The cost of next-generation sequencing is now approaching that of early GWAS panels, but is still out of reach for large epidemiologic studies and the millions of rare variants expected poses challenges for distinguishing causal from non-causal variants. We review two types of designs for sequencing studies: two-phase designs for targeted follow-up of genomewide association studies using unrelated individuals; and family-based designs exploiting co-segregation for prioritizing variants and genes. Two-phase designs subsample subjects for sequencing from a larger case-control study jointly on the basis of their disease and carrier status; the discovered variants are then tested for association in the parent study. The analysis combines the full sequence data from the substudy with the more limited SNP data from the main study. We discuss various methods for selecting this subset of variants and describe the expected yield of true positive associations in the context of an on-going study of second breast cancers following radiotherapy. While the sharing of variants within families means that family-based designs are less efficient for discovery than sequencing unrelated individuals, the ability to exploit co-segregation of variants with disease within families helps distinguish causal from non-causal ones. Furthermore, by enriching for family history, the yield of causal variants can be improved and use of identity-by-descent information improves imputation of genotypes for other family members. We compare the relative efficiency of these designs with those using unrelated individuals for discovering and prioritizing variants or genes for testing association in larger studies. While associations can be tested with single variants, power is low for rare ones. Recent generalizations of burden or kernel tests for gene-level associations to family-based data are appealing. These approaches are illustrated in the context of a family-based study of colorectal cancer. While this would tend to induce a spurious association between any variants in LD with the GWAS SNPs and disease even under the null hypothesis that they are not causal, this bias can be avoided by adjusting for the sampling fractions, and additional information available in the full study can also be incorporated. The basic principles were developed in a series of seminal papers by Norman Breslow with various colleagues  technologies that could in principle (given a large enough sample size and deep enough sequencing) uncover step analysis for better power while being robust to bias from population stratification , but the statistical efficiency for discovery or association testing per subject genotyped is typically higher using unrelated controls than using unaffected siblings or other relatives  could affect its function, so aggregating variants within genes may also improve power. To address this need, a host of “burden” tests have been developed based on counts of rare variants, weighted in various fashions  Study of the risk of second breast cancers among survivors of a first breast cancer, focusing on radiation dose to the contralateral breast . For the purpose of comparing different designs, we have selected some samples from multiple-case families and some from unrelated cases or controls in various ways. Ultimately these data would be used to compare designs empirically in terms of the yield of significant findings by subsampling from these real data .As an example of a family-based design, we are currently performing deep targeted resequencing of 11 replicated regions identified by previous GWASs as associated with colorectal cancer (CRC), using ~4200 samples drawn from the Colon Cancer Family Registries (C-CFR). The C-CFR is an international collaboration of registries of families ascertained through CRC in various ways, some population-based, some from high-risk genetic clinics, some including population controls or control families . The aim of a targeted resequencing study is therefore to exhaustively re-sequence the region to identify One obvious method of prioritization would be on the basis of novelty, i.e., to focus attention on variants that have not been seen previously (or only rarely) among population controls. With the growing catalog of sequence variants in public databases like the 1000 Genomes Project, many causal variants are likely already to have been discovered and those that are novel are likely to be so rare that there would be very little power testing their association individually with disease. Furthermore, most novel variants are likely to be neutral. Nevertheless, the discovery of a novel association with disease is important, irrespective of whether or not the existence of the variant has been previously reported, but a discovery of a novel variant and its association with disease is particularly noteworthy. The same applies to filtering based on differences in allele frequencies between cases and controls within the sequencing subset  at loci v and corresponding regression coefficients β = (βv), e.g., a general linear model of the form f[E(Yi)] = G′iβ, and a second (variant)-level model for the distribution of these regression coefficients as a function of prior covariates Zv, e.g., a linear regression model of the form E(βv) = Z′vπ (or) perhaps a model for their variances or covariances ] = Z′vα , in contrast to filtering approaches, which can lead to substantial loss of power if either sensitivity or specificity is low.Hierarchical modeling  by genotyping; (ii) by imputation; or (iii) by joint analysis.The first of these is the simplest, but most expensive. One simply does custom genotyping in the main study of the prioritized variants. Under the hypothesis that any causal variants are likely to have been discovered by sequencing and that they survived prioritization, then the genotype data for the main study should be sufficient and associations can be tested directly, with appropriate correction for the effective number of independent tests performed ] WiGi = 0, where pi(β) = expit(G′iβ) and Wi = Nsi/nsi, si being the sampling stratum to which subject i belongs and Ns and ns the main study and substudy sample sizes respectively. While simple in concept, the disadvantage is that the only information used from the main study is the stratum sample sizes. A refinement of this approach is to replace the empiric weights based on the realized sample sizes by predicted weights based on a logistic regression of sampling probabilities on additional covariates available for all main study participants. Recent papers show how this basic approach can be stabilized by using “calibrated weights” without requiring assumptions about the validity of an imputation model using influence residuals , weighted likelihood (WL), and semi-parametric likelihood . Fortunately, the design is often relatively insensitive to these parameters, so that a balanced design in which the various strata are represented by equal numbers proportional allocation of substudy subjects across strata. If instead one is designing both the main study and substudy de novo or if custom follow-up genotyping of the main study is planned, then the relative sample sizes of the two phases also need to be considered. In either case, there are likely to be multiple hypotheses being tested, so optimization of power for a specific type of variant may be less helpful than a global optimization. For this purpose, we have previously considered Asymptotic Relative Cost Efficiency, a quantity inversely proportional to the total cost times the variance of the parameter of interest, combining main and substudy data , what proportion would be truly causal, and both novel and causal?Among the discovered variants in each category , what is the power for testing association in the main study, after Bonferroni adjustment for the number of markers tested?Putting all these together, what is the expected overall yield of novel, causal discoveries?To illustrate the potential yield from a sequencing substudy, we consider whole genome sequencing of a subset of 200 genetically enriched subjects, with the intent of following up a subset of discovered variants by testing their associations in a larger study of 700 cases and 1400 controls. The sample sizes used for illustration derive from the WECARE study ; while optimization of these values is possible, the results seem to be relatively insensitive across a broad range of choices. The specific results are somewhat more sensitive to the specific model parameters, only one being presented here, but the general patterns remained consistent across all values we considered.We also simulated gene- and pathway-level burden tests  being tested in the second stage to be comparable to those discovered in the first. We compare the relative efficiency of this family-based design with a conventional two-stage case-control design with comparable costs.We evaluated these designs by simulating 4-generation pedigrees with 22 members in each. We sampled haplotypes from the same simulated population described earlier and randomly dropped genes through the pedigrees, generating phenotypes with randomly selected rare variants as causal with the same RR distribution and retaining those pedigrees with some minimum number of cases (Methods section Simulation of Family-Based Designs). To address the first question, families with various numbers of affected individuals were ascertained, and from each of these we selected individuals to sequence in various ways . We then tabulated the following statistics for causal and non-causal variants by the relationship of the cases to each other.Rule-based criterion: the number of families for which all affected members carry the variant and no unaffected ones did among the subset sequenced;Likelihood ratio (LR) criterion: the ratio of the retrospective likelihoods under the simulated penetrances and allele frequencies vs. the null penetrance (the average rate in the ascertained families); while similar to the lod score used in linkage analysis, here a single-locus likelihood is used to test association with a directly-observed variant, not markers in LD with an unobserved locus;Bayes factor (BF) criterion: similar to the likelihood ratio, but based on the marginal probabilities under the simulated prior distributions of penetrances and allele frequencies;Score test criterion: the score test derived from the retrospective likelihood, evaluated under the null hypothesis.