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The genomics era has brought useful tools to dissect the genetic architecture of complex traits. We propose a reaction norm model (RNM) to tackle genotype-environment correlation and interaction problems in the context of genome-wide association analyses of complex traits. In our approach, an environmental risk factor affecting the trait of interest can be modeled as dependent on a continuous covariate that is itself regulated by genetic as well as environmental factors. Our multivariate RNM approach allows the joint modelling of the relation between the genotype (G) and the covariate (C), so that both their correlation (association) and interaction (effect modification) can be estimated. Hence we jointly estimate genotype-covariate correlation and interaction (GCCI). We demonstrate using simulation that the proposed multivariate RNM performs better than the current state-of-theart methods that ignore G-C correlation. We apply the method to data from the UK Biobank (N= 66,281) in analysis of body mass index using smoking quantity as a covariate. We find a highly significant G-C correlation, but a negligible G-C interaction. In contrast, when a conventional G-C interaction analysis is applied (i.e., G-C correlation is not included in the model), highly significant G-C interaction estimates are found. It is also notable that we find a significant heterogeneity in the estimated residual variances across different covariate levels probably due to residual-covariate interaction. Using simulation we also show that the residual variances estimated by genomic restricted maximum likelihood (GREML) or linkage disequilibrium score regression (LDSC) can be inflated in the presence of interactions, implying that the currently reported SNP-heritability estimates from these methods should be interpreted with caution. We conclude that it is essential to correctly account for both interaction and correlation in complex trait analyses and that the failure to do so may lead to substantial biases in inferences relating to genetic architecture of complex traits, including estimated SNP-heritability.

The purpose of this study was to study changes in choroidal thickness (ChT) and choroidal blood perfusion (ChBP), and the correlation between them, in guinea pig myopia. METHODS. The reliability of optical coherence tomography angiography (OCTA) for measuring ChT and ChBP was verified in guinea pigs, after cervical dislocation (n ¼ 7) or temporal ciliary artery transection (n ¼ 6). Changes in refraction, axial length, ChT, and ChBP were measured during spontaneous myopia (n ¼ 9), monocular form-deprivation myopia (FDM, n ¼ 13), or lens-induced myopia (LIM, n ¼ 14), and after 4 days of recovery from FDM and LIM. RESULTS. The abolition (by cervical dislocation) or reduction (by temporal ciliary artery transection) of ChBP, and of the associated changes in ChT, were verified by OCTA, thus validating the method of measurement. In the spontaneous myopia group, ChT and ChBP were reduced by 25.2% and 31.9%, respectively. In FDM eyes, mean 6 SD ChT and ChBP decreased significantly compared with the untreated fellow eyes (ChT fellow: 76.13 6 9.34 lm versus 64.76 6 11.15 lm for FDM; ChBP fellow: 37.87 6 6.37 3 10 3 versus 30.27 6 6.06 3 10 3 for FDM) and increased after 4 days of recovery (ChT: 77.94 6 12.57 lm; ChBP: 37.41 6 6.11 3 10 3). Effects of LIM were similar to those of FDM. Interocular differences in ChT and ChBP were significantly correlated in each group (FDM: R ¼ 0.71, P < 0.001; LIM: R ¼ 0.53, P < 0.001). CONCLUSIONS. ChT and ChBP were significantly decreased in all three models of guinea pig myopia, and they both increased during recovery. Changes in ChT were positively correlated with changes in ChBP. Therefore, it is possible that the changes of ChT are responsible for the changes of ChBP or vice versa. Keywords: myopia, choroidal thickness, choroidal blood perfusion, guinea pig M yopia is commonly recognized as an ocular disorder that carries significant risks of visually blinding complications. 1,2 In recent decades, the prevalence and severity of myopia have been on the rise, and it is estimated that by 2050 there will be 4.76 billion people with myopia and 0.94 billion with high myopia. 3-6 Meanwhile, the total cost of myopia correction is also increasing, becoming a relatively large economic burden in urbanized countries. 7-9 With the drastic increase in the public health impact, as well as the socioeconomic burden of myopia, many researchers have focused on investigating the mechanisms underlying myopia development. Twenty years ago, in a seminal study, Wallman et al. found that choroidal thickness (ChT) in chicks significantly increased and decreased in response to positive and negative lens-induced defocus, causing hyperopic and myopic refractive shifts, respectively. 10 On removal of the imposed negative lens defocus, the choroid of the now myopic eye thickened, moving the retina forward toward the defocused image plane. Such bidirectional growth regulation has stimulated researchers to study the choroid as a target tissue for myopia control, and ChT has been investigated as a surrogate marker for...

