Participants
Parents of 5,879 twins participating in the Twins Early Development Study (TEDS) completed and returned questionnaires when twins were aged 12. TEDS is a community-based, population representative study of twins born in England and Wales between 1994 and 1996 [22]. Exclusions were conducted for genetic syndromes, including Fragile X and cystic fibrosis, chromosomal abnormalities, including Down Syndrome and cerebral palsy, extreme perinatal or prenatal difficulties, and missing first contact or zygosity data. Participants with confirmed ASC (N = 80) were included. The final sample comprised 5,689 twin pairs, including 927 monozygotic (MZ) male pairs, 1,124 MZ female pairs, 865 dizygotic (DZ) male pairs, 989 DZ female pairs, and 1,784 DZ opposite-sex pairs. Zygosity was ascertained through DNA testing and parent ratings of twin resemblance [23]. All participants provided written informed consent prior to participation. TEDS has full ethical approval from the King’s College London Research Ethics Committee.
Measures
Autistic traits
Parents completed the Childhood Autism Spectrum Test (CAST [24]), a 30-item questionnaire that enquires about various autistic traits, such as lack of social interest, pronounced interests, and difficulties with conversation. Each question was answered ‘yes’ or ‘no’, meaning the maximum possible score was 30. Scores over 15 predict ASC diagnoses with 100 % sensitivity and 97 % specificity [25]. The measure was divided into three scales based on DSM-IV criteria, which were employed in previous studies [13, 14]: social difficulties (‘Social’), communication atypicalities (‘Communication’), and repetitive, restricted behaviours and interests (RRBI). The number of items, possible range of scores, and Cronbach’s α values for each subscale are shown in Table 1.
Table 1 Descriptive statistics, phenotypic correlations, and twin correlations
Traits of ADHD
Parents completed the ADHD subscale of the Conners’ Parent Rating Scale (‘Conners ADHD’ [26] ), a measure formed of 18 statements. Each statement described a behaviour characteristic of ADHD; parents rated, on a three-point scale, how true each statement was of their child. The highest possible score was 54. Conners ADHD is a valid assessment of ADHD traits; individuals with ADHD display significantly higher scores on the measure than controls [26]. Consistent with previous recommendations [26], the measure was divided into two subscales, which closely corresponded to DSM-IV criteria for ADHD: Hyperactivity/Impulsivity and Inattention. Possible ranges of scores, number of items, and Cronbach’s α for both subscales are provided in Table 1.
Data analysis
Twin analyses of the full sample
Data were prepared for analysis by first log transforming any skewed subscales (see Table 1), and then regressing the effects of sex and age out of all measures, as is standard behavioural genetic procedure [27]. Analyses were then performed on standardised residual scores using Mx [28].
First, phenotypic associations between the CAST and Conners ADHD subscales were established using phenotypic correlations (r
ph), correlation coefficients estimated from structural equation models. Second, twin correlations, which are the foundation of twin analysis, were estimated. Cross-trait cross-twin correlations provide one with an initial indication of the extent to which covariance between two traits is influenced by genetic and environmental factors. These involved correlating one twin’s score on a CAST subscale with their co-twin’s score on a Conners ADHD subscale. Cross-trait cross-twin correlations were estimated separately for MZ and DZ twins. These estimates cannot exceed r
ph between two traits. As MZ twins are assumed to share all of their segregating DNA code with one another, while DZ twins share, on average, 50 %, additive genetic (A) influences on the covariance between two traits are implicated if the MZ cross-trait cross-twin correlation exceeds the DZ estimate. As MZ twins are assumed to be genetically identical, any within pair MZ differences are assumed to be caused by nonshared environment (E), environmental factors that differ across twins in a pair and create differences between them (measurement error is included in this term). Hence, if the MZ cross-trait cross-twin correlation between two traits is less than r
ph between them, E is implicated on their covariance. Shared environmental (C) influences, on the other hand, are common to both twins in a pair and heighten their similarity; these influences are indicated if the DZ cross-trait cross-twin correlation exceeds half the MZ statistic. Alternatively, non-additive genetic (D) influences are implicated if the DZ cross-trait cross-twin correlation is less than half the MZ estimate. These correlations were estimated from a constrained saturated model (see below).
Finally, multivariate structural equation twin models were fitted to data to formally estimate A, C, D, and E. Cholesky decompositions, presented here as correlated factors solutions [29], were tested. For each trait, A, C (or D, if this is suggested by the twin correlations), and E were estimated. The additive genetic correlation (r
A) then estimates A overlap between traits. This estimate falls between 0 and 1; estimates of 1 suggest total genetic overlap across two traits, while estimates of 0 would suggest that the genetic influences on two traits are totally independent of one another. Shared environmental (r
C), nonshared environmental (r
E), and non-additive genetic (r
D) correlations can also be computed, and operate in the same manner. The model then computes bivariate heritability, which estimates the extent to which A can explain r
ph between two traits, from the univariate A estimates and r
A. Equivalent statistics are calculated for C, E, and D.
ACE and ADE models were tested. Parameters in these models can either be equated across sexes, or allowed to differ in magnitude across sexes (quantitative sex differences). Such differences are indicated when male and female twin correlations differ. In order to test for quantitative sex differences, a saturated model that allowed twin correlations to differ by sex was fitted. These estimates were then equated across sexes.