(Methods section Family-based Criteria for Prioritization of Variants). The score test was evaluated both at the single-variant and the regional level, the latter using the family-based SKAT tests , the relative difference comparing causal and null variants goes the other direction, and the relative probability of prioritization also increases for more subjects per pedigree and fewer pedigrees sequenced, for a considerable increase in the overall relative probability of discovery and prioritization.This trade-off is explored further in Figure Comparing designs with two individuals sequenced per pedigree shows little difference in the probability of discovery across the relationships among the pairs Figure , but shoObviously, the more stringent the cutoff for any of these criteria, the fewer the variants that would be prioritized, but non-causal variants tend to be eliminated much faster than causal variants Figure , so the all causal variants discovered, prioritized, and replicated) for any of these designs is only about 20% (for a sample size of 1000 families), the majority of those not found are either very rare or have very small effect sizes. Of particular interest are the numbers of novel variants (those not in the 1000 Genomes Project database) that are discovered, prioritized, and replicated. Since these too are predominately rare, power for them is even lower, but depending upon the total number that actually exist, they could still represent a substantial yield of true positive findings.We compared the power of a two-stage family-based design with that of a conventional case-control design. The overall power for any design with independent tests in the two stages is simply the product of the powers for the two stages . The probabilities of discovery, prioritization, and replication are illustrated in Table 1 = 0.001 in stage I, for a yield of 159 true positive replicated associations at a cost of $18 M (about 2/3 the cost-efficiency of the family-based design). Of course, with different cost ratios, these optimal designs would change, as illustrated in Table These comparisons are provided for the “optimal” designs of each type and one alternative design that yields better power at modestly larger cost. Assuming costs of $1000 per family for enrollment and obtaining pedigree phenotypes, $100 per subject enrolled in a case-control design, $5000 per whole-genome sequence, and $0.05 per subject-genotype, the optimal family-based design turns out to require 540 pedigrees in stage I and 1260 in stage II at a critical value of the score test for prioritizing variants of 3.0; this yields 167 true-positive replicated associations out of 1000 simulated at a cost of $12 M. The corresponding optimal case-control design would require 1400 case-control pairs in stage I, 5600 in stage II at a critical value of αIncluded in the Colorectal Cancer Family Registries are a few large families for whom all available family members have either been genotyped for previously replicated GWAS SNPs or whole exome sequence variants. We analyzed one of these—a large Australian pedigree comprising 145 individuals with a total of 7 colorectal, 1 Lynch syndrome, and 9 other cancer cases. Genotypes for 32 GWAS-associated SNPs were available for 49 of the members, including 5 of the CRC and Lynch cases and 4 of the other cancers. These data were used to illustrate the effect of subsampling. We selected individuals under various criteria, calculated LR, BF, and score statistics using only the SNP data for these selected individuals  under the null hypothesis. A slightly different form, λ′ = λ − v with ν being the degrees of freedom of the test, is also reasonable. In this particular problem, we used l*(.) shown in the previous section in place of l(.). It has been shown  is amenable for standard likelihood ratio tests.Our general strategy for optimization of any of these two-phase designs aims to solve the following problem. Suppose we have collected phase I data on  Thomas, . However Thomas, , it is lNyv, Pr, β0  to be either known or pre-specified. To obtain these quantities, we simulated 1000 data sets as described in section Simulation of Two-phase Designs, and consider these data sets as the underlying “super-population.” Then we used the estimates of Pr, β0 and the average values of Nyv from this super-population as the input to the optimization procedure. Hence we used a fixed optimal design for all simulation replicates, using the SPML. Compared to solving the optimization problem for each replicate, this strategy represents a solution to the “expected” problem.This problem setting requires c copies of a variant in the subsample from the Poisson distribution for each MAF and RR bin, summing the expected counts over all sampling strata, and in a similar manner, we computed the probability of observing c' copies among 1000 population controls. The total yield of discovered novel variants is then the sum over these bins of the number of variants in each bin times the probability of seeing >c and <c′ copies.The estimates in Table c and c' given in Table For association testing in the main study, we computed the NCP for the Mantel-Haenszel test (stratified by age and FH) for each bin and then computed power by reference to the cumulative normal distribution with Bonferroni correction for either the total number of discovered variants or only the number of novel variants. These are again summed over all RR and MAF bins to estimate the expected yield for various values of p, each comprising 1–20 genes g, further subdivided into three regions r . Starting and ending locations of each gene and is sub-regions were selected at random and all variants v within these regions were included. Pathways, genes, and variants were selected as causal with probabilities πP, πG, and πv respectively, where πv for variant v depends upon the type of region and its MAF. Thus, a variant has a causal effect only if all three levels are designated as causal. Each causal variant was assigned a log RR βv as a sum of pathway, gene, and variant-level effects, each being the absolute value of a normal deviate with zero mean and variance σ2P, σ2G, and σ2v, respectively, σ2v also depending upon the type of region and MAF. We drew two haplotypes at random for each potential subject and computed the genetic log RR as the sum of the βvs for each variant they carried. Subjects were assigned at random to an age stratum and then to disease  and FH strata with probabilities depending upon their age and genetic RR. This process was continued until the target number of subjects in each age, FH, and disease stratum was obtained and a random subset of these was designated as the sequencing sample. In the real WECARE study, we prioritized the youngest cases, those with a positive FH, and radiotherapy subjects with the longest latency for sequencing. In this way, we selected 201 subjects out of the total of 2199 available for sequencing; the distribution of the entire study sample and the sequencing subsample by age, FH, and laterality is provided in Table To compare the power of single-variant and burden tests, we selected variants from the haplotypes in a multi-level fashion as follows. We defined 100 pathways For the analysis, we scanned the subsample to identify all variants seen at least twice. All single variants that were seen more frequently than expected (by an amount depending on the number of comparisons) based on the general population MAFs and similarly all pathways, genes, or regions that were seen more frequently than expected were prioritized. These are tested for case-control association in the main study, using a Cochran-Mantel-Haenzsel (CMH) test, stratified by age and FH, with Bonferroni adjustment for the number of comparisons at each level.vs for each causal variant a subject carries, and assigned disease status accordingly, adjusting the intercept to yield a population prevalence of 5%. Families with the required number of cases (set to 4 for most of the results reported here) were retained and the process continued until 1000 such families were ascertained. Various criteria were used to select a subset of family members whose genotypes were to be retained for analysis , while retaining the phenotype information for the entire pedigree.Family-based simulations used a fixed pedigree structure of 4 generations with two offspring in each generation for a total of 22 members in 7 nuclear families. We sampled two haplotypes at random for each of the founders from the simulated haplotype population and dropped them at random without recombination through the non-founders. As before, we chose causal variants and their RRs depending upon MAF, computed the genetic log RR as the sum of the βfmin families and the number of these that were prioritized by having the target genotype configuration . The distributions of causal and non-causal variants for each criterion are shown in Figure For each of the causal and a random sample of the non-causal variants, we computed the likelihood ratio, Bayes factor, and score statistics (described below) and tabulated these values for different configurations of genotypes among the sequenced members and their relationships to each other. For the rule-based prioritization, we also tabulated the number of variants found in at least Variants were classified on the basis of the number of families in which all sequenced cases carried the variant and any sequenced controls did not.Gbs the observed sequence data, βv the genetic RR and qv the minor allele frequency for variant v, the likelihood ratio isGobsv, Y) = ∑GunobsvPr(Y|Gv)Pr(Gv). These calculations were done evaluating the likelihood under the simulated RR and minor allele frequency for each variant under the alternative hypothesis and under the induced marginal population risk for the null hypothesis.Following the principles described in Petersen et al. , we estiq, or even their true probability distributions, so we used the simulated probability distributions for Pr(q) and Pr(β |q), averaging over a random samples of 100 parameter values drawn from their null and alternative distributions.The likelihood ratio criterion requires a maximization of the likelihood under the alternative hypothesis, which can be unstable for rare variants. To avoid this, Petersen et al.  compute Tv for a single variant v derived from a multivariate logistic model for the phenotypes of the entire pedigree and the genotypes of the sequenced subset asYf is the vector of phenotypes for family f, pf is the family-specific disease prevalence, Kf is the kinship matrix, Gfv the vector of genotypes for variant v, and qfv is the mean of Gv among the sequenced members. The Gfv − qfv deviations are set to zero for untyped individuals, but the inclusion of the kinship terms for typed-untyped pairs allows their phenotypes to contribute. This statistic has mean zero under the null hypothesis and asymptotic variance var(Tv) = Σftfv2. For the purpose of prioritizing variants we used the score test Tv2/var(Tv) for each variant and select the top-ranked ones at some cutoff. This provides a pure within-family comparison, but those families for which all sequenced individuals are no carriers or all are carriers become uninformative. A more powerful test that exploits both between- and within-family information replaces the pf and qfv by and, the corresponding means over all families. The regional (SKAT) test for all variants in region R is simply [Σf (Σv ∈ Rt2fv)]2/Σf (Σv ∈ Rtfv2)2.We computed the score statistic min in each bin by rescaling the NCPs by the ratio of sample sizes and referred them to the non-central chi square distribution. To extend our simulation results to the whole genome, we multiplied the predicted number of simulated null variants meeting our discovery and prioritization criteria by 20,000,000/1000. The total number of variants carried forward to stage 2 is then simply the sum over all MAF and RR bins of the product of the number of variants in the population times the probabilities of discovery and prioritization. Power for stage two was computed in a similar manner by rescaling the NCPs by the stage 2 sample size and referring it to the non-central chi square distribution with Bonferroni correction for this number of tests carried forward. Thus, the yield of causal variants discovered, prioritized, and replicated is the sum of the number of variants in the population times the probability of discovery, prioritization, and replication over all MAF and RR bins. In each MAF bin, we also computed the Poisson probability that a variant would not have been seen at least twice in 1000 population controls and computed the power for novel variants in a similar manner.Using family-based simulation described above, we tabulated the average number of families in the simulated sample in which each variant was seen at least once and the NCP as the mean of the simulated score statistics by bins of MAF and RR. To compare designs with different stage 1 sample sizes and discovery thresholds, we rescaled the numbers of families carrying a given variant by the ratio of proposed and simulated sample sizes and recomputed the probability of discovery by reference to the Poisson distribution in each bin. In a similar manner, we computed the probability of prioritization at stage one at threshold λCalculations for case-control designs were similar, except that no simulation was required. The probability of discovery could be computed directly from the Poisson distribution in the combined case and control sample and the NCP s for the chi square test for allelic association computed in the usual way for a 2×2 contingency table of allele counts by case-control status.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


