Refractive errors have often been considered as dichotomous traits in genetic and epidemiological studies; however, the choice of the threshold used to define case/control status has varied from study to study (Hammond et al., 2001; He et al., 2004; Quek et al., 2004; Huynh et al., 2007; Vitale et al., 2008; Dirani et al., 2010; Fan et al., 2011; Li et al., 2015a). In order to determine an optimal trait definition for detecting commonly-occurring genetic variants with additive effects on refractive errors, SNP-heritability estimates were calculated with GCTA for corneal astigmatism, refractive astigmatism and spherical equivalent classified either as continuous or dichotomous traits, and using a grid of case thresholds for the latter (namely, 0.50, 0.75, 1.00, 1.25 and 1.50 D of astigmatism or -0.50, -0.75, -1.00, -1.25 and -1.50 D of spherical equivalent). Following previous precedents (Schulze and McMahon, 2004; Corvin, Craddock and Sullivan, 2010; Koran et al., 2014), this approach was predicated on the assumption that the trait definition capturing the greatest SNP-heritability would be the one most likely to highlight genome-wide significant loci in subsequent GWAS of these traits.
For corneal astigmatism, SNP-heritability was greatest using a case definition threshold of 0.50 D (h2SNP = 0.094) and negligible for a case threshold of 1.50 D
(Table 5.3). However, there appeared to be no meaningful difference in SNP-heritability across the range of trait definitions tested, since all of the confidence intervals overlapped (Table 5.3, Figure 5.2). For refractive astigmatism, SNP-heritability estimates were generally higher than those for corneal astigmatism (h2SNP: range 0.015-0.158; Table 5.3, Figure 5.2). Using case thresholds of increasing
magnitude between 0.50 D and 1.25 D inclusive yielded increasing SNP-heritability estimates, although the large standard errors meant that, again, there was no statistical support for meaningful differences across the range of case thresholds tested. SNP-heritability estimates for spherical equivalent were similar for all case thresholds of examined (h2SNP: range 0.462-0.491; Table 5.3, Figure 5.2) with
considerable overlap between estimates. Estimates of SNP-heritability were numerically lower but with much narrower standard errors when astigmatism and spherical equivalent were modelled as continuous traits compared to dichotomous trait analyses (continuous trait h2SNP (SE): corneal astigmatism = 0.061 (0.021);
refractive astigmatism = 0.046 (0.020); spherical equivalent = 0.387 (0.022)), although once more, not to a sufficient extent to attain statistical support (Table 5.3, Figure 5.2).
Table 5.3: Estimates of SNP-heritability (h2SNP) for corneal astigmatism, refractive astigmatism and spherical equivalent. Analyses were conducted using GCTA-GREML. h2SNP = SNP-heritability; SE = standard error; P-value = test of the null hypothesis (h2SNP = 0).
Trait Case Threshold (D) Case Prevalence h2SNP SE P-value
Population Sample Corneal Astigmatism (N = 27,707) Continuous - - 0.061 0.021 1.19 x 10-3 0.50 0.72 0.70 0.094 0.036 3.53 x 10-3 0.75 0.46 0.45 0.053 0.033 0.051 1.00 0.28 0.27 0.086 0.038 9.86 x 10-3 1.25 0.17 0.17 0.042 0.046 0.175 1.50 0.11 0.10 0.000 0.057 0.500 Refractive Astigmatism (N = 28,378) Continuous - - 0.046 0.020 7.74 x 10-3 0.50 0.73 0.71 0.015 0.035 0.332 0.75 0.47 0.45 0.091 0.032 2.00 x 10-3 1.00 0.30 0.28 0.105 0.036 1.45 x 10-3 1.25 0.19 0.18 0.158 0.045 1.24 x 10-4 1.50 0.12 0.11 0.057 0.055 0.143 Spherical Equivalent (N = 28,378) Continuous - - 0.387 0.022 5.05 x 10-85 -0.50 0.35 0.33 0.462 0.036 2.61 x 10-43 -0.75 0.30 0.29 0.469 0.038 1.74 x 10-41 -1.00 0.27 0.27 0.491 0.039 7.04 x 10-42 -1.25 0.25 0.24 0.463 0.040 1.30 x 10-34 -1.50 0.23 0.22 0.476 0.042 2.20 x 10-33
5.4 Discussion
This investigation of SNP-heritability in a large European ancestry cohort demonstrated that corneal and refractive astigmatism have low SNP-heritabilities (h2SNP = 0.06 and 0.05 respectively), while spherical equivalent demonstrated a
moderate SNP-heritability (h2SNP = 0.39). For all three traits, the SNP-heritability
models best supported additive effects predominantly contributing to trait variation with a negligible contribution from dominance effects.
