There is great interest to sequence unrelated or pedigree samples for detecting rare variant quantitative trait associations. In order to reduce the cost of sequencing and improve power, many studies sequence selected samples with extreme traits. Existing methods for detecting rare variant associations were developed for unrelated samples. Methods are needed to analyze (selected or randomly ascertained) pedigree samples.
We propose a unified framework of modeling extreme trait genetic associations (MEGA) with rare variants. Using MEGA and appropriate permutation algorithms, many rare variant tests can be extended to family data. As an application, we compared study designs using both sib-pairs and unrelated individuals. Extensive simulations were carried out using realistic population genetic and complex trait models.
It is demonstrated that when extreme sampling is implemented within equal-sized cohorts of unrelated individuals or sib-pairs, analyzing unrelated individuals is consistently more powerful than studying sib-pairs. A higher portion of rare variants can be identified through sequencing unrelated samples compared to sibs. Alternatively, if samples are ascertained using fixed thresholds from an infinite-sized population, sequencing one sib with the most extreme trait from each extreme concordant sib-pair is consistently the most powerful design.
MEGA will play an important role in the analysis of sequence-based genetic association studies.
Extreme sampling; Next-generation sequencing; Pedigree samples; Quantitative trait loci; Rare variants
It is generally known that risk variants segregate together with a disease within families but this information has not been used in the existing statistical methods for detecting rare variants. Here we introduce two weighted sum statistics that can apply to either genome-wide association data or resequencing data for identifying rare disease variants: weights calculated based on sibpairs and odd ratios, respectively. We evaluated the two methods via extensive simulations under different disease models. We compared the proposed methods with the weighted sum statistic (WSS) proposed by Madsen and Browning, keeping the same genotyping or resequencing cost. Our methods clearly demonstrate more statistical power than the WSS. In addition, we found using sibpair information can increase power over using only unrelated samples by more than 40%. We applied our methods to the Framingham Heart Study (FHS) and Wellcome Trust Case Control Consortium (WTCCC) hypertension datasets. Although we did not identify any genes as reaching a genome-wide significance level, we found variants in the candidate gene angiotensinogen (AGT) significantly associated with hypertension at P=6.9×10-4, whereas the most significant single SNP association evidence is P=0.063. We further applied the odds ratio weighted method to the IFIH1 gene for type 1 diabetes in the WTCCC data. Our method yielded a P value of 4.82×10-4, much more significant than that obtained by haplotype-based methods. We demonstrated that family data are extremely informative in searching for rare variants underlying complex traits, and the odds ratio weighted sum statistic is more efficient than currently existing methods.
We evaluate four association tests for rare variants—the combined multivariate and collapsing (CMC) method, two weighted-sum methods, and a variable threshold method—by applying them to the simulated data sets of unrelated individuals in the Genetic Analysis Workshop 17 (GAW17) data. The family-wise error rate (FWER) and average power are used as criteria for evaluation. Our results show that when all nonsynonymous SNPs (rare variants and common variants) in a gene are jointly analyzed, the CMC method fails to control the FWER; when only rare variants (single-nucleotide polymorphisms with minor allele frequency less than 0.05) are analyzed, all four methods can control FWER well. All four methods have comparable power, which is low for the analysis of the GAW17 data sets. Three of the methods (not including the CMC method) involve estimation of p-values using permutation procedures that either can be computationally intensive or generate inflated FWERs. We adapt a fast permutation procedure into these three methods. The results show that using the fast permutation procedure can produce FWERs and average powers close to the values obtained from the standard permutation procedure on the GAW17 data sets. The standard permutation procedure is computationally intensive.
Genome-wide association studies are a powerful approach used to identify common variants for complex disease. However, the traditional genome-wide association methods may not be optimal when they are applied to rare variants because of the rare variants’ low frequencies and weak signals. To alleviate the difficulty, investigators have proposed many methods that collapse rare variants. In this paper, we propose a novel ranking method, which we call stability selection based on random collapsing, to rank the candidate rare variants. We use the simulated mini-exome data sets of unrelated individuals from Genetic Analysis Workshop 17 for the analysis. The numerical results suggest that the selection based on a random collapsing method is promising for identifying functional rare variants in genome-wide association studies. Further research to examine the error control property of the proposed method is underway.