PRDM10 with coronary artery disease and multiple genes in the major histocompatibility complex (MHC) with type 1 diabetes. The results of our analyses highlight that genome-wide association studies have the potential to offer an exciting opportunity for gene discovery through association with rare variants, conceivably leading to substantial advancements in our understanding of the genetic architecture underlying complex human traits.Genome-wide association studies have been successful in identifying loci contributing effects to a range of complex human traits. The majority of reproducible associations within these loci are with common variants, each of modest effect, which together explain only a small proportion of heritability. It has been suggested that much of the unexplained genetic component of complex traits can thus be attributed to rare variation. However, genome-wide association study genotyping chips have been designed primarily to capture common variation, and thus are underpowered to detect the effects of rare variants. Nevertheless, we demonstrate here, by simulation, that imputation from an existing scaffold of genome-wide genotype data up to high-density reference panels has the potential to identify rare variant associations with complex traits, without the need for costly re-sequencing experiments. By application of this approach to genome-wide association studies of seven common complex diseases, imputed up to publicly available reference panels, we identify genome-wide significant evidence of rare variant association in  There has been much recent debate as to the role of rare genetic variation, defined here to have a minor allele frequency (MAF) of less than 1%, in explaining the ‘missing heritability’ of complex traits . Using tThe most comprehensive approach to characterising the contribution of rare variants to the genetic component of complex traits is through large-scale, next-generation re-sequencing studies . DespiteHere, we formulate methodology for the detection of complex trait association with accumulations of minor alleles within genes, or some other functional unit, using data from directly typed and/or imputed rare variants. We report the results of simulations to investigate the power of alternative design strategies for assaying and characterising rare genetic variation to detect association with a quantitative trait in a 50 kb gene. Our study considers a simple model of rare variant association with the trait, and assesses the impact on power of the number of individuals present in the reference panel. We also present results of an application of our methodology to rare variant association analysis of seven common complex diseases undertaken by the Wellcome Trust Case Control Consortium (WTCCC) , using GN rare variants, here defined to have MAF less than 1%, within the same exon, gene or some other functional unit, in a sample of unrelated individuals. Let in denote the number of rare variants at which the ith individual has been successfully genotyped in the functional unit. Furthermore, let ijG denote the genotype of this individual at the jth rare variant, coded as 0 for the common homozygote, and 1 otherwise. We can model the phenotype, iy, of this individual in a generalised linear regression framework as a function of the proportion of rare variants at which they carry at least one minor allele [g is the link function and β is the expected increase in the phenotype for an individual carrying a full complement of minor alleles at rare variants in the functional unit compared to an individual carry none. It follows that β/N is the increase in the expected phenotype of an individual for each rare variant at which they carry a minor allele. The likelihood contribution of the ith individual, in to allow for differential call rates between samples. We can thus construct a likelihood ratio test by comparing the maximised weighted likelihoods of two models via analysis of deviance: (i) the null model where β = 0; and (ii) the alternative model for which β is unconstrained. The resulting test statistic has an approximate χ2 distribution with one degree of freedom. The flexibility of the generalised linear regression framework allows for generalisation of this approach to take account of non-genetic risk factors as covariates.We test for association of a complex trait with accumulations of minor alleles at r allele , given bE(ijG) = 1 – ijh, where ijh is the posterior probability of a common homozygote call in the ith individual at the jth rare variant. The posterior probabilities, ijh, of imputed genotype calls are easily recovered from standard imputation software such as IMPUTEv2 [It is straightforward to accommodate imputed rare variants in the functional unit within the generalised linear regression framework by considering the posterior distribution of genotype calls. Specifically, we replace missing genotypes  by their expectation, http://www.well.ox.ac.uk/GRANVIL). The open-source software has been designed to efficiently handle analysis of directly genotyped and imputed rare variants on a genome-wide scale, and can accommodate both quantitative traits and binary phenotypes in a generalised linear modelling framework, as described above. The user supplies a file containing the boundaries of each functional unit to be analysed, together with SNPTEST format sample and genotype files, and specifies the rare variant MAF threshold. GRANVIL is distributed with scripts to generate graphical summaries of GWAS rare variant analysis results, including quantile-quantile and Manhattan plots.The methodology described above has been implemented in the GRANVIL software, and is freely available for download  direct re-sequencing of the analysis cohort; (ii) direct genotyping of the analysis cohort for all rare variants present in the reference panel; (iii) direct genotyping of the analysis cohort for variants on a GWAS chip with the same characteristics as the Illumina Human660W-Quad BeadArray in terms of density and MAF; and (iv) direct genotyping of the analysis cohort for variants on the GWAS chip, supplemented with imputation of untyped variants present in the reference panel using IMPUTEv2 .δ, of any individual causal variant; (ii) the total MAF, Q, of all causal variants in the region; and (iii) their joint contribution to the overall trait variance, expressed as 100λ%. Here, we considered reference panels of R = 120, R = 500 and R = 4,000 individuals. The number of individuals was chosen to represent a range of reference panels incorporating those available from the 1000 Genomes Project (pilot release), through to those we might expect from future large-scale deep re-sequencing efforts, such as the UK10K initiative (http://www.uk10k.org/). For each model, we generated 500 replicates of data as follows.−8 per base (in each generation) and a uniform recombination rate of 1 cM per Mb, for an effective population size of 10,000 individuals. In total, we simulated a region of 1,050 kb, including a 50 kb gene and 500 kb up- and down-stream to allow for an imputation buffer to improve accuracy by avoiding edge effects and taking advantage of the expected long-range linkage disequilibrium (LD) with rare variants [Generate an ancestral recombination graph  for a pojq for the jth variant. Select a variant as causal from amongst those with MAF jq < δ, at random. Continue selecting causal variants in this way, without replacement, until the total MAF of all causal variants is Q.Calculate the MAF at each variant across the 50 kb gene in the population of 40,000 chromosomes, denoted by ith individual across all causal variants in the 50 kb gene, denoted by im. The phenotype, iy, of the ith individual is then simulated from a Gaussian N distribution, where σ is determined by the spectrum of causal variants and their joint contribution, λ, to the overall trait variance, and iμ = 1 if im > 0, and 0 otherwise. Full details of the derivation of the residual trait variance, σ2, are provided in the Appendix.Select a random sample of 4,000 chromosomes from the population, paired together to form the analysis cohort. Determine the number of minor alleles carried by the R chromosomes from the remainder of the population to be haplotypes in the reference panel. Assuming no genotyping or phasing errors in the reference panel, record the haplotype of each of these chromosomes across all variants in the 1,050 kb region.Select a random sample of 2P-value, denoted by SEQp.Begin by considering the strategy in which the analysis cohort has been directly re-sequenced in the 50 kb gene. Assuming no sequencing errors, record the genotype of each individual at each variant with MAF < 1% in the analysis cohort. Test for association of the quantitative trait with an accumulation of minor alleles at these variants using GRANVIL, and record the P-value, denoted by GENp.Then consider the scenario in which the analysis cohort has been directly genotyped for all variants in the 50 kb gene which are present in the reference panel. Assuming no genotyping errors, record the genotype of each individual at each variant present in the reference panel with MAF < 1% in the analysis cohort. Test for association of the quantitative trait with an accumulation of minor alleles at these variants using GRANVIL, and record the GWASn, present on the Illumina Human660W-Quad BeadArray in that interval. Select GWASn variants at random and without replacement, with ascertainment probability P-value, denoted by GWASp.Next consider the scenario in which the analysis cohort has been directly genotyped only for variants on a GWAS chip. Select a random 1,050 kb region of the genome, and determine the number of variants, P-value, denoted by IMPp.Finally, consider the scenario in which the analysis cohort has been directly genotyped only for variants on the GWAS chip, but are subsequently supplemented with imputation of untyped variants present in the reference panel. Assuming no genotyping errors, record the genotype of each individual at each variant across the 1,050 kb region, irrespective of MAF. Impute the genotype of each individual in the analysis cohort at each variant present in the reference panel in the 50 kb gene using IMPUTEv2 [We have considered a simple underlying model for the association of the trait with multiple rare causal variants within the same gene. We assumed that the expected trait value of each individual is increased by the presence of a minor allele at any causal variant. The trait association model was then parameterised in terms of: (i) the maximum MAF, P-value is less than 0.05. We also calculated the mean numbers of rare variants in the 50 kb gene: (i) in the population of 40,000 chromosomes; (ii) identified through direct re-sequencing of the analysis cohort; (iii) present on the reference panel and identified through direct genotyping of the analysis cohort; (iv) present on the GWAS chip; (v) present on the reference panel and well imputed (info score greater than 0.4) in the analysis cohort.Over all simulated data sets, we calculated the power of each design strategy at a nominal 5% significance level as the