The lack of statistical support in favour of a particular threshold for defining astigmatism cases and controls (or myopic vs. non-myopic individuals) (Table 5.3) meant that the selection of an optimal threshold for subsequent GWAS analyses had to made arbitrarily. Hence, a threshold value of 1.00 D of astigmatism was adopted to define case status, since this value has been widely used in the literature (Huynh et al., 2007). The smaller standard errors obtained for analyses of astigmatism and spherical equivalent when analysed as continuous traits suggest that this coding scheme, i.e. continuous traits rather than dichotomous traits, should be used as the primary outcome for GWAS to be conducted using the full genetic data release from the UK Biobank.
With regard to spherical equivalent, the estimate of SNP-heritability obtained here (h2SNP = 0.387; P < 1 x 10-10) was slightly greater than a previously published
estimate, which suggested a SNP-heritability of 0.35 (Guggenheim et al., 2015). It is important to note that the sample used to generate this previous estimate consisted of children aged 7-15 years-old whereas the current investigation utilised
a much older sample (40-69 years old) and heritability estimates are sensitive to population demographics and changes in environmental exposures, such as age and amount of time spent outdoors (Visscher et al., 2008). More recently, the CREAM consortium estimated SNP-heritability to be between 0.17 and 0.21 in their European ancestry cohorts, but much lower at ~0.05 in their Asian ancestry sample (Tedja et al., 2018). The samples included in the investigation by Tedja et al. (2018) were all aged 25 years and above but were obtained from study groups in various locations globally, thus resulting in reduced homogeneity in their sample compared to the UK Biobank White British sample. To date, no additional estimates of SNP- heritability for spherical equivalent / myopia or astigmatism have been published, apart from conference abstracts (Miyake et al., 2013; Hysi et al., 2014).
In general, SNP-heritability estimates for spherical equivalent have been reported to be approximately a third to half of heritability estimates obtained from twin studies (Hammond et al., 2001; Dirani et al., 2006); however, SNP-heritability estimates for corneal and refractive astigmatism from this study are approximately a tenth of heritability estimates reported from twin studies of these respective traits (Hammond et al., 2001; Dirani et al., 2006; Grjibovski et al., 2006). This large difference in heritability estimate between the SNP-based study conducted here and prior twin studies for the astigmatism traits may be due to the differences in the variants investigated by these two methods. Heritability in twin studies captures the effects of all variants, irrespective of their allele frequency and effect size, whereas rare variants are excluded from SNP-heritability estimation (Yang et al.,
predominantly due to rare variants (MAF < 0.01), gene-gene or gene-environment interaction effects, or shared environment effects.