The genomics era has brought useful tools to dissect the genetic architecture of complex traits. Here we propose a multivariate reaction norm model (MRNM) to tackle genotype–covariate (G–C) correlation and interaction problems. We apply MRNM to the UK Biobank data in analysis of body mass index using smoking quantity as a covariate, finding a highly significant G–C correlation, but only weak evidence for G–C interaction. In contrast, G–C interaction estimates are inflated in existing methods. It is also notable that there is significant heterogeneity in the estimated residual variances (i.e., variances not attributable to factors in the model) across different covariate levels, i.e., residual–covariate (R–C) interaction. We also show that the residual variances estimated by standard additive models can be inflated in the presence of G–C and/or R–C interactions. We conclude that it is essential to correctly account for both interaction and correlation in complex trait analyses.

In this, the first published study focusing on the efficacy of u-ACP and b-ACP in total arch replacement for type A aortic dissection, the b-ACP group did not demonstrate significantly lower 30-day mortality or PND rate compared with the u-ACP group. Future large-sample studies are warranted to thoroughly examine this critical issue.

In guinea pigs, choroidal thickness (ChT) and choroidal blood perfusion (ChBP) simultaneously decrease in experimental myopia, and both increase during recovery. However, the causal relationship between ChBP and myopia requires further investigation. In this study, we examined the changes of ChBP with three different antimyopia treatments. We also actively increased ChBP to examine the direct effect on myopia development in guinea pigs. METHODS. Experiment 1: Guinea pigs wore occluders on the right eye for two weeks to induce form-deprivation myopia (FDM). Simultaneously they received daily antimyopia treatments: peribulbar injections of atropine or apomorphine or exposure to intense light. Experiment 2: The vasodilator prazosin was injected daily into the form-deprivation eyes to increase ChBP during the two-week induction of FDM. Other FDM animals received appropriate control treatments. Changes in refraction, axial length, ChBP, ChT, and hypoxia-labeled pimonidazole adducts in the sclera were measured. RESULTS. The antimyopia treatments atropine, apomorphine, and intense light all significantly inhibited myopia development and the decrease in ChBP. The treatments also reduced scleral hypoxia, as indicated by the decrease in hypoxic signals. Furthermore, actively increasing ChBP with prazosin inhibited the progression of myopia, as well as the increase in axial length and scleral hypoxia. CONCLUSIONS. Our data strongly indicate that increased ChBP attenuates scleral hypoxia, and thereby inhibits the development of myopia. Thus ChBP may be a promising target for myopia retardation. As such, it can serve as an immediate predictor of myopia development as well as a long-term marker of it.

As a key variance partitioning tool, linear mixed models (LMMs) using genome-based restricted maximum likelihood (GREML) allow both fixed and random effects. Classic LMMs assume independence between random effects, which can be violated, causing bias. Here we introduce a generalized GREML, named CORE GREML, that explicitly estimates the covariance between random effects. Using extensive simulations, we show that CORE GREML outperforms the conventional GREML, providing variance and covariance estimates free from bias due to correlated random effects. Applying CORE GREML to UK Biobank data, we find, for example, that the transcriptome, imputed using genotype data, explains a significant proportion of phenotypic variance for height (0.15, p -value = 1.5e-283), and that these transcriptomic effects correlate with the genomic effects (genome-transcriptome correlation = 0.35, p -value = 1.2e-14). We conclude that the covariance between random effects is a key parameter for estimation, especially when partitioning phenotypic variance by multi-omics layers.