proportion of replicates for which the corresponding κ, where here we considered κ = 0% (no missing genotype data) and κ = 1%. Errors were introduced first into the reference panel (Step 4), and then into the analysis cohort . Missing genotype data were then introduced at random .One potential limitation of our simulation study is the assumption of no sequencing errors, perfect phasing of the reference panel, and no missing or miscalled genotypes. These errors might be expected to be most detrimental to our proposed imputation strategy since this process requires an accurate GWAS scaffold and phased reference panel. To address this issue, we have also performed simulations to assess the robustness of our results to re-sequencing errors and missing or miscalled genotypes. We introduced a simple model of errors [We considered 14,000 cases of seven common complex diseases  and 3,000 shared controls from the WTCCC [r2 < 0.2) with MAF of at least 5%, and projected samples onto principal components demonstrating clear separation between 12 UK regions of residence [To allow for fine-scale population structure, which may have greater impact on rare variant association signals than common SNPs because of recent founder effects [We imputed the high-quality samples up to the Phase I 1000 Genomes Project reference panel (June 2011 interim release) consisting of 1,094 phased individuals from multiple ancestry groups [P < 0.05, to detect association with a quantitative trait, for each of the design strategies for assaying rare genetic variation in the gene. For these results, we assumed that multiple rare causal variants in the gene jointly contribute to 5% of the overall trait variation. The panels correspond to two specific trait association models: (A) the maximum MAF of any individual causal variant is 1%, and the total MAF of all causal variants is 5%; and (B) the maximum MAF of any individual causal variant is 0.5%, and the total MAF of all causal variants is 2%. Under the second of these models, we expect fewer rare variants within the gene to be causal, since the total MAF is lower. A higher proportion of non-causal variants within the gene would be expected to reduce power overall, irrespective of the design strategy and/or the number of individuals in the reference panel [R = 4,000. We expect most of the rare variation in the analysis cohort to be captured by such large reference panels . Rare variants not captured by the reference panel  are less likely to have a major impact on the joint contribution of causal variation in the gene under our simulation model, and thus would not be expected to lead to a dramatic reduction in power.Our results highlight a number of general conclusions across these trait association models. As expected, the most powerful strategy to detect rare variant association is to re-sequence the analysis cohort. In the absence of sequencing errors, this ‘gold-standard’ strategy provides complete coverage of rare genetic variation in the gene within the analysis cohort. Nevertheless, genotyping the analysis cohort for all rare variants present in the reference panel generally results in a relatively small reduction of power, particularly for R = 500 to R = 4,000 are not as great as from R = 120 to R = 500, particularly for an association model incorporating causal variants with MAF up to 1% . However, we are still able to recover much of the power of the gold-standard re-sequencing strategy through imputation of the analysis cohort from the GWAS scaffold, and we maintain considerable advantages over genotyping of the GWAS chip alone.r2 > 0.2) set of 27,770 high-quality autosomal SNPs with MAF > 5% to construct 10 axes of genetic variation of UK population structure. By projecting samples onto the corresponding principal components, we observed that the first three axes of genetic variation were strongly associated with the region of residence of samples . Of the autosomal variants on the array, 456,868 passed SNP QC filters. We then applied EIGENSTRAT to an LD-pruned  [P < 1.7 × 10−6) are highlighted in red. There was no evidence of residual population structure, not accounted for by the three axes of genetic variation, with genomic control inflation factors [PRDM10 (P = 4.9 × 10–8). The gene contained 122 well-imputed rare variants with mean MAF of 0.23%. Accumulations of minor alleles across these variants were associated with decreased risk of disease: odds ratio 0.828 (0.774–0.886) per minor allele. We also observed 10 genes with genome-wide significant evidence of rare variant association with type 1 diabetes, all located within the major histocompatibility complex (MHC) (HLA-DRA (P = 2.0 × 10−13), which has been previously implicated in susceptibility to type 1 diabetes [TNXA, with odds ratio 2.346 (1.772–3.107) per minor allele.We observed genome-wide significant evidence of association of coronary artery disease with rare variants in the gene ex (MHC) . The strTNXA . After adjustment, three additional MHC genes achieved genome-wide significant evidence of rare variant association with type 1 diabetes: HLA-DMA (P = 1.1 × 10−7), SKIV2L (P = 2.6 × 10−7) and TNXB (P = 4.1 × 10−7).Common SNPs in the MHC have been previously associated with the disease [GWAS has been extremely successful in identifying genetic loci contributing effects to a wide range of complex human traits [We demonstrate here, by simulation, that imputation from an existing scaffold of GWAS genotype data using publicly available high-density reference panels, such as those made available through the 1000 Genomes Project [We have considered a relatively simple underlying model for the association of the trait with multiple rare variants within the gene. More complex models might incorporate selection and/or different directions of effect of the causal variants on the trait. However, at present, we do not fully appreciate the likely effect of rare variants within a gene or pathway on complex human traits, although it is clear that the true underlying association model will impact the power of GRANVIL. Nevertheless, it is less obvious that the underlying association model will impact the relative performance of GRANVIL applied to rare variation derived from imputation as compared to that assayed through re-sequencing.Our simulation study assumes that the analysis cohort and reference panel are ascertained from the same population, and thus are perfectly matched in terms of their rare variant profile. However, with publicly available reference panels, this is unlikely to be the case. Indeed, the Phase I 1000 Genomes Project reference panel (June 2011 interim release) consists of phased individuals from multiple populations that together incorporate a wide range of ancestry groups [Our simulation study also assumes that all rare causal variants in the gene have the same impact on the trait, for example, that they all result in loss-of-function of the gene product. The GRANVIL software makes the same underlying assumption, and hence power to detect rare variant association will be maximised. Under alternative models of rare variant association with the trait, which consider causal variants within the gene to result in both loss- and gain-of-function of the gene product, the power of GRANVIL will be reduced for all design strategies. For these models, powerful methods exist for detecting association with rare genetic variation [PRDM10 at genome-wide significance. This gene has not been previously implicated in susceptibility to coronary artery disease or related cardio-metabolic phenotypes, and this association signals warrant follow-up in independent cohorts, either through genotyping of rare variants in the gene or re-sequencing. We also identified genome-wide significant evidence of association of type 1 diabetes with accumulations of minor alleles at rare variants in multiple genes from the MHC. This region has been previously associated with type 1 diabetes, both through common variant GWAS and analysis of classical human leukocyte antigen (HLA) haplotypes. Further work is required to dissect the complex genetic contribution of common and rare variation in this region to susceptibility to type 1 diabetes and other autoimmune disorders.The encouraging results of our simulation study prompted us to re-assess the evidence of rare variant association with seven diseases from the WTCCC experiment [The results of our analyses presented here have major implications for the design and analysis of genome-wide rare variant association studies of complex human traits. Our results clearly highlight the potential for the detection of rare variant associations by using existing GWAS genotype data, supplemented with imputation from publicly available high-density reference panels, without the need for costly whole-genome re-sequencing experiments. Although imputation can never replace the gold-standard approach of whole-genome re-sequencing, it provides a powerful, cost-effective alternative that only requires a scaffold of GWAS genotype data, which may already be available. This message will bring encouragement to research groups who do not have sufficient funding to consider whole-genome, or even whole-exome sequencing as a financially viable approach to assaying rare genetic variation. It is clear that GWAS still have the potential to offer an exciting opportunity for gene discovery, conceivably leading to substantial advancements in our understanding of the genetic architecture underlying complex human traits.


Variation in human intelligence is approximately 50% heritable, but understanding of the genes involved is limited. Several forms of genetic variation remain under-studied in relation to intelligence, one of which is copy number variation (CNV). Using single-nucleotide polymorphism (SNP) -based microarrays, we genotyped CNVs genome-wide in a birth cohort of 723 New Zealanders, and correlated them with four intelligence-related phenotypes. We found no significant association for any common CNV after false discovery correction, which is consistent with previous work. In contrast to a previous study, however, we found no effect on any cognitive measure of rare CNV burden, defined as total number of bases inserted or deleted in CNVs rarer than 5%. We discuss possible reasons for this failure to replicate, including interaction between CNV and aging in determining the effects of rare CNVs. While our results suggest that no CNV assayable by SNP chips contributes more than a very small amount to variation in human intelligence, it remains possible that common CNVs in segmental duplication arrays, which are not well covered by SNP chips, are important contributors. A large body of work comparing monozygotic and dyzygotic twin sets indicates that approximately half of the variation in human intelligence as measured by standard tests is genetic, with estimates ranging between 40 and 80% Prior to the emergence of high-throughput genotyping technologies, investigation of the genetics of intelligence focused on particular candidate genes selected on the basis of known aspects of gene function Since 2004 genome-wide microarray technology and whole genome sequencing have revealed that copy number variations (CNVs), deletions or duplications of sections of DNA as large as several mega bases, are present in all individuals and are responsible for a large proportion of normal human genetic variation, in fact more than SNPs in terms of numbers of variable nucleotides Body asymmetry, presumably reflecting mild developmental perturbation, is associated with reduced intelligence in individuals unaffected by clinically defined developmental disorders Common CNVs, i.e. variants with population frequencies greater than 5%, are also under-studied extensively in relation to cognitive ability. To our