Previously described methods for the combined analysis of common and rare variants have disadvantages such as requiring an arbitrary classification of variants or permutation testing to assess statistical significance. Here we propose a novel method which implements a weighting scheme based on allele frequencies observed in both cases and controls. Because the test is unbiased, scores can be analyzed with a standard t-test. To test its validity we applied it to data for common, rare, and very rare variants simulated under the null hypothesis. To test its power we applied it to simulated data in which association was present, including data using the observed allele frequencies of common and rare variants in NOD2 previously reported in cases of Crohn’s disease and controls. The method produced results that conformed well to those expected under the null hypothesis. It demonstrated more power to detect association when rare and common variants were analyzed jointly, the power further increasing when rare variants were assigned higher weights. 20,000 analyses of a gene containing 62 variants could be performed in 80 minutes on a laptop. This approach shows promise for the analysis of data currently emerging from genome wide sequencing studies.
common; rare; variant; sequence; genome; exome
Technological advances make it possible to use high-throughput sequencing as a primary discovery tool of medical genetics, specifically for assaying rare variation. Still this approach faces the analytic challenge that the influence of very rare variants can only be evaluated effectively as a group. A further complication is that any given rare variant could have no effect, could increase risk, or could be protective. We propose here the C-alpha test statistic as a novel approach for testing for the presence of this mixture of effects across a set of rare variants. Unlike existing burden tests, C-alpha, by testing the variance rather than the mean, maintains consistent power when the target set contains both risk and protective variants. Through simulations and analysis of case/control data, we demonstrate good power relative to existing methods that assess the burden of rare variants in individuals.
Developments in sequencing technology now enable us to assay all genetic variation, much of which is extremely rare. We propose to test the distribution of rare variants we observe in cases versus controls. To do so, we present a novel application of the C-alpha statistic to test these rare variants. C-alpha aims to determine whether the set of variants observed in cases and controls is a mixture, such that some of the variants confer risk or protection or are phenotypically neutral. Risk variants are expected to be more common in cases; protective variants more common in controls. C-alpha is sensitive to this imbalance, regardless of its origin—risk, protective, or both—but is ideally suited for a mixture of protective and risk variants. Variation in APOB nicely illustrates a mixture, in that certain rare variants increase triglyceride levels while others decrease it. The hallmark feature of C-alpha is that it uses the distribution of variation observed in cases and controls to detect the presence of a mixture, thus implicating genes or pathways as risk factors for disease.
Because of the low frequency of rare genetic variants in observed data, the statistical power of detecting their associations with target traits is usually low. The collapsing test of collective effect of multiple rare variants is an important and useful strategy to increase the power; in addition, family data may be enriched with causal rare variants and therefore provide extra power. However, when family data are used, both population structure and familial relatedness need to be adjusted for the possible inflation of false positives. Using a unified mixed linear model and family data, we compared six methods to detect the association between multiple rare variants and quantitative traits. Through the analysis of 200 replications of the quantitative trait Q2 from the Genetic Analysis Workshop 17 data set simulated for 697 subjects from 8 extended families, and based on quantile-quantile plots under the null and receiver operating characteristic curves, we compared the false-positive rate and power of these methods. We observed that adjusting for pedigree-based kinship gives the best control for false-positive rate, whereas adjusting for marker-based identity by state slightly outperforms in terms of power. An adjustment based on a principal components analysis slightly improves the false-positive rate and power. Taking into account type-1 error, power, and computational efficiency, we find that adjusting for pedigree-based kinship seems to be a good choice for the collective test of association between multiple rare variants and quantitative traits using family data.
Next-generation sequencing technology allows investigation of both common and rare variants in humans. Exomes are sequenced on the population level or in families to further study the genetics of human diseases. Genetic Analysis Workshop 17 (GAW17) provided exomic data from the 1000 Genomes Project and simulated phenotypes. These data enabled evaluations of existing and newly developed statistical methods for rare variant sequence analysis for which standard statistical methods fail because of the rareness of the alleles. Various alternative approaches have been proposed that overcome the rareness problem by combining multiple rare variants within a gene. These approaches are termed collapsing methods, and our GAW17 group focused on studying the performance of existing and novel collapsing methods using rare variants. All tested methods performed similarly, as measured by type I error and power. Inflated type I error fractions were consistently observed and might be caused by gametic phase disequilibrium between causal and noncausal rare variants in this relatively small sample as well as by population stratification. Incorporating prior knowledge, such as appropriate covariates and information on functionality of SNPs, increased the power of detecting associated genes. Overall, collapsing rare variants can increase the power of identifying disease-associated genes. However, studying genetic associations of rare variants remains a challenging task that requires further development and improvement in data collection, management, analysis, and computation.
1000 Genomes Project; association; collapsing methods; next-generation sequencing
Next-generation sequencing technologies are rapidly changing the field of genetic epidemiology and enabling exploration of the full allele frequency spectrum underlying complex diseases. Although sequencing technologies have shifted our focus toward rare genetic variants, statistical methods traditionally used in genetic association studies are inadequate for estimating effects of low minor allele frequency variants. Four our study we use the Genetic Analysis Workshop 17 data from 697 unrelated individuals (genotypes for 24,487 autosomal variants from 3,205 genes). We apply a Bayesian hierarchical mixture model to identify genes associated with a simulated binary phenotype using a transformed genotype design matrix weighted by allele frequencies. A Metropolis Hasting algorithm is used to jointly sample each indicator variable and additive genetic effect pair from its conditional posterior distribution, and remaining parameters are sampled by Gibbs sampling. This method identified 58 genes with a posterior probability greater than 0.8 for being associated with the phenotype. One of these 58 genes, PIK3C2B was correctly identified as being associated with affected status based on the simulation process. This project demonstrates the utility of Bayesian hierarchical mixture models using a transformed genotype matrix to detect genes containing rare and common variants associated with a binary phenotype.
Using the exome sequencing data from 697 unrelated individuals and their simulated disease phenotypes from Genetic Analysis Workshop 17, we develop and apply a gene-based method to identify the relationship between a gene with multiple rare genetic variants and a phenotype. The method is based on the Mantel test, which assesses the correlation between two distance matrices using a permutation procedure. Using up to 100,000 permutations to estimate the statistical significance in 200 replicate data sets, we found that the method had 5.1% type I error at an α level of 0.05 and had various power to detect genes with simulated genetic associations. FLT1 and KDR had the most significant correlations with Q1 and were replicated 170 and 24 times, respectively, in 200 simulated data sets using a Bonferroni corrected p-value of 0.05 as a threshold. These results suggest that the distance correlation method can be used to identify genotype-phenotype association when multiple rare genetic variants in a gene are involved.
Genotyping of rare variants on a large scale is now possible using next-generation sequencing. The sample selection is a crucial step in designing the genetic study of a complex disease and knowledge of the efficiency and limitations of the population-based and family-based designs can help making the appropriate choice.
The 9 contributions to the Group 5 of the Genetic Analysis Workshop 17 evaluated the population-based and family-based designs by comparing the results obtained with various methods applied on the mini-exome simulations. These simulations consisted of 200 replicates comprising unrelated individuals and 8 extended pedigrees with genotypes and various phenotypes. The methods tested for association with a population-based and/or a family-based design, tested for linkage with a family-based design or estimated heritability.
In this paper, we summarize the strength and weaknesses of both designs. While a population-based design seems more suitable to detect the effect of multiple rare variants, a family-based design can potentially enrich the sample in very rare variants, for which the effect would be concealed at the population level. However, as of today, the main limitation is still the expensive cost of next-generation sequencing.
Genetic Analysis Workshop; 1000 genome project; next-generation sequencing; linkage; association; aggregation; familial relatedness; population stratification; heritability
Tiled regression is an approach designed to determine the set of independent genetic variants that contribute to the variation of a quantitative trait in the presence of many highly correlated variants. In this study, we evaluate the statistical properties of the tiled regression method using the Genetic Analysis Workshop 17 data in unrelated individuals for traits Q1, Q2, and Q4. To increase the power to detect rare variants, we use two methods to collapse rare variants and compare the results with those from the uncollapsed data. In addition, we compare the tiled regression method to traditional tests of association with and without collapsed rare variants. The results show that collapsing rare variants generally improves the power to detect associations regardless of method, although only variants with the largest allelic effects could be detected. However, for traditional simple linear regression, the average estimated type I error is dependent on the trait and varies by about three orders of magnitude. The estimated type I error rate is stable for tiled regression across traits.
