Generalized correlation coefficient for genome-wide association analysis of cognitive ability in twins

Introduction

Cognitive function is an important phenotype involving multiple mental abilities including learning, thinking, reasoning, remembering, problem-solving, decision-making, and attention. Thus, cognitive function affects health and quality of life in the elderly. Recent twin and family studies have shown that the heritability of general cognitive function is more than 50% in adolescence through adulthood to older age [1], suggesting a substantial genetic contribution to the phenotype. Despite the relatively large number of genome-wide association studies (GWASs) of cognition performed to date, a lot of the heritability is still unexplained. For instance, Savage et al., 2018 [2] reported the largest GWAS of intelligence to date (N = 269,867), identifying 205 significantly associated genomic loci and h²_SNP = 0.22. In addition, different limitations in current GWASs might be the reason for the situation due to the distribution of cognitive measurements as well as the complex relationship between SNP genotypes and cognitive performance. One of the assumptions in the popular linear models used for GWAS is normality of the phenotype of interest. Unfortunately, the distribution of cognitive measurements is typically skewed [3]. Also, the additive genetic effect has been the most popular assumption in current genetic association studies and the only genetic model addressed in studies using linear models. However, the pattern of genetic associations is likely more complex, including both linear (additive) and non-linear (non-additive) relationships [4, 5].

As a recent development, the generalized measure of dependency for analysis of omics data has been proposed [4–6]. The concept of a generalized measure of association comes from the rank correlation and information theory. The rank correlation was defined by Hoeffding’s D by measuring the difference between the joint rank of two random variables x and y and the product of their marginal rank [7]. In 2012, Reshef [8] and his colleagues proposed the maximal information coefficient (MIC), which belongs to a larger class of maximal information-based nonparametric exploration (MINE), as a measure of association. MIC is able to not only measure two-variable dependence by calculating a score that is approximately equal to a coefficient of determination (R²) relative to the regression function, but also to detect non-linear relationships between variables. Recently, Murrell et al., 2016 [9] proposed an approach similar to MIC that additionally included the advantages of fast convergence with rising sample size and having more power to detect the relationships compared to MIC. Both MIC and Murrell’s method follow desired properties of bivariate association, generality and equitability [9]. Murrell and his colleagues have suggested a new measure of bivariate association, which is the same as R², but powerful when the parametric form of association is unknown. A point of particular importance is that through applying this method both generality and equitability can be attained by estimating a generalized R² based on density approximation. We believe that this method has advantages that merit it to be considered in GWAS as the associations between the SNP dosage and the phenotype are expected to be complex. More importantly, this method does not rely on strict assumptions such as normality of the phenotype distribution as well as linearity of the genetic effect (or an additive genetic effect, which is assumed in most GWAS). Additionally, when related samples such as twins or family data are included in association studies, more model assumptions are imposed. Hence, the assumption-free or generalized measurements of association may be advantageous in genetic association studies.

In this study, we aimed to compare the performance of popular linear regression models and the generalized correlation coefficient (GCC) method to identify genetic variants, genes and pathways in Danish and Chinese GWASs of cognitive function.

Results

The study population comprised Danish and Chinese GWAS data. A description of the two samples is illustrated in Table 1. The means of cognitive function in Danish and Chinese data are 45.86 and 21.01 respectively. We validated the three models, GCC, Kinship, and mixed-linear model (LME), by estimating type I error rates after simulating genotypes for one SNP and a random phenotype (standard normal) for 1000 replications. The type I error rates estimated for GCC, Kinship and LME were 0.052, 0.052 and 0.050, respectively. This indicates that the three models are generally unbiased.

Discussion

The literature on GWAS data analysis has been dominated by multiple assumptions (e.g. additive or dominant genetic effects, and normal distribution of phenotypes), which, if not fulfilled, could be speculated to be responsible for low statistical power, missing heritability and the lack of replication of GWAS findings. Our study, through model comparison and validation of GWAS results from two independent samples of different ethnicity, illustrates the strength of the GCC method over popular linear models, with more replicated GCC-based results and cognition-implicated SNPs and functional pathways.

Among the two genome-wide significant SNPs identified in the GCC-based GWAS in the Danish sample, rs71419535 is near THSD7B, which is associated with melanoma, metabolism, and Cutaneous Malignant 1 diseases. Variation in this gene has been shown to associate with multiple system atrophy, which is an adult-onset neurodegenerative disorder [10]. The other SNP, rs905838, is near CTD-2533K21.4, which is a novel transcript highly expressed in brain hippocampus. Among the two genome-wide significant SNPs found in the GCC-based GWAS in the Chinese sample, rs2292999 on chromosome 3 is located near ABCC5, which is expressed in both brain and muscle tissue, and rs17019635 on chromosome 3 near GRID2, which is expressed in the brain. The ABCC5 gene has previously been found to encode a general glutamate conjugate and analog transporter that can limit the brain levels of endogenous metabolites, drugs, and toxins [11]. ABCC5 is additionally related to the ‘Blood-Brain Barrier’ and ‘Immune Cell Transmigration’ pathways. Glutamate is the principal excitatory neurotransmitter in the brain. It is crucial for learning and memory in everyday brain functions but causes excitotoxic damage in traumatic brain injury and stroke [11, 12]. The GRID2 gene is highly expressed in brain and associated with depression. This gene plays a role in synapse organization between parallel fibers and Purkinje cells (a class of GABAergic neurons in the cerebellum in the brain). The implications of GABAergic neurotransmission in Alzheimer’s disease (AD) have been discussed [13–15], and in the processes of learning and memory, changes in GABAergic function could be an important factor in both early and later stages of AD pathogenesis [15]. Furthermore, the two top genes from the GCC-based GWAS found in both the Danish and Chinese samples, CSMD1 and PTPRD, are very interesting; a variant in CSMD1 was recently associated with cognitive function [16], and in a very recent study, the PTPRD gene was discussed as a druggable target, and a marker for and an important constituent of brain circuits of likely importance for major brain-based phenotypes [17].

