Genetic-based susceptibility to bilirubin neurotoxicity and chronic bilirubin encephalopathy (kernicterus) is still poorly understood. Neonatal jaundice affects 60–80% of newborns, and considerable effort goes into preventing this relatively benign condition from escalating into the development of kernicterus making the incidence of this potentially devastating condition very rare in more developed countries. The current understanding of the genetic background of kernicterus is largely comprised of mutations related to alterations of bilirubin production, elimination, or both. Less is known about mutations that may predispose or protect against CNS bilirubin neurotoxicity. The lack of a monogenetic source for this risk of bilirubin neurotoxicity suggests that disease progression is dependent upon an overall decrease in the functionality of one or more essential genetically controlled metabolic pathways. In other words, a “load” is placed on key pathways in the form of multiple genetic variants that combine to create a vulnerable phenotype. The idea of epistatic interactions creating a pathway genetic load (PGL) that affects the response to a specific insult has been previously reported as a PGL score. We hypothesize that the PGL score can be used to investigate whether increased susceptibility to bilirubin-induced CNS damage in neonates is due to a mutational load being placed on key genetic pathways important to the central nervous system's response to bilirubin neurotoxicity. We propose a modification of the PGL score method that replaces the use of a canonical pathway with custom gene lists organized into three tiers with descending levels of evidence combined with the utilization of single nucleotide polymorphism (SNP) causality prediction methods. The PGL score has the potential to explain the genetic background of complex bilirubin induced neurological disorders (BIND) such as kernicterus and could be the key to understanding ranges of outcome severity in complex diseases. We anticipate that this method could be useful for improving the care of jaundiced newborns through its use as an at-risk screen. Importantly, this method would also be useful in uncovering basic knowledge about this and other polygenetic diseases whose genetic source is difficult to discern through traditional means such as a genome-wide association study. Chronic bilirubin encephalopathy  is caused by exposure to toxic levels of unconjugated bilirubin (UCB) in severely jaundiced newborns resulting in deposition of bilirubin in the brain Shapiro, . NeonataDespite the widespread use of TSB levels as a guide for intervention in jaundiced newborns, TSB alone has been shown repeatedly to be a poor predictor of neurological impairment  score method to decipher the genetic factors that contribute to increased susceptibility to bilirubin neurotoxicity. Finally, we summarize our proposal and describe the current status of this ongoing project.The study of molecular genetics has identified more than 6000 different monogenetic diseases, mostly through familial linkage analysis. Autosomal dominant, autosomal recessive, and X-linked genetic diseases with complete penetrance were the first and easiest to identify by linkage analysis. Later, genome-wide association studies (GWAS) were developed to identify genes contributing to incompletely penetrant and poly-genetic diseases. Both methods have successfully identified key genetic contributors to various diseases. However, these genetic analyses have also had many failures. Studies of thousands of individuals have failed to uncover significant genetic heritability for numerous diseases (the “missing heritability” problem), leading to a re-evaluation of the basic tenants of GWAS  otherwise healthy newborns. About 7% of jaundiced infants receive phototherapy ,  (hemolysis) or impaired elimination of bilirubin. Most genetic abnormalities linked to the presentation of bilirubin encephalopathy are related to production and elimination. Hemolysis may occur as a result of immune mechanisms , increased fragility of RBC [Glucose-6-phosphate dehydrogenase (G6PD) deficiency], or from bleeding . Decreased elimination is enhanced in infants with genetic variations in the enzyme or the promotor regions of UDP-glucuronosyltransferase 1A1 , the type of treatment administered and other known risk factors such as acidosis or sepsis Shapiro, . FurtherClinical observations have shown that in cases where TSB reaches extremely high levels  and SNPs. Second, unlike GWAS and linkage analysis, the PGL score method involves the calculation of a risk score. Third, the method can be performed using a smaller sample size than in GWAS studies because the number of variables is dependent on candidate pathway size, thus reducing the required sample size to achieve adequate statistical power. Finally, the PGL method allows detection of combinatorial epistatic interactions that would otherwise have been missed by both GWAS and linkage analysis.The decision to use a biased approach comes with the understanding that the available knowledge will very likely present only a partial picture of the entire genetic heritability. However, the hope is that if enough of the biological background is known, then the analysis will prove to be useful and actionable. By accepting a higher rate of false negatives, we will find it is then possible to drastically reduce the number of genes and thus variants being surveyed. Reducing the number of SNPs being investigated allows for a corresponding reduction in sample size, opening up analysis to rarer diseases. Huebinger et al. used their knowledge of injury and infection to select the Toll-like receptor signaling pathway to assess whether an increased PGL risk score within this pathway could predict the outcome following burn trauma   mutations can cause defects in RBC metabolism  and the solute transporter SLCO1B1 that facilitates UCB uptake and influences the ability to clear bilirubin. Poorly functioning variants of either gene can contribute to hyperbilirubinemia   between the IC (susceptible) compared to SC (resistant) brain regions in normal adult brains using the resources of the Allen Brain Atlas. From these genes we selected 100 genes with the largest increase in expression level in the IC vs. SC (3A) and 100 genes with the largest increase in expression level in the SC vs. IC (3B), as measured by fold change, for a total of 200 genes. For the creation of Tier 3 C and D we identified those genes whose expression was significantly different (p < 0.05) between GP (susceptible) and PU (resistant) brain regions. And as with 3A and 3B we selected 100 genes with the largest increase in expression level in the GP vs. PU, (3C) and 100 genes with the largest increase in expression level in the PU vs. GP (3D), as measured by fold change, for a total of 200 genes.For the creation of Tier 3 A and B we identified those genes whose expression was significantly different , heterozygous (score of “1”) and homozygous detrimental (score of “2”). The initial calculation results in the raw risk score where each SNP is treated equally. The risk score is then weighted to better represent the impact of each of the SNPs. For this step Huebinger et al. chose to use the adjusted odds ratio from previously reported studies for each SNP between each individual locus and either death or sepsis. For loci without previously published data, the value was left unweighted. The data could then be analyzed further by Mann-Whitney U Test to investigate whether the PGL risk score alone can predict developing sepsis. In addition, the multivariate logistic regression test could be used to investigate the simultaneous effect of multiple variables as risk factors for various outcomes. A synopsis of the PGL workflow can be seen in Figure For their analysis Huebinger et al. chose to adjust for age, gender, race, total body surface area burned, and inhalation injury. They were able to show that each unit increase in weighted PGL risk scores was associated with increased probability of both complicated sepsis and death. By analyzing data from only 155 burn trauma patients and using only 6 SNPs at 6 different loci, they showed that a larger PGL risk score indicated increased odds of both sepsis and mortality in response to burn trauma. This work, along with other similar pathway load work  from QIAGEN Redwood City. Ingenuity® Variant Analysis™ allows for multiple types of SNP filtering to create a list of screened causal variants that are present in a significant number of the case group vs. controls. The causal variant filter is based on the American College of Medical Genetics and Genomics (ACMG) categorization guidelines . The causal variant list can also be filtered to include only those genes present in each of the gene set tiers.To develop a SNP set for each tier, we will collect whole exome sequence data from patients with moderate to high TSB levels (10–25 mg/dL and >25 mg/dL respectively) both with and without evidence of classic auditory or motor dysfunction. We will identify positive “hits” through a pipeline utilizing the Partek Genomics Suite and Flow . Causal variants in this study will then be identified through the use of QIAGEN's Ingenuity® Variant Analysis™ software   score Ng,  or the CWhