Use of quantitative genetic model fitting in twin studies is now
standard and is fully described elsewhere.
30 31 The
technique is based on the comparison of the covariances (or
correlations) within MZ and DZ twin pairs. It allows separation of the
observed phenotypic variance into additive (A) or dominant (D) genetic
components and common (C) or unique (E) environmental components. E
also contains measurement error. The broad-sense heritability, which
estimates the extent to which variation in liability to disease in a
population can be explained by genetic variation, can be defined as the
ratio of genetic variance (A + D) to total phenotypic variance (A + D +
C + E).
The maximum likelihood modeling methods used in twin analysis (modeling
twin covariances) assume that the trait being analyzed must be normally
distributed. This is not true for cortical cataract (see
Fig. 2 ). The genetic and environmental contributions can, however, be
quantified by assuming there is a continuous underlying liability to
disease (involving multiple genetic and environmental factors). The
correlation in liability among twins can be estimated from the
frequencies of disease-concordant and disease-discordant pairs, using a
multiple threshold model.
30 32 Multiple thresholds were
created by categorizing the amount of cortical cataract into eight
categories for both clinical and digital grading systems, rather than
using continuous data of cortical scores. Age, an important risk factor
in cortical cataract, is the same for twins and so would inflate both
MZ and DZ correlations if not accounted for.
33 Therefore,
polyserial correlation matrices, including correlations between age (a
continuous trait) and cataract (categorical data), were calculated for
MZ and DZ twin pairs using PRELIS.
34 These polyserial
correlation matrices were used in the Mx genetic modeling
program.
35 Figure 3 illustrates the twin model used for analysis.
The significance of variance components A, C, and D and age was
assessed by removing each sequentially in submodels and testing the
deterioration in model fit after each component was dropped from the
full model. This leads to a model explaining the variance and
covariances with as few parameters as possible. Submodels were compared
with the full model by hierarchic χ
2 tests. The
difference in χ
2 values between submodel and
full model is itself approximately distributed asχ
2, with degrees of freedom (df) equal to the
difference in df of submodel and full model. Data handling and
preliminary analyses were done with STATA.
36