Although some significant pathways were identified from the GWAS results generated using all models, more biologically meaningful pathways were found when using the GCC method. Importantly, more genes and pathways identified from the CGG GWAS results were replicated in the Chinese sample than was the case for the linear models. Some replicated pathways from the GCC model GWAS results were pathways in calcium signaling, Type II diabetes mellitus, long-term depression, melanogenesis, axon guidance, focal adhesion, MAPK-signaling, Hedgehog signaling, GnRH signaling, and some related to cardiomyopathy (Table 2). The replicated pathways from the linear model GWAS results were related to focal adhesion, Wnt signaling, and T cell receptor signaling (Table 2).

Calcium signaling and potassium channels have been reported in aging-related diseases, including cognitive function. Calcium signaling is a crucial messenger between synapse and nucleus as calcium transient in nucleus is needed for neuroadaptations to switch on the necessary genes [18]. Additionally, dysregulated expression of calcium signaling genes has been shown to occur with progression of Alzheimer’s-type pathology in the aging brain [19]. Type II diabetes mellitus is discussed in numerous studies because of the presumed role of it in increasing the risk of cognitive impairment and dementia [20, 21]. Focal adhesion is involved in integrin adhesion, communication between the extracellular matrix and the actin cytoskeleton, and the regulation of many cell types. Loss of cell adhesion can lead to cell death and altered focal signaling has been linked to synaptic loss, which may cause AD [22, 23]. There is evidence that axon guidance might play a role in some brain disorders such as Parkinson’s and AD [24].

The Wnt signaling pathway is also important and many recent studies have discussed and reported this pathway in relation to aging and AD, where the loss of canonical Wnt signaling has been found to be involved in the pathogenesis of AD, and play a role in synaptic plasticity and maintenance in the adult brain [25, 26].

In the literature, there is evidence regarding the role of MAPK-signaling, long-term depression, Hedgehog signaling, GnRH signaling, melanogenesis, T cell receptor pathways, cancer, vascular smooth muscle cells and hypertrophic cardiomyopathy (HCM) on cognitive function, Alzheimer’s, Parkinson's and Huntington’s diseases, and age-related neurodegenerative disorders [19, 27–34].

Moreover, worth mentioning are the pathways ‘neuroactive ligand receptor interaction’ and ‘Alzheimer's disease’ that were identified among the 28 KEGG pathways identified from the 476 genes overlapping between the gene-based analysis of Danish and Chinese GCC-based GWAS results (Supplementary Table 15). The neuroactive ligand receptor interaction is important as it comprises genes involved in transmission across chemical synapses [19], and cognitive decline is the earliest sign of AD.

In Figure 4, it is indicated that the statistical significance or the p-values for the same SNPs identified by the GCC and the kinship models are very different. This can potentially be explained by the fact that the linear model is unable to capture SNPs with non-additive effects, while SNPs with an additive effect are best fitted by the linear model. Based on this, we believe that to detect SNPs with an additive effect and SNPs with a non-additive effect both the GCC and a linear model should be applied on the same data when performing a GWAS, i.e. with GCC as a complementary approach to the conventional linear model. As shown in Figure 4, the number of SNPs with a non-additive effect is relatively large compared to the number of SNPs with an additive effect in both the Danish and Chinese samples. This finding is highly important because it suggests that a considerable number of significant SNPs could have been missed in GWASs performed so far due to the search being limited to SNPs with an additive genetic effect.

A limitation of the GCC method, and different from the conventional linear models that report regression coefficients with a direction of effect (+ or -), is that the association parameter from GCC, A, has no direction, which is understandable because direction of effect does not make sense in case of a non-linear relationship. We argue that, as a hypothesis-free or agnostic approach, the primary goal is to identify reliably significant SNP markers. The pattern of association for specific markers can be examined empirically by plotting the data to reveal the various relationships not limited to minus or plus. For SNPs not captured by the linear model, the linear model results can still provide reference information about the direction of the GCC correlation. However, as an assumption-free approach, GCC is inherently robust in handling correlated or structured samples in association testing. The QQ plots in Figure 3 all show that the statistical significance estimated by GCC is not affected by the twin correlation in our samples, with genomic inflation factors comparable to those found for kinship and mixed effect models, which are models specifically dealing with the twin correlation in our samples. In fact, the null distribution for estimating GCC is calculated based on the marginal distributions of the correlated twin samples. As a result, the association assessment by GCC is conditional on the correlated structure in the twin samples, ensuring unbiased estimates of statistical significance. Moreover, unlike the linear models, GCC is insensitive to outliers or extreme phenotype values. All of the above features make GCC a valuable approach for GWAS of complex phenotypes.

Conclusions

As a generalized measurement of association, GCC is capable of capturing different patterns of genotype-phenotype correlation, not limited to additive genetic effects. As an assumption-free approach, GCC is robust in dealing with correlated samples, e.g. twins, and skewed phenotype distributions, e.g. cognition, as compared to the linear models. By exemplifying and illustrating the advantages and the necessity of GCC in GWAS, this study could serve as a precedent for application and further development of assumption-free methods to complement current GWAS on cognitive traits and on other complex traits as well.

Materials and Methods

Supplementary Materials

Supplementary Figures

Supplementary Tables