knowledge there is only one published GWAS, which examined 178 SNPs known to tag common CNVs in 1250 individuals, and correlated them with 11 intelligence-related phenotypes CNVs were detected using SNP-based Illumina 660W-Quad bead chips and called by PennCNV software following standard QC procedures Previously used standards of high individual CNV count, potentially indicating DNA degradation, are 40 Where CNVs overlapped, we used standard modules of the Plink software package (version 1.07) to define them as identical or separate, and to assign each CNV a frequency within the dataset. Following Yeo et al., (2011) Our test subjects were 723 individuals participating in the Christchurch Health and Development study (CHDS), a birth cohort consisting of children born in the Christchurch New Zealand urban area within a four-month period during mid-1977. The participants have been assessed at regular intervals using various biological and behavioural measures Child cognitive ability was assessed at ages 8, 9 years using the revised Wechsler Intelligence Scale for Children The Test of Scholastic Abilities (TOSCA) provides a measure of the extent to which a child exhibits the skills and competencies necessary to deal with the academic requirements of high school education The Burt Word Reading Test On the basis of participant reports of their educational history and attainment of qualifications sample members were classified on a 7-point scale reflecting their highest level of academic attainment by age 25 years Assessment of cognitive outcomes up to age 13 was limited to the sub-sample of the cohort resident in the Canterbury region . As a result the sample sizes assessed on the WISC-R and TOSCA are somewhat lower than for the measures assessed in young adulthood.At ages 18, 21, 25 and 30 participants were questioned about patterns of alcohol use/misuse since the previous assessment. As part of this questioning relevant items from the Composite International Diagnostic Interview All phases of the CHDS were subject to ethical approval from the Canterbury (NZ) Regional Health and Disability Ethics Committee and all aspects of data collection were with the written consent of research participants.In 723 individuals we found a total of 22,249 CNVs with a mean length of 60,867 base pairs (bp). Locations and genotypes of all CNVs called can be found in We first attempted to replicate the results of Yeo et al., (2011) For each outcome the table shows the observed Pearson correlations with three measures of rare CNV status: i) the length of rare deletions; ii) the length of rare insertions; and iii) the total number of rare CNVs. The correlations are estimated for each of three samples: i) the total available gene chip sample assessed on each cognitive/academic outcome; ii) the sample filtered to exclude subjects with a high CNV count (over 40 CNVs); and iii) the subset of the filtered sample who met DSM-IV diagnostic criteria for alcohol dependence from age 18–30 years. None of these correlations was statistically significant (P>0.1).To examine the extent to which the findings may have been influenced by the inclusion of subjects with moderate or severe cognitive impairment, we re-analysed the data excluding all subjects who scored more than two standard deviations below the mean on the cognitive test measures. The resulting correlations were negligibly different from those reported in Overall nine correlations were statistically significant at the p<0.05 level, no more than would be expected by chance. Five of these correlations were accounted for by two CNVRs: CNVR50 showed significant positive correlations with three of the four outcomes, and CNVR17 significant negative associations with two outcomes. However, after application of a Bonferroni correction for multiple comparisons only one correlation  reached significance using the Bonferroni corrected p value (p = 0.0009), in association with overall academic achievement at age 25. Further examination showed that CNVR46 had negative and non-significant correlations with other cognitive/achievement outcomes, suggesting that this correlation could easily reflect chance variation in the data. None of the nominally significant CNVRs overlapped with any SNP listed as being significant at any level by three previous large GWAS on cognitive ability Reanalysis of the data to exclude potential outliers or those with moderate/severe cognitive impairment did not substantively alter these findings. In each case the observed pattern of correlations was consistent with those reported in Our findings do not provide strong evidence for an association between any common CNV region and cognitive/academic performance scores, and we were unable to detect any effect of rare CNV burden on these outcomes. Given previous evidence that CNVs can affect intelligence-related phenotypes, the most obvious explanation for our negative results is that we didn’t sample a sufficient number of functional CNVs. In view of the fact that we couldn’t detect any enrichment of non-significant correlations, we cannot argue that testing a larger number of individuals by our methods would reveal significant associations. However, it is likely that our chip probes missed some important variants, particularly segmental duplication arrays, as these are not easily assayable by SNP chips or other standard genotyping methods de novo mutations rather than commonly segregating alleles In general, common variants are expected to have smaller phenotypic effects than rare ones Theoretically, it is also possible that population-specific variants were involved. However, while our study participants were born in New Zealand and Yeo et al. (2011) In conclusion, our results are in line with previous work showing that individual common variants assayable by SNP chips do not have strong effects on cognitive ability, and suggest that total burden of rare CNVs is also not a major contributor. There are currently more promising approaches to elucidating the genetic component of intelligence. These include larger studies to identify individual functional rare variants, new statistical methods allowing evaluation of the effects of agglomerations of common variants Table S1All CNV data. Genomic coordinates are HG18.(XLS)Click here for additional data file.Table S2Locations and gene contents of CNVRs associated with cognitive measures at a nominal level (P<0.05). No P values were significant after false discovery correction. Coordinates are HG18.(XLS)Click here for additional data file.


A: expected value) but can also be estimated using molecular markers . Nevertheless, evolutionary biologists, unlike animal breeders, remain cautious about using marker-based relatedness coefficients to study complex phenotypic traits in populations. In this paper, we review published results comparing five different pedigree-free methods and use simulations to test individual-based models  using marker-based relatedness coefficients, with a special focus on the influence of mating systems. Our literature review confirms that Ritland’s regression method is unreliable, but suggests that animal models with marker-based estimates of relatedness and genomic selection are promising and that more testing is required. Our simulations show that using molecular markers instead of pedigrees in animal models seriously worsens the estimation of heritability in outcrossing populations, unless a very large number of loci is available. In selfing populations the results are less biased. More generally, populations with high identity disequilibrium (consanguineous or bottlenecked populations) could be propitious for using marker-based animal models, but are also more likely to deviate from the standard assumptions of quantitative genetics models (non-additive variance).Estimating the genetic variance available for traits informs us about a population’s ability to evolve in response to novel selective challenges. In selfing species, theory predicts a loss of genetic diversity that could lead to an evolutionary dead-end, but empirical support remains scarce. Genetic variability in a trait is estimated by correlating the phenotypic resemblance with the proportion of the genome that two relatives share identical by descent . The latter is traditionally predicted from pedigrees (Φ A), either in an experiment using specific relatedness classes  or in a population with pedigree data ranging over several generations The genetic variance available for a trait in a population informs us about its potential ability to evolve in response to novel selective challenges A) could improve the estimation of evolutionarily relevant parameters for quantitative traits  With the ongoing rise of next generation sequencing, high density SNP panels become available and the realised proportion of the genome that two individuals share identical by descent can be estimated with increasing accuracy Different methods are available to estimate quantitative genetic parameters from molecular marker data  F) and then a declining towards zero at F = 1 Being able to accurately estimate the genetic variance of a trait is particularly important for inbred or selfing species that have been described as evolutionary dead ends due to the potential loss of genetic diversity Besides direct effects on genetic variability, selfing generates a correlation in heterozygosity and/or homozygosity across loci, called identity disequilibrium versus molecular markers, with a special focus on how mating systems affects the efficiency of these methods.In this paper we review published results comparing several pedigree-free methods used to estimate quantitative genetics parameters for complex phenotypic traits in wild populations. We then report results from simulations aimed at further comparing the performance of individual-based models  using pairwise relatedness predicted from the pedigree As a preliminary step, we searched the literature (using keywords in Web of Science) looking for studies comparing methods for estimating quantitative genetic parameters using molecular markers, for example a pedigree-based animal model and another method, or a simulation study. Our review is based on the classification published by Garant & Kruuk et al.In order to compare additive genetic variances among traits or taxa, it is common practice to scale it with the total phenotypic variance (heritability) or with the trait mean (coefficient of additive genetic variation). As proposed by Houle 2h), where 2h the parameter and the sampling error, E or one of the marker-based methods (marker). However, the review of empirical results only provides us with single estimates ped and marker to compare and we cannot say anything about the extent to which either or both are biased and which has smaller sampling error. We therefore only tested whether ped and marker significantly differed for each of the marker-based methods using linear models and also compared their standard errors. Most studies considered several traits that would be wrongly considered as independent. We took this into account by adding a random effect for study. For simulation studies, we report the bias and standard error of the estimators ped or marker. Again, we tested for an influence of the method used (pedigree or marker-based methods) on the bias using linear mixed models with study as a random effect followed by posthoc tests (with Bonferroni correction) to identify significant pairwise differences. Studies using genomic selection methods generally evaluate the accuracy of the model as the correlation between the estimated breeding value and the real breeding value. We report these accuracies.The performance of a statistical inference can be evaluated by the bias, defined as E and assessed the relationship between