Quantitative genetic model
Based on the differences in genetic similarity for twins with different zygosities, MZ twins have a correlation of 1 for additive genetic effects (A), representing the combined effect of alleles at a locus and across loci that add up, whereas DZ twins have a correlation of 0.531,32. Dominance genetic effects (D ord 2) also contribute to twin pair similarity and the index interaction of gene alleles at the same locus (dominance), and are assumed correlated 1 between MZ-twins and 0.25 between DZ-twins. Furthermore, both types of twins are assumed to have an equal correlation of 1 for environmental effects that both twins share (C orc 2), such as perinatal and home environment, whereas unique environmental effects that twins in pairs do not share (E or e 2), such as accidents, are modelled with a correlation of 0 between twins. Thus, a higher correlation in MZ twins than in DZ twins would represent the effect of the higher proportion of genes shared among MZ twins 33.
The multivariate genetic model estimates the genetic and environmental contributions to the phenotypic correlation between asthma and FENO and the degree that can be accounted for by sensitization to aeroallergens and blood eosinophils. The phenotypic correlations were decomposed into combinations of A, D, C, and E, depending on which model was fitted. We fitted a series of structural equation models estimating the maximum-likelihood genetic and environmental variance components of variables, and the covariance between these. We performed likelihood ratio tests to find the best-fitting model.
We were interested in the correlation between asthma and FENO and what potentially could affect this correlation in terms of genetic and environmental influences from other factors. Therefore, we proceeded to fit a four-variate “Cholesky model” to disentangle the sources of variance and covariance into genes and environment. In a Cholesky model, the order the variables appear is important; the “left” variables influence the variables to the “right,” but not vice versa 34 (see Figure 1) to allow estimation of the influence (i.e., genetic and/or environmental) of allergen-specific IgE level and eosinophils on the association between asthma and FENO. Since we were interested if allergen-specific IgE level and eosinophils could influence asthma and and FENO we decided to model the variables in this order.
We fitted an ACE model, i.e., a model with A, C, and E sources of variance and covariance. We also fitted an ADE model, AE model, and CE model. We tested whether the nested models had poorer fits to the data using likelihood ratio tests. We also used the Akaikes Information Criterion (AIC) to assess the model fit. The AIC favors model parsimony and allows for comparisons across non-nested models. In addition, we compared other models with the ACE model (base) to assess model fit.
Figure 1 shows the Cholesky (here, the AE model is taken as an example, AE=additive genetic effects and unique/unshared environmental effects) by the observed variables (allergen-specific IgE level, eosinophils, asthma, and FENO) in relation to the unobserved latent factors (A1-4 and E1-4), which are connected by the paths a11-44 and e11-44. Thus, the variance in, and covariance between, asthma and FENO may be explained by the variance in allergen-specific IgE level and eosinophils, but not vice versa. Analyses were performed using the statistical software R35, version 3.6.1, and the package OpenMx34, version 2.15.5.
Additional details on calculated contributions to the correlations between asthma and FENO are provided in the Online Supplemental material.