Large genome-wide association studies have been performed to detect common genetic variants involved in common diseases, but most of the variants found this way account for only a small portion of the trait variance. Furthermore, candidate gene based resequencing suggests that many rare genetic variants contribute to the trait variance of common diseases. Here we propose two designs, sibpair and unrelated-case designs, to detect rare genetic variants in either a candidate gene based or genome-wide association analysis. First we show that we can detect and classify together rare risk haplotypes using a relatively small sample with either of these designs, and then have increased power to test association in a larger case-control sample. This method can also be applied to resequencing data. Next we apply the method to the Wellcome Trust Case Control Consortium (WTCCC) coronary artery disease and hypertension data, the latter being the only trait for which no genome-wide association evidence was reported in the original WTCCC study, and identify one interesting gene associated with hypertension and four associated with coronary artery disease at a genome-wide significance level of 5%. These results suggest that searching for rare genetic variants is feasible and can be fruitful in current genome-wide association studies, candidate gene studies or resequencing studies.
Recently there has been great interest in identifying rare variants associated with common diseases. We apply several collapsing-based and kernel-based single-gene association tests to Genetic Analysis Workshop 17 (GAW17) rare variant association data with unrelated individuals without knowledge of the simulation model. We also implement modified versions of these methods using additional information, such as minor allele frequency (MAF) and functional annotation. For each of four given traits provided in GAW17, we use the Bayesian mixed-effects model to estimate the phenotypic variance explained by the given environmental and genotypic data and to infer an individual-specific genetic effect to use directly in single-gene association tests. After obtaining information on the GAW17 simulation model, we compare the performance of all methods and examine the top genes identified by those methods. We find that collapsing-based methods with weights based on MAFs are sensitive to the “lower MAF, larger effect size” assumption, whereas kernel-based methods are more robust when this assumption is violated. In addition, many false-positive genes identified by multiple methods often contain variants with exactly the same genotype distribution as the causal variants used in the simulation model. When the sample size is much smaller than the number of rare variants, it is more likely that causal and noncausal variants will share the same or similar genotype distribution. This likely contributes to the low power and large number of false-positive results of all methods in detecting causal variants associated with disease in the GAW17 data set.
Related cases may be included in case-control association studies if correlations between related individuals due to identity-by-descent (IBD) sharing are taken into account. We derived a framework to test for association in a case-control design including affected sibships and unrelated controls. First, a corrected variance for the allele frequency difference between cases and controls was directly calculated or estimated in two ways on the basis of the fixation index FST and the inbreeding coefficient. Then the correlation-corrected association test including controls and affected sibs was carried out. We applied the three strategies to 20 candidate genes on the Genetic Analysis Workshop 15 rheumatoid arthritis data and to 9187 single-nucleotide polymorphisms of replicate one of the Genetic Analysis Workshop 15 simulated data with knowledge of the "answers". The three strategies used to correct for correlation give only minor differences in the variance estimates and yield an almost correct type I error rate for the association tests. Thus, all strategies considered to correct the variance performed quite well.
We applied a new approach based on Mantel statistics to analyze the Genetic Analysis Workshop 14 simulated data with prior knowledge of the answers. The method was developed in order to improve the power of a haplotype sharing analysis for gene mapping in complex disease. The new statistic correlates genetic similarity and phenotypic similarity across pairs of haplotypes from case-control studies. The genetic similarity is measured as the shared length between haplotype pairs around a genetic marker. The phenotypic similarity is measured as the mean corrected cross-product based on the respective phenotypes. Cases with phenotype P1 and unrelated controls were drawn from the population of Danacaa. Power to detect main effects was compared to the X2-test for association based on 3-marker haplotypes and a global permutation test for haplotype association to test for main effects. Power to detect gene × gene interaction was compared to unconditional logistic regression. The results suggest that the Mantel statistics might be more powerful than alternative tests.