Previously, twin studies have suggested the heritability of corneal and refractive astigmatism to be predominantly due to dominance effects (Hammond et al., 2001; Dirani et al., 2006; Grjibovski et al., 2006). However, the investigation conducted here failed to reveal the presence of a non-zero dominance effects component for the SNP-heritability of either trait. Zhu et al. (2015) and Nolte et al. (2017) obtained similar results across a wide range of traits when using GCTA-GREMLd, i.e. the dominance effects component of SNP-heritability was negligible despite prior evidence for the presence of a dominance effects component in twin studies of these traits. Using an alternative method, Zaitlen et al. (2013) also suggested dominance effects made only a small contribution to heritability estimates across several traits, however, the exact contribution could not be fully quantified. Considering these dominance effects results for other complex traits, the causes behind them and those from the investigation here can be rationalised in several ways. One of the simpler arguments is that the sample sizes used in these more recent studies were insufficient to deliver the necessary level of statistical power to detect a non-zero dominance effects component (Zhu et al., 2015); however, the sample sizes used in the analyses here were more than double those of the other studies using these methods, thus boosting the ability to detect a non-zero dominance effects component of SNP-heritability. Another possible explanation for the lack of a dominance effects component relates to the model used to calculate the SNP-heritability estimates. As suggested by Huang and Mackay (2016), the
partitioning of trait variance into its separate components is dependent on the model(s) applied, since effects of one variance component can also contribute to another component, for example some dominance effects can be misallocated as additive effects.
The models applied when using GCTA-GREMLd utilise the classical interpretations of additive and dominance effects (Huang and Mackay, 2016); however, use of alternative, albeit arbitrarily defined definitions, could be utilised as suggested by Huang and Mackay (2016). With these alternative definitions, the presence of a statistically supported non-zero dominance effects component to SNP-heritability may become evident for the traits examined here.
The first part of this investigation interrogated the extent to which uncorrected population effects inflated SNP-heritability estimates. Although the results appear reassuring at first glance, when interpreting these results more generally it is important to note the potential limitations and the assumptions that were made. Firstly, it must be remembered that the SNP-heritability estimates presented here refer to the contribution of a subset of genetic variants to phenotypic variance, and thus would be likely to be lower than twin / family study estimates whereby all genetic contributors are considered. Furthermore, should an alternative selection of variants be used, such as using only directly genotyped variants, there is potential for SNP-heritability estimates to differ. Secondly, the population prevalences used when converting from the observed to the liability scale were obtained from the full
should be obtained from an independent, ancestry matched source; however no single study has reported population-based prevalence values for each of the thresholds tested here. Vitale et al. (2008) reported 31% prevalence for refractive astigmatism ≥1.00 D in non-Hispanic white ancestry individuals aged ≥40 years. However, when that sample was split by age into those aged 40-59 years and ≥60 years, there was a considerable difference in refractive astigmatism prevalence (28% vs. 50%). In a meta-analysis of European population cohorts, Williams et al. (2015b) reported a lower prevalence of refractive astigmatism ≥1.00 D (mean age- standardised prevalence 24%); however, there was a notable increase in prevalence with age throughout their age ranges (median age 62 years). Collier Wakefield, Annoh and Nanavaty (2016) investigated corneal astigmatism in pre-operative cataract patients in the UK. Here, higher prevalences of corneal astigmatism were reported for all thresholds, however their sample was of an older age range (mean age 72 years) than other published studies and that of the UK Biobank sample (UK Biobank median age 58 years). These previously published prevalence estimates for astigmatism suggest that using population prevalences based on the full UK Biobank cohort can be justified since these prevalences are not markedly different after considering the increasing magnitude of astigmatism with age.
With respect to heritability, from the evidence presented both here and in previous publications, it appears that the partitioning of variance into separate genetic components lacks sufficient accuracy to be meaningful and any inferences based on heritability should ideally be confined to the total genetic contribution rather than the partitioned components. As SNP-heritability estimation methods have stated
previously, using an additive effects model (as is most commonly done), captures almost all of the total genetic contribution of the considered variants to trait variation and should be deemed sufficient for this approach (Polderman et al., 2015; Huang and Mackay, 2016).
Overall, this investigation of SNP-heritability in a large European ancestry cohort demonstrated that both corneal and refractive astigmatism have a low SNP-heritability, whereas spherical equivalent has a moderate SNP-heritability. Furthermore, for all of the traits examined here, the SNP-heritability appears to be of an additive nature with a negligible contribution from dominance effects.