25 As MZ pairs share the same segregating genes but DZ pairs share only half, any greater similarity between MZ pairs allows an estimation of this additional gene-sharing, using the equal-environment assumption. To quantify the genetic and environmental contributions to a dichotomous variable, such as the presence or absence of β-PPA, an underlying, continuous liability to β-PPA is assumed, which is affected by multiple genetic and environmental factors.
26 Structural equation modeling uses variance–covariance matrix algebra to separate the observed phenotypic variance into additive (G) or dominant (D) genetic components and common (C) or unique (E) environmental components (E also includes measurement error). MZ twins share the same G genetic component, DZ twins 0.5, and MZ twins the D genetic component, whereas DZ twins share only 0.25 of D, since there is a one-in-four chance that two siblings will share a dominant allele transmitted from one parent. Thus, the known twin–twin relationships were used in maximum likelihood methods to estimate the best-fitting model that fits the variance–covariance data obtained in the study. Dividing each of these components by the total variance yields the different standardized components of variance—for example, the heritability, which can be defined as the ratio of additive genetic variance to total phenotypic variance.
As β-PPA is a bivariate variable (yes/no) and refractive error is measured as a continuous variable (mean SE), to include both variables in a single model, polychoric correlations were estimated by using a saturated model, with refractive error divided into deciles to recode it from a continuous measurement to a categorical one, allowing it to be modeled with the dichotomous β-PPA data. The univariate models were extended to include the bivariate cases of SE and β-PPA, to allow assessment of the extent to which any correlation between these two variables could be explained by common genes.