Searching for rare genetic variants associated with complex diseases can be facilitated by enriching for diseased carriers of rare variants by sampling cases from pedigrees enriched for disease, possibly with related or unrelated controls. This strategy, however, complicates analyses because of shared genetic ancestry, as well as linkage disequilibrium among genetic markers. To overcome these problems, we developed broad classes of “burden” statistics and kernel statistics, extending commonly used methods for unrelated case-control data to allow for known pedigree relationships, for autosomes and the X chromosome. Furthermore, by replacing pedigree-based genetic correlation matrices with estimates of genetic relationships based on large-scale genomic data, our methods can be used to account for population-structured data. By simulations, we show that the type I error rates of our developed methods are near the asymptotic nominal levels, allowing rapid computation of P-values. Our simulations also show that a linear weighted kernel statistic is generally more powerful than a weighted “burden” statistic. Because the proposed statistics are rapid to compute, they can be readily used for large-scale screening of the association of genomic sequence data with disease status.
burden test; kernel statistic; rare variants; pedigree data; genome sequence data
To enable the assessment of compound heterozygosity, we propose a simple approach for incorporating genotype phase in a rare variant collapsing procedure for the analysis of DNA sequence data. When multiple variants are identified within a gene, knowing the phase of each variant may provide additional statistical power to detect associations with phenotypes that follow a recessive or additive inheritance pattern. We begin by phasing all marker data; then, we collapse nonsynonymous single-nucleotide polymorphisms within genes on each phased haplotype, resulting in a single diploid genotype for each gene, which represents whether one or both haplotypes carry a nonsynonymous variant allele. A recessive or additive association test can then be used to assess the relationship between the collapsed genotype and the phenotype of interest. We apply this approach to the unrelated individuals data from Genetic Analysis Workshop 17 and compare the results of the additive test with a dominant test in which phase is not informative. Analysis of the first phenotype replicate shows that the FLT1 gene is significantly associated with both Q1 and the binary affection status phenotype. This association was detected by both the additive and dominant tests, although the additive phase-informed test resulted in a smaller p-value. No false-positive results were detected in the first phenotype replicate. Analysis of the average values of all phenotype replicates correctly identified five other genes important to the simulation, but with an increase in false-positive rates. The accuracy of our method is contingent on correct phase determination.
Both family- and population-based samples are used to identify genetic variants associated with phenotypes. Each strategy has demonstrated advantages, but their ability to identify rare variants and genes containing rare variants is unclear. To compare these two study designs in the identification of rare causal variants, we applied various methods to the population- and family-based data simulated by the Genetic Analysis Workshop 17 with knowledge of the simulated model. Our results suggest that different variants can be identified by different study designs. Family-based and population-based study designs can be complementary in the identification of rare causal variants and should be considered in future studies.
Existing methods for analyzing rare variant data focus on collapsing a group of rare variants into a single common variant; collapsing is based on an intuitive function of the rare variant genotype information, such as an indicator function or a weighted sum. It is more natural, however, to take into account the single-nucleotide polymorphism (SNP) interactions informed directly by the data. We propose a novel tree-based method that automatically detects SNP interactions and generates candidate markers from the original pool of rare variants. In addition, we utilize the advantage of having 200 phenotype replications in the Genetic Analysis Workshop 17 data to assess the candidate markers by means of repeated logistic regressions. This new approach shows potential in the rare variant analysis. We correctly identify the association between gene FLT1 and phenotype Affect, although there exist other false positives in our results. Our analyses are performed without knowledge of the underlying simulating model.
In the past few years, case-control studies of common diseases have shifted their focus from single genes to whole exomes. New sequencing technologies now routinely detect hundreds of thousands of sequence variants in a single study, many of which are rare or even novel. The limitation of classical single-marker association analysis for rare variants has been a challenge in such studies. A new generation of statistical methods for case-control association studies has been developed to meet this challenge. A common approach to association analysis of rare variants is the burden-style collapsing methods to combine rare variant data within individuals across or within genes. Here, we propose a new hybrid likelihood model that combines a burden test with a test of the position distribution of variants. In extensive simulations and on empirical data from the Dallas Heart Study, the new model demonstrates consistently good power, in particular when applied to a gene set (e.g., multiple candidate genes with shared biological function or pathway), when rare variants cluster in key functional regions of a gene, and when protective variants are present. When applied to data from an ongoing sequencing study of bipolar disorder (191 cases, 107 controls), the model identifies seven gene sets with nominal p-values0.05, of which one MAPK signaling pathway (KEGG) reaches trend-level significance after correcting for multiple testing.