The fit of each model was compared against that of a saturated model of the observed data. For each model, the −2LL fit statistic was computed. Model fit was assessed using the likelihood-ratio test (LRT), which capitalises on the fact that differences in −2LL between two models are χ2 distributed, with degrees of freedom equal to the difference in number of estimated parameters. Significant χ2 results suggest that a given model is a significantly poorer fit than the saturated model. Model fit was further assessed using Akaike’s Information Criteria (AIC) and Bayesian Information Criteria (BIC). Lower, preferably negative, AIC values indicate good model fit, while models with more negative BIC estimates are to be favoured. Selection of the best-fitting model was based on BIC, which performs better than either the LRT or AIC in larger samples [30]; when comparing two models, the model with the more negative BIC estimate is regarded as better-fitting, with differences of 10 or more argued to show that a given model is a good fit [31].
Analysis of the extremes
DeFries–Fulker analysis [32, 33] was used to analyse extreme scores on the CAST and Conners ADHD subscales. DeFries–Fulker analysis is a regression analysis of means. The univariate procedure is designed to estimate group heritability (\(h^{ 2}_{\text{g}}\)), which refers to genetic influences on extreme scores [30]. Bivariate DeFries–Fulker analysis is concerned with testing for bivariate heritability (h
2.xy); in these analyses, this refers to the extent to which the genes that cause extreme scores on one trait influence continuous scores on another trait [32]. In performing univariate and bivariate DeFries–Fulker analyses, it is possible to estimate genetic correlations between extreme scores on two measures [33].
For the univariate DeFries–Fulker analyses, extreme scorers, termed probands, were selected from the sample used in the twin analyses on the basis of scoring within the highest 5 % of the z-score distribution on a measure of interest. Scores were then transformed so that the mean proband score on the measure of interest was 1, while the control mean was 0. In transforming scores in this manner, one can gain an indication of \(h^{ 2}_{\text{g}}\) by examining the mean scores of co-twins of probands. If the DZ co-twin mean is closer to 0 than the MZ co-twin mean, then greater resemblance between MZ twins than DZ twins is suggested. Much like how one interprets twin correlations, this can be taken as evidence of \(h^{2}_{\text{g}}\) on a trait. Univariate DeFries-Fulker analysis more formally estimates \(h^{2}_{\text{g}}\) through a regression equation for predicting co-twin scores on a given measure from proband scores and zygosity. The regression coefficient of co-twin scores on zygosity is an estimate of \(h^{2}_{\text{g}}\). The estimate of \(h^{2}_{\text{g}}\) should not exceed the mean scores of MZ co-twins, unless non-additive genetic effects are influential. In this instance, estimates were fixed to equal the mean MZ co-twin score.
In bivariate DeFries–Fulker analysis, probands were selected on the basis of scoring within the highest 5 % of the z-score distribution on a given measure; the measure used to select probands is the selection variable. The outcome variable is the second measure of interest. Thus, the bivariate procedure is directional in that a CAST subscale could be used as the selection variable and a Conners ADHD subscale used as the outcome variable, and vice versa.
Prior to conducting bivariate DeFries–Fulker analysis, the phenotypic associations between the selection and outcome variables were tested using phenotypic group correlations. These were calculated by dividing proband’s mean z-score on the selection variable by their mean z-score on the outcome variable, and can be interpreted in the same manner as correlation coefficients. Subsequently, data were prepared for bivariate analysis by dividing scores on both measures by the zygosity-specific proband mean for the selection variable [34]. Transforming scores in this manner meant that the mean score on the selection variable for probands was 1, while the mean score for controls on the outcome measure was 0. The co-twin means provide an indication of the extent of h
2.xy between two measures; if the DZ co-twin mean on the outcome variable is closer to 0 than MZ co-twin means, h
2.xy between the selection and outcome variables is indicated. The bivariate DeFries–Fulker regression equation, which predicts co-twin scores on the outcome measure from proband scores on the selection measure and zygosity, was then used to formally estimate h
2.xy. The regression coefficient of co-twin scores on zygosity is an estimate of h
2.xy. Again, this estimate only exceeds the mean scores on the outcome variable for MZ co-twins if non-additive genetic influences are in operation; as in the univariate analysis, h2.xy was fixed to equal the MZ co-twin mean for the outcome variable in these instances. These analyses were conducted using the CAST subscales as selection variables, and then using the Conners ADHD subscales as selection variables.
The results of the univariate and bivariate DeFries–Fulker analyses were then used to calculate genetic correlations between extreme CAST subscale scores and extreme Conners ADHD subscale scores, using the equation:\(\sqrt {\frac{{\left( {\beta_{xy} \times \beta_{yx} } \right)}}{{\left( {\beta_{x} \times \beta_{y} } \right)}}}\) [35]. β
xy
and β
yx
represent h
2.xy estimates, while β
x
and β
y
are \(h^{2}_{\text{g}}\) estimates for both measures.