the bias and the number of markers available (or simulated) using a mixed linear model for each method, with study as a random effect.N = 500 individuals evolving for a number of generations. Individuals are diploid and unrelated at generation 0 . Generations are non-overlapping. We simulate the genotype of each individual at ML+QTLL unlinked loci. The QTLL loci are causal loci whereas the ML loci are biallelic non-coding marker loci. Initial allele frequencies are drawn from the distribution expected at mutation – drift equilibrium using a Dirichlet distribution QTLL) with five alleles each. Allelic effects are randomly drawn from a normal distribution for each allele. The phenotype of an individual is the sum of the two allelic effects at each of the QTLL loci  plus a random factor (ijε) drawn from a normal distribution representing the environmental effect:We simulate a population of constant size S = 0.9) to simulate inbred populations. The simulation program is written in C++ and runs in batch using a custom python script, with 20 replicates per parameter set. The code is available as supplementary material (Zipfile S1).The variances of the distribution of allelic and environmental effects are adjusted to simulate heritabilities of 0.15, 0.3 and 0.6. The next generation is built either by random mating of pairs of individuals or with a set proportion of selfing (A) between pairs of individuals. Genotypes at the ML marker loci were used to estimate pairwise relatedness using the coefficient introduced by Loiselle et al.i,jK). It does not assume Hardy-Weinberg equilibrium and performs well, even in the presence of rare alleles y = Za+e where y is the phenotype, Z is a design matrix and a the vector of additive genetic effects; e is the vector of residual effect. The pedigree or the marker loci information were then used to specify a variance–covariance structure for the vector of additive genetic effects a, shaped as 2.ΦA.A2σ when using an animal model including the pedigree or as 2.i,j.σA2K when replacing the ΦA matrix by a marker-based relatedness matrix. For selfing populations, we used 2.ΦA.A2σ/(1+ F) and 2.i,j.σA2K/(1+ F) to account for inbreeding F was the average inbreeding coefficient. F was either estimated using pedigrees or approximated as S/(2–S) F = 0.82 for S = 0.9). We used restricted maximum likelihood to estimate the additive genetic variance and the standard errors with the program ASReml v3.0 ML vary between 384, 1500, 3000 or 5000 SNPs. We also manipulated the marker-based relatedness matrix to summarize the information and examined how this influenced the bias in genetic variance estimates. It has become common practice in association studies (GWAS) to truncate the marker-based relatedness matrix by replacing any negative value by zero. We transformed our matrix accordingly.We simulated populations evolving for 10 generations and performed analyses at generation 10, using pedigree and marker-based animal models (method 4 in the review section). Every generation, the pedigree information  was recorded and used to calculate the relatedness coefficient (Φ2h). We estimated the precision of the estimation using sampling errors, defined as E(2. We compared the bias and sampling errors in heritability estimators (pedigree versus molecular markers) using Wilcoxon signed rank tests. We tested for the effect of the mating regime, trait heritability and number of markers on the bias in heritability estimates using linear models.As in the review section for simulation studies, we measured the bias in heritability as E or by rare alleles in the causal variants. All analyses were run in R version 2.15.1.The identity disequilibrium created by consanguineous matings could improve marker-based estimates of the expected proportion of identity by descent 2 = 22.2; p = 2.5×10−06), the relatedness classes  and the reconstructed pedigrees  but not for the animal model  or genomic selection . As shown by We collected 39 papers comparing heritability estimates based on molecular data or pedigree information. Among those, 24 reported empirical results  while 152h) (n = 10) than for the pedigree method , the marker-based animal models  or the genomic selection . There was no significant difference between these three methods (p>0.750). The number of simulation results testing methods 2 and 3 in the dataset we collected was insufficient to compare their biases. The average biases for each method are shown in Using the 15 simulation studies, we calculated the bias as E(– h2) . The mixThe average value of the bias in heritability tended to increase for traits with low heritabilities . The bias in outcrossing populations was reduced when using truncated marker-based relatedness coefficients  but not in selfing populations .Simulation results confirmed that using pedigree information in an animal model provides accurate estimates of heritability for both outcrossing and selfing populations, even with low heritabilities .A. We ans 0.072; .C. Resul53,1F = 155.0; p<10−16), but it should be pointed out that with low heritabilities (0.15) the model sometimes failed to converge or estimated an additive variance not significantly different from zero.In outcrossing populations, the absolute value of the bias with the marker-based method increased with higher simulated heritabilities . The distribution of pairwise relatedness in selfing populations may explain such a better performance in estimating heritability et al.Selfing decreased the bias in marker-based heritability estimates. With a heritability of 0.3, for example, the bias was more than seven times larger in outcrossing compared to selfing populations . If marker-based relatedness coefficients are truncated, the effect becomes non-significant  and a lower number of markers is required to get an accurate estimate of heritability. In selfing populations, there is no relationship between the bias and the number of marker used . 384 markers seem already sufficient to estimate heritability reasonably well. Surprisingly, the sampling error of the estimates did not decrease with the number of loci.Reviewing empirical and simulation studies of quantitative genetics in wild populations using marker-based estimates of relatedness confirms that it is extremely difficult to derive reliable estimates for quantitative genetic parameters in wild populations using Ritland’s pairwise regression model, as suggested by several authors Our review showed that animal models including marker-based relatedness matrices (method 4) offer promising prospects. Nevertheless, our simulations show that using molecular markers instead of pedigrees seriously worsens the estimation of quantitative genetics parameters in outcrossing populations, even if an increased number of loci and truncated relatedness coefficients improved the result. Conversely, our simulations in selfing populations suggest that pedigree-free methods are successful. We discuss several arguments that could help explain this contrast, in the light of our simulation results and the literature available about inbreeding.N to be full-sibs) but not so much in selfing populations (full-sibs from selfing events have ΦA >0.5). More generally, the variance in relatedness in a population is strongly affected by its size and mating system . Such a sampling design constrains the variance in pairwise relatedness in outcrossing populations (no parent-offspring relatedness and a probability of 1/stem see . Variancstem see  but thisA) A more serious issue is that uncertainty in relatedness estimates is ignored when estimating heritability using this pedigree-free method and this could be a problem if uncertainty is high. Previous studies have shown that marker-based estimates of inbreeding coefficients are improved by non-random mating because it generates identity disequilibrium It is worth pointing out that in our simulations, we used the complete pedigree , exempt from errors. Even in domestic animals, pedigree errors have been estimated to range between 1% and 10% Finally, our simulations do not consider non-genetic sources of resemblance between relatives . Such non-genetic effects are expected to overestimate heritability quite markedly Stebbins et al.AV and DV are the additive and dominance variances, cov is the covariance between the additive effect of alleles and their autozygous dominance deviation, DIV is the total variance due to autozygous dominance effects, H* is the inbreeding depression and AAV the variance due to additive-additive epistatic effects (other epistatic variances are neglected here). Each variance component is preceded by a probability measure , keeping in mind that their estimation is not straightforward without a complex experimental design ijd in Harris D in selfing populations is not as inaccurate as in outcrossing populations, where it is rarely examined. Theoretical models also predict that inbreeding depression resulting from deleterious recessive alleles should be purged with selfing A using the animal model can be inflated by variance due to additive-additive epistasis, directly proportional to ΦA2. Importantly, this is also true for outcrossing species, even if we expect lower effects Yet, in selfing populations, inbreeding generates additional variance components specifically associated with dominance effects of alleles when autozygous  (detailed in equation (4) in Shaw R) when there is directional dominance and epistasis. Simulations suggest that evolution in partially selfing populations can strongly differ from the predictions obtained using the breeders’ equation , even if the later accounts for inbreeding depression It remains that such estimates of additive variance may not be sufficient to predict the response to selection . The dashed lines represent y = x.(DOC)Click here for additional data file.Figure S2Slight increase in the bias with lower heritabilities or lower number of markers. The panels A and B show the relationship between the bias in heritability estimate and the value of heritability for the empirical data (in A – bias expressed as marker - pedigree) or the simulation data (in B – bias expressed as E(2h)). The panels C and D show the relationship between the bias in heritability estimate and the number of microsatellites or SNPs used. As explained in the text, the bias did not systematically increase for traits with low heritabilities but was more variable. Surprisingly, we found no overall relationship between the bias and the number of markers used in empirical data.(DOC)Click here for additional data file.Figure S3Influence of population size and mating regime on the variance in pairwise relatedness in a population. Selfing could improve marker-based estimation of heritability because it affects the structure and the variance of pairwise relatedness, as has been shown for the inbreeding coefficient. We assessed the effect of the reduced effective population size in selfing populations (Ne = N/(1+ F)) by simulating populations with varying census size  and different mating regimes (outcrossing in black and 90% selfing in grey). Error bars stand for the standard error estimated from 10 replicated simulations. This figure confirms that pairwise relatedness coefficients have a higher mean and a larger variance in selfing compared to outcrossing populations and that this effect extends beyond the simple influence of population size (e.g. large excess of variance in a selfed population of N = 50 compared to an outcrossed population of N = 100). The identity disequilibrium created by selfing might explain such higher variance in relatedness.(DOC)Click here for additional data file.Table S1Full data literature review.(XLS)Click here for additional data file.Zipfile S1Simulation program in C++.(ZIP)Click here for additional data file.