Inexpensive, high-throughput sequencing has transformed the field of case-control association studies. For the first time, it may be possible to identify the genetic underpinnings of complex diseases, by sequencing the DNA of hundreds (even thousands) of cases and controls and comparing patterns of DNA sequence variation. However, complex diseases are likely to be caused by many variants, some of which are very rare. Taken one at a time, the association between variant and disease phenotype may not be detectable by current statistical methods. One strategy is to identify regions where important variants occur by “collapsing” variants into groups. Here, we present a new collapsing approach, capable of detecting subtle genetic differences between cases and controls. We show, in extensive simulations and using a benchmark set of genes involved in human triglyceride levels, that the approach is potentially more powerful than existing methods. We apply the new method to an ongoing sequencing study of bipolar cases and controls and identify a set of genes found in neuronal synapses, which may be implicated in bipolar disorder.
Recent advances in next-generation sequencing technologies facilitate the detection of rare variants, making it possible to uncover the roles of rare variants in complex diseases. As any single rare variants contain little variation, association analysis of rare variants requires statistical methods that can effectively combine the information across variants and estimate their overall effect. We here propose a novel Bayesian generalized linear model for analyzing multiple rare variants within a gene or genomic region in genetic association studies. Our model can deal with complicated situations that have not been fully addressed by existing methods, including issues of disparate effects and non-functional variants. Our method jointly models the overall effect and the weights of multiple rare variants and estimates them from the data. This approach produces different weights to different variants based on their contributions to the phenotype, yielding an effective summary of the information across variants. We evaluate the proposed method and compare its performance to existing methods on extensive simulated data. The results show that the proposed method performs well under all situations and is more powerful than existing approaches.
Bayesian Analysis; Complex Diseases; Disparate Effects; Genetic Association; Hierarchical Models; Rare Variants; Sequence Data
Genome-wide association studies for complex traits are based on the common disease/common variant (CDCV) and common disease/rare variant (CDRV) assumptions. Under the CDCV hypothesis, classical genome-wide association studies using single-marker tests are powerful in detecting common susceptibility variants, but under the CDRV hypothesis they are not as powerful. Several methods have been recently proposed to detect association with multiple rare variants collectively in a functional unit such as a gene. In this paper, we compare the relative performance of several of these methods on the Genetic Analysis Workshop 17 data. We evaluate these methods using the unrelated individual and family data sets. Association was tested using 200 replicates for the quantitative trait Q1. Although in these data the power to detect association is often low, our results show that collapsing methods are promising tools. However, we faced the challenge of assessing the proper type I error to validate our power comparisons. We observed that the type I error rate was not well controlled; however, we did not find a general trend specific to each method. Each method can be conservative or nonconservative depending on the studied gene. Our results also suggest that collapsing and the single-locus association approaches may not be affected to the same extent by population stratification. This deserves further investigation.
Linkage- and association-based methods have been proposed for mapping disease-causing rare variants. Based on the family information provided in the Genetic Analysis Workshop 17 data set, we formulate a two-pronged approach that combines both methods. Using the identity-by-descent information provided for eight extended pedigrees (n = 697) and the simulated quantitative trait Q1, we explore various traditional nonparametric linkage analysis methods; the best result is obtained by assuming between-family heterogeneity and applying the Haseman-Elston regression to each pedigree separately. We discover strong signals from two genes in two different families and weaker signals for a third gene from two other families. As an exploratory approach, we apply an association test based on a modified family-based association test statistic to all rare variants (frequency < 1% or < 3%) designated as causal for Q1. Family-based association tests correctly identified causal single-nucleotide polymorphisms for four genes (KDR, VEGFA, VEGFC, and FLT1). Our results suggest that both linkage and association tests with families show promise for identifying rare variants.
Genome-wide association studies have been successful at identifying common disease variants associated with complex diseases, but the common variants identified have small effect sizes and account for only a small fraction of the estimated heritability for common diseases. Theoretical and empirical studies suggest that rare variants, which are much less frequent in populations and are poorly captured by single-nucleotide polymorphism chips, could play a significant role in complex diseases. Several new statistical methods have been developed for the analysis of rare variants, for example, the combined multivariate and collapsing method, the weighted-sum method and a replication-based method. Here, we apply and compare these methods to the simulated data sets of Genetic Analysis Workshop 17 and thereby explore the contribution of rare variants to disease risk. In addition, we investigate the usefulness of extreme phenotypes in identifying rare risk variants when dealing with quantitative traits. Finally, we perform a pathway analysis and show the importance of the vascular endothelial growth factor pathway in explaining different phenotypes.