Introduction
Genome-wide association (GWA) studies have identified hundreds of variants associated with obesity and type 2 diabetes [
1‐
9]. However, GWA studies of type 2 diabetes and obesity have usually focused on testing additive models. An additive model assumes that the disease risk of heterozygous individuals is exactly halfway between those of the two homozygous groups. Non-additive effects include dominant and recessive effects. These effects are common in monogenic disorders, but there are only a few examples in common diseases and traits [
10]. For obesity and type 2 diabetes, the strongest evidence of a non-additive effect is at the
CDKAL1 locus, where a previous study demonstrated a recessive effect [
11]. The GIANT Consortium previously tested 32 BMI-associated variants for deviations from the additive model but, overall, found no evidence of deviation from additivity in 105,643 individuals [
5].
There are at least three reasons why it is important to test for non-additive associations between common genetic variants and type 2 diabetes and obesity. First, a genome-wide approach that tests alternative models could identify new variants and candidate genes because the correct model may have more statistical power. Second, the correct model of inheritance could explain more of the variation in the trait, and hence account for some of the ‘missing heritability’ [
12]. Third, the presence of recessive or dominant effects may inform follow-up physiological studies in vivo and in humans: for example, by prioritising recruit-by-genotype efforts on heterozygous as well as homozygous individuals.
The UK Biobank provides an excellent opportunity to test for deviation from additivity in a single large cohort, as genome-wide genetic data and detailed phenotypic data are available in the initial release of data from over 120,000 British individuals [
13]. In this study we used the UK Biobank to perform GWA tests for deviations from the additive model for BMI, obesity and type 2 diabetes. We also investigated whether evidence of deviation was present for previously published single nucleotide polymorphisms (SNPs) associated with these traits.
Discussion
Our analyses of 120,286 UK Biobank individuals suggest that most genetic variants associated with BMI and type 2 diabetes operate through a per-allele additive effect. Our findings suggest that dominant and recessive effects at common variants have a minimal role in explaining variation in BMI and risk of obesity and type 2 diabetes. Our results are consistent with a previous smaller study of 6,715 individuals that concluded that deviations from additivity contribute little to missing heritability for a wide range of traits [
18]. There were exceptions for the
FTO–BMI association and the
CDKAL1–type 2 diabetes association.
The 16% of individuals carrying two copies of the BMI-raising allele at the
FTO locus had more than twice the expected BMI difference compared with individuals carrying no BMI-raising alleles than would have been expected under a purely additive model. Assuming an average height in males of 1.78 m, it is equivalent to homozygous carriers of the BMI-increasing allele being 2.53 kg heavier than homozygous carriers of the opposite allele, whereas heterozygous carriers would be only 0.86 kg heavier. Previous studies have shown that the vast majority of this increased weight is fat mass [
1]. The results are also consistent with a study of the
FTO variant in polycystic ovary syndrome [
19]. For type 2 diabetes, we found evidence of a recessive effect at the
CDKAL1 locus. The evidence that heterozygous carriers of the risk allele were at increased risk of type 2 diabetes was minimal and, combined with previous data from the deCODE study, suggests the true biological effect at this locus is recessive. Although accounting for non-additive effects at these loci only explained a small amount of additional variation in risk of obesity and type 2 diabetes, understanding why these associations demonstrate non-additivity may provide new insights into biological mechanisms at these loci.
A strength of our study is that we used a single large, relatively homogeneous dataset with full access to individual-level genotype and phenotype data. We had >80% power to detect dominance deviation from additivity, explaining 0.04% of the phenotypic variance at
p = 3 × 10
−9. This is equivalent to being able to detect a purely recessive effect of 0.4 kg/m
2 for a BMI allele with a frequency of 0.25, for example. We had less power for the type 2 diabetes analysis (approximately ×6.5 less [
16]). To have equivalent power to our BMI analysis we would require approximately 26,000 cases and 740,000 controls. Our analyses show how single large studies such as the UK Biobank will provide added value to existing meta-analyses approaches in GWA studies.
Our analyses have some limitations. We analysed imputed variants, and our statistical power to detect deviations from additivity might have been reduced if variants were not perfectly captured and/or we analysed imperfect markers for causal alleles. Non-biological explanations for the non-additive effects include ‘haplotype effects’ due to linkage disequilibrium with other causal alleles. In such situations, alleles of SNPs showing evidence of non-additivity are partially correlated with a much stronger causal SNP with an additive effect [
20,
21]. This is unlikely to be the case at the
FTO or
CDKAL1 loci. These loci have been studied extensively through re-sequencing and fine-mapping efforts and no substantially stronger individual variants have been identified; and for
FTO, rs1421085 was recently proposed as the most likely causal variant [
17]. The rs1421085 SNP disrupts a binding site for
ARID5B, which increases the expression of
IRX3 and
IRX5 during adipocyte differentiation. This results in the production of more white adipocytes, a reduction in mitochondrial thermogenesis and an increase in lipid storage, although it is not clear why this would lead to non-additive effects on BMI.
The detection of non-additive genetic effects for BMI is potentially complicated by the skewed distribution of BMI. Effects that seem recessive could be artefacts of the skewed nature of the BMI distribution, as variation in BMI is wider towards the more overweight end of the distribution. To limit this effect we inverse-normalised BMI and performed additional sensitivity analyses (including ‘robust regression’—an alternative to ‘least squares regression’) that account for different variances of a trait, which may be the case for
FTO [
22] (data not shown), to limit the influence of the skewed distribution. We found, however, no evidence that BMI-increasing alleles were more likely to have recessive effects than BMI-lowering alleles (ESM Table
4 and ESM Fig.
4). Alternatively, artificially truncating the BMI distribution into a normal distribution could reduce the power to detect recessive effects of BMI-increasing alleles. However, we saw very little reduction in statistical confidence of known BMI associations when using the inverse-normalised scale compared with the natural BMI scale.
In conclusion, we have performed tests of deviation from additivity for BMI, obesity and type 2 diabetes. Overall, there was little evidence of dominant and recessive effects. However, we found replicable examples of non-additive effects at FTO on BMI and obesity, and at CDKAL1 on type 2 diabetes risk. Recessive effects have implications for the mechanism of action of these loci but do not explain appreciably more of the ‘missing heritability’.
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