PDGFRA on chromosome 4q12 , Pmeta = 7.87×10−9) were identified to be significantly associated with corneal astigmatism, exhibiting consistent effect sizes across all five cohorts. This highlights the potential role of variants in PDGFRA in the genetic etiology of corneal astigmatism across diverse Asian populations.Corneal astigmatism refers to refractive abnormalities and irregularities in the curvature of the cornea, and this interferes with light being accurately focused at a single point in the eye. This ametropic condition is highly prevalent, influences visual acuity, and is a highly heritable trait. There is currently a paucity of research in the genetic etiology of corneal astigmatism. Here we report the results from five genome-wide association studies of corneal astigmatism across three Asian populations, with an initial discovery set of 4,254 Chinese and Malay individuals consisting of 2,249 cases and 2,005 controls. Replication was obtained from three surveys comprising of 2,139 Indians, an additional 929 Chinese children, and an independent 397 Chinese family trios. Variants in  PDGFRA gene on chromosome 4q12 is significantly associated with corneal astigmatism. These polymorphisms in the PDGFRA gene exhibit strong and consistent effects over all five Asian cohorts. PDGFRA is a receptor for platelet-derived growth factor, which is expressed in many retinal tissues in the eyes and appears to contribute to ocular development. Results from our study further suggest the potential role of PDGFRA in the regulation of corneal biometrics.Corneal astigmatism is associated with reduced visual acuity and an increased risk of developing refractive amblyopia. Although it is highly heritable, there is no prior study on the genetic etiology of corneal astigmatism. Our genome-wide meta-analysis across 8,513 individuals in five genome-wide surveys from three genetically diverse populations in Asia reveals that genetic variants in the  Astigmatism is a condition where light rays are prevented from focusing at a single point in the eye, resulting in blurred vision at any near or far distance. While astigmatism comprises cornea and non-corneal components, it typically results from the unequal curvature of two principle meridians in the anterior surface of the cornea known as corneal astigmatism Astigmatism is highly prevalent across most populations and poses a significant burden to global public health with at least 1 in 3 adults above 30 years of age suffering from astigmatism of −0.5 diopters (D) or less Although the precise cause of astigmatism is unknown, genetic factors have been implicated in the etiology of corneal astigmatism. Studies have reported a higher risk of developing astigmatism in individuals whose sibling or parents have astigmatism Here we report the findings from the meta-analyses of five genome-wide association studies (GWAS) performed in 8,513 individuals from three Asian populations. The discovery phase of our study comprises 4,254 individuals from two population-based GWAS performed in adults of Chinese and Malay ethnicities from the Singapore Prospective Study Program (SP2) and the Singapore Malay Eye Study (SiMES) respectively. The replication phase comprises of data from three other genome-wide surveys of: (i) 2,139 Indian adults from the Singapore Indian Eye Study (SINDI); (ii) 929 Chinese school children from the Singapore Cohort Study of the Risk Factors for Myopia (SCORM); and (iii) 397 Chinese trios of parents and astigmatic offsprings from the Singaporean Chinese in the Strabismus, Amblyopia and Refractive Error Study (STARS).The characteristics of the post-QC samples from the five studies are summarized in GC = 1.006, SiMES λGC = 1.007) or in the meta-analysis of both studies . Suggestive evidence of association  were seen in each of SP2 and SiMES  gene on chromosome 4q12  attained genome-wide significance in the combined analysis , and the minor allele frequencies of these SNPs are consistently similar across all five studies  in the meta-analysis across all five studies. This SNP alone explains 0.41% of the variation in corneal cylinder power. In addition, a general genetic model identified that the 5.5% of the individuals in the combined cohorts that carry the TT genotype at rs7677751 had a 1.65-fold  increase in the risk of developing corneal astigmatism compared to those that are not carrying any copies of the risk allele  contains two types of subunit, a- and β- PDGFRA, which are differentially expressed on the cell surface PDGFR-a binds to three forms of PDGF  and mediates many biological process including embryonic development, angiogenesis, cell proliferation and differentiation. The role of PDGFRA in cellular growth and proliferation is underlined by its contribution to the pathogenesis of gastrointestinal stromal tumours PDGF and its receptors are expressed in corneal epithelium, stromal fibroblasts and endothelium PDGF and its receptors can mediate corneal fibroblast migration, matrix remodeling and play an important role in corneal wound healing PDGF resulted in keratinocyte elongation using rabbit corneal stroma tissue PDGFRA in the regulation of ocular development and parameters cannot be excluded, and our study suggests that genetic polymorphisms within PDGFRA may be involved in the regulation of corneal biometrics resulting in the occurrence of corneal astigmatism.The et al. reported that 4q12  was significant linked with myopia from a genome-wide linkage study of 221 dizygotic twin pairs P = 0.065) for refractive error in African-American families PDGFRA and (i) the onset of high myopia; (ii) the refractive error as a quantitative trait. We did not observe any striking association between the identified variants with either outcomes, suggesting that the association of PDGFRA with corneal astigmatism is probably not through any shared etiology with myopia.In addition, Hammond PDGFRA. Interestingly, among the SNPs identified, rs2228230 is coding-synonymous  and resides in exon 18, while rs3690 is within the untranslated-3′ region. These three SNPs  are strongly correlated with each other (pair-wise Pearson correlation coefficient r ranging from 0.77 to 0.81), although the association evidence at the latter two SNPs did not reach genome-wide significance. As the next closest gene (GSX2) from the 5′ end of PDGFRA is 127 kb away and is not within the LD block with our identified SNPs , given this stringency comes at the expense of decreasing the number of individuals in each study. We additionally performed a secondary analysis treating corneal cylinder power as a quantitative trait. Strong statistical evidence was consistently observed at the three leading SNPs  that is commonly adopted in clinical practice and eye-trait epidemiology PDGFRA thus suggests that part of the underlying biological pathway responsible for astigmatism development is common to multiple populations, although there may be population-specific genetic variants that our current study is not sufficiently powered to identify.Owing to the relatively small sample sizes within each of the five GWAS studies, we have chosen to prioritize our survey to identify genetic variants that contribute to the etiology of corneal astigmatism in multiple Asian populations. While Malays have been observed to be genetically closer to the Chinese, the Asian Indians tend to be genetically closer to the Caucasians PDGFRA plays the same role in pediatric and adults populations will however need further investigation.Our study has included two pediatric Chinese populations (SCORM and STARS) with school or pre-school children who are still progressing to their final phenotype. It was documented that a high degree of astigmatism occurs during infancy and the early childhood This study adhere to the Declaration of Helsinki. Ethics approvals have been obtained from the Institutional Review Boards of the Singapore Eye Research Institute, Singapore General hospital, National University of Singapore and National Healthcare Group, Singapore. In all cohorts, participants provided written, informed consent at the recruitment into the studies. For studies involving children who were still minors (SCORM and STARS), written informed consent was obtained from the children's parents.Participants included in SP2 were recruited from a revisit of four previously conducted population-based surveys in Singapore: Thyroid and Heart Study 1982–1984 SiMES is a population-based cross-sectional survey on eye diseases for Malay adults aged 40 to 80 years living in Singapore. It was conducted between August of 2004 and June of 2006. The details of the study design and methods have been previously described SINDI is a population-based survey of major eye diseases th annual examination of the study (children at age 10 to 12 years). Complete post-filtering data on corneal astigmatism measurements and SNP data were available in 929 SCORM children.A total of 1,979 children in grades 1, 2, and 3 from three schools were recruited from 1999 to 2001 with detailed information described elsewhere STARS is a population-based survey of Chinese families with children aged 6 to 72 months residing in the south-western and western region of Singapore. Disproportionate random sampling by 6-month age groups resulted in the recruitment and subsequent eye examination of 3,009 Chinese children between May 2006 and November 2008. Details of the study design and methodology have been previously described All studies used a similar protocol to measure ocular phenotypes including corneal curvature, autorefraction and cylinder power by a team of eye care professionals. Participants in SP2, SIMES and SINDI underwent non-cycloplegic automated refractive assessments using the autorefractor . For SCORM and STARS, cycloplegic measurements  were performed 30 minutes after three drops of 1% cyclopentolate which were administered 5 minutes apart.Corneal curvature radii in the horizontal and vertical meridian were determined with keratometry in millimeters −16), the mean corneal cylinder power over both eyes was used to define corneal astigmatism. Averaging ocular measurements between two eyes in genetic studies has been suggested to be statistically more powerful than using the information from only one eye As the corneal cylinder power between the right and left eyes are strongly correlated across all five cohorts , SINDI  and STARS , the Illumina Human610 Quad Beadchips was used for genotyping all DNA samples. For the 1,116 SCORM children, DNA samples were genotyped on the Illumina HumanHap 550 Duo Beadchips.−7. Using the subset of SNPs passing the first round QC, samples were then excluded based on the following conditions: (i) per-sample call rates of less than 95%; (ii) excessive heterozygosity (defined as the sample heterozygosity to be beyond 3 standard deviations from the mean sample heterozygosity); (iii) cryptic relatedness; (iv) gender discrepancies; and (v) deviation in population membership from population structure analysis. A second round of SNP QC was then applied to the remaining samples passing quality checks. We excluded SNPs with missingness >5%, gross departure from HWE , MAF<1% and low concordance between duplicate samples on different genotype platforms (relevant to SP2 samples only).Detailed data quality control (QC) procedures for each study were provided in the supplementary information . In briePopulation structure was ascertained using principal components analyses (PCA) with the EIGENSTRAT program For the STARS trios, we additionally excluded samples and trio-sets on the basis of excessive Mendelian inconsistencies defined as having >1% of the post-QC SNPs exhibiting Mendelian errors. SNPs with more than 10% Mendelian errors are excluded from the association analyses, and the genotypes leading to Mendelian errors in all other remaining SNPs are coded as missing. As family trios are more robust to the presence of population structure, we did not exclude any samples due to population structure.http://pngu.mgh.harvard.edu/~purcell/plink/) as the primary analysis tool. A logistic regression adjusted for age and gender is used to model the association of genetic markers with corneal astigmatism. For each of SiMES and SINDI, the top 5 principal components of genetic ancestry from the EIGENSTART PCA were also included as covariates to adjust for population stratification in these populations. We assumed an additive genetic model where the genotypes of each SNP is coded as 0, 1, and 2 for the number of minor alleles carried, in keeping with increments in allelic dosage. For family GWAS association tests in STARS, a transmission disequilibrium test (TDT) is used to measure significant distortions in transmission of an allele from heterozygous parents to the affected offspring under the condition of Mendel's law The genome-wide association tests were performed using PLlNK  for the family trios. As the distribution of the quantitative trait of corneal cylinder power is skewed . We adopt the method by Kazeem and Farrall Meta-analyses are performed using weighted-inverse variance estimated from fixed-effect modeling in METAL  are used to validate the putative findings. In addition, a genome-wide meta-analysis of all five datasets is also performed. Genotyping quality of all reported SNPs in this paper have been visually assessed by checking the intensity clusterplots.Results from a genome-wide meta-analysis of the SNPs common to SP2 and SiMES are used in the discovery phase to identify putative variants that are associated with the onset of corneal astigmatism, defined as a Figure S1P-values for association between all SNPs and corneal astigmatism in the combined meta-analysis of the discovery cohorts (A) individual cohort SP2, (B) SiMES, and (C) SP2+SiMES.Quantile-Quantile (Q-Q) plots of (TIF)Click here for additional data file.Figure S210 in the combined discovery cohort of SP2 and SiMES. The blue horizontal line presents the threshold of suggestive significance (P = 1.00×10−5). (B) Regional SNP association plot for the corneal astigmatism (≤−0.75D) by the association scatter plot for SNPs in the PDGFRA gene in the combined meta-analysis for discovery cohort SP2+SiMES.(A) Manhattan plot of log(TIF)Click here for additional data file.Figure S3P-values for association between all SNPs and corneal astigmatism in the combined meta-analysis of the fiver cohorts SP2, SiMES, SINDI, SCORM and STARS. (B) Manhattan plots of P-values for the association on corneal astigmatism in the meta-analysis of five cohorts.(A) Quantile-Quantile (Q-Q) plot of (TIF)Click here for additional data file.Figure S4Forest plots of association of homozygotes TT of rs7677751 for corneal stigmatism (≤−0.75 D). Odds ratios for individuals carrying two copies of the risk allele T of rs7677751 are estimated for the five Asian populations. Homozygous odds ratio for family-base data (STARS) is calculated based on previously described method (TIF)Click here for additional data file.Figure S5Linkage disequilibrium (LD) calculated in terms of D' for Singapore Chinese samples from SP2 (A), Malays samples from SiMES (B) and Indians panels from SINID (C). Black squares show perfect LD whereas shades of grey show decreasing LD.(TIF)Click here for additional data file.Figure S6−11), (B) SiMES , (C) SINDI , (D) SCORM . Fitted line is predicated from the linear regression by regressing corneal curvature on corneal cylinder power values.Scatter plots of corneal cylinder power in diopters (D)  versus corneal curvature in millimeter (mm) among the common datasets consisted of these two phenotypes. (A) SP2 Click here for additional data file.Figure S7st eigenvector against 2nd eigenvector, (B) 2nd eigenvector against 3rd eigenvector.Principal component analysis (PCA) of discovery cohort SP2 and SiMES with respect to the population panels in phase 2 of the HapMap samples . (A) 1(TIF)Click here for additional data file.Figure S8st eigenvector against 2nd eigenvector, (B) 2nd eigenvector against 3rd eigenvector, (C) 3rd eigenvector against 4th eigenvector and (D) 1nd eigenvector against 5th eigenvector. The first 5 principal components were used as covariates to account for population structure.Principal component analysis (PCA) was performed in SiMES to assess the extent of population structure. Each figure represents a bivariate plot of two principal components from the PCA analysis of genetic diversity within SiMES. (A) 1(TIF)Click here for additional data file.Figure S9st eigenvector against 2nd eigenvector, (B) 2nd eigenvector against 3rd eigenvector, (C) 3rd eigenvector against 4th eigenvector and (D) 1nd eigenvector against 5th eigenvector. The first 5 principal components were used as covariates to account for population structure.Principal component analysis (PCA) was performed in SINDI to assess the extent of population structure. Each figure represents a bivariate plot of two principal components from the PCA analysis of genetic diversity within SINDI. (A) 1(TIF)Click here for additional data file.Figure S10Histogram of average corneal cylinder power and the normal transformed values for non-familial cohorts: SP2, SiMES, SINDI, and SCORM. The values of corneal cylinder power were transformed by a normal quantile transformation (TIF)Click here for additional data file.Table S1Minor allele frequencies (MAFs) of the top SNPs across different populations.(DOCX)Click here for additional data file.Table S2P-value≤5×10−6) identified from combined meta-analysis of five Asian population cohorts.Top SNPs ((DOCX)Click here for additional data file.Table S3The association results in the five cohorts and combined meta-analysis under different scenarios with varying threshold to define the cases and controls for corneal astigmatism. Cases are defined as corneal cylinder power ≤−1.0D in setting (A) and (B), while controls are defined as corneal cylinder power >−0.75D(A) or >−0.5D (B) in case-control design. For family-based STARS cohort in setting (A) and (B), we performed TDT on those families with corneal astigmatic children only (≤−1.0D). Similarly, cases are defined as corneal cylinder power ≤−1.5D in setting (C) and (D), while controls are defined as corneal cylinder power >−0.75D(C) or >−0.5D (D) in case-control design. For STARS cohort in setting (C) and (D), we performed TDT on those families with corneal astigmatic children only (≤−1.5D).(DOCX)Click here for additional data file.Table S4P-value≤1×10−5) identified from the meta-analysis of five GWAS with corneal astigmatism as a quantitative trait. A*: effect allele; no allelic effect size (β) estimated for STARS (parent-trios design) using FBAT on family-based quantitative trait.Top SNPs ((DOCX)Click here for additional data file.Text S1Detailed QC procedures for SP2, SiMES, SINDI, SCORM and STARS.(DOCX)Click here for additional data file.


In genome wide association studies (GWAS), family-based studies tend to have less power to detect genetic associations than population-based studies, such as case-control studies. This can be an issue when testing if genes in a family-based GWAS have a direct effect on the phenotype of interest over and above their possible indirect effect through a secondary phenotype. When multiple SNPs are tested for a direct effect in the family-based study, a screening step can be used to minimize the burden of multiple comparisons in the causal analysis. We propose a 2-stage screening step that can be incorporated into the family-based association test (FBAT) approach similar to the conditional mean model approach in the Van Steen-algorithm (Van Steen et al.,  Some of the recently published genome-wide association studies identified the same genetic locus as a disease susceptibility locus for different complex diseases . When there is a region with a strong association with both the endo-phenotype and phenotype, identifying SNPs in the region that are still associated with the phenotype of interest after accounting for the association with the endo-phenotype requires testing for a direct causal effect for every SNP in the region. In order to increase power to detect this direct genetic effect, we propose a 2-stage testing strategy to minimize the burden of multiple comparisons in the causal analysis  have been genotyped at a specific marker locus. Assuming there is no bias due to ascertainment conditions, the variable Xi denotes the coded genotype of the offspring and Si denotes the parental genotypes for individual i. If genotypic data is unavailable for the parents but genotypic information is available on the subject's siblings, the variable Si denotes the sufficient statistic by Rabinowitz and Laird  to adjust the phenotype Yi to Yi − γ1Ki. A family-based association test (FBAT) on this adjusted phenotype is then a test for the direct genetic effect in the family-based setting (provided that the distribution of the test statistic acknowledges the uncertainty in the estimated effect γ1) ,To reduce the number of multiple comparisons, we adapt the conditional mean model approach in the VanSteen-algorithm  and model (2) when the null hypothesis holds that there is no direct effect and, moreover, there is no confounding due to population substructure. For testing the null hypothesis of no direct genetic effect, model (2) can thus be used to estimate the parameter γ1 in a screening step without biasing the significance level since Xi is not included in this model, provided there is no confounding due to population substructure.As shown in the proof given in the appendix, the parameter γ1 in model (2), which does not involve the genetic marker X. Li since including factors such as Li in the phenotypic adjustment would introduce bias if the common risk factor Li is associated with the DSL Xi . μi)*) is the predicted value for K under a linear regression model for K with the covariates Li and E(Xi|Si), and σ*2k denotes the residual variance in that model. The variance correction given in Equation (5) is needed to account for estimating γ1 in the proposed phenotype adjustment For the screening step, each subject contributesX is not used in this test statistic. For step 2, this smaller subset of SNPs are used to test the null hypothesis of no direct effect using the test statistic based on Equation (1) proposed by Vansteelandt et al. (1 in model (1), which does involve the genetic marker X. Using this association test with the adjusted phenotype Yi and the DSL; i.e., the association between the target phenotype Yi and the DSL is solely a result of the association between the secondary phenotype Ki and the DSL. Adjusting for estimating γ1 based on model (1), the test statistic is distributed chi-square with one degree of freedom under the null hypothesis of no direct effect of X on Y and has the following formi denotes the residual from model (1). μi)) is the predicted value for K under a linear regression model for K with the covariates Li, Xi, and E(Xi|Si), and σ2k denotes the residual variance in that model. The variance correction given in Equation (8) is needed to account for estimating γ1 in the proposed phenotype adjustment Xi. Similarly, Equation (5) is similar to Equation (8), but Equation (8) contains the genetic marker Xi.For step 1, the test statistic given in Equation (4) can be used for the screening step to pick the SNPs with the highest power since t et al. (6)Ti={XK and Y is different in models (1) and (2), even in the absence of population admixture. Model (1) represents the causal effect of K on Y under the alternative hypothesis, but model (2) does not represent the causal effect of K on Y because there is a remaining spurious association between X and Y along the path K ← X → Y in Figure X → K or the X → Y link is strong. This scenario is explored further in the simulation section of this paper.Note that under the alternative hypothesis, the association between n models  and (2),Because the test statistic for the screening step given in Equation (4) is susceptible to population stratification, we examined this scenario in the simulation section as well. Principal component analysis (PCA) can be used in the screening step to correct for population stratification.1 based on model (2) in the screening step and compare it to the approach proposed by Vansteelandt et al. (1 based on model (1). Similar to Vansteelandt et al.  and X and Y (X → Y). We increased the correlation between X and K from 0.025 to 0.05 and then 0.075. We also increased the correlation between X and Y from 0.05 to 0.10 and then 0.15. The power of both statistics remained very close. At most, the power of the Vansteelandt et al. statistic  is susceptible to population stratification, we examined a few scenarios where population stratification was present. We simulated half of the subjects to have allele frequency of 5, 5, 20, and 40% and the other half of the subjects to have allele frequency of 10, 45, 25, and 45%, respectively. Similar to Tables  is susceL, the collection of common risk factors between FEV1 and height. For rs2415815 a SNP associated with both height and FEV1, the test statistic equals 0.044 with corresponding p-value equal 0.83. As a result, we fail to reject the null hypothesis and conclude that there is no evidence that the SNP acts directly on FEV1 other than via body height.We evaluated the practical relevance of the proposed adjustment principle by an application to the Framingham Heart Study with 1400 probands , this increases the number of multiple comparisons and can decrease power. If too few SNPs are chosen in the screening step , this decreases the number of multiple comparisons, but one may fail to detect the causal SNP since too few SNPs were chosen. Care needs to be given to the number of SNPs chosen in the screening step (Van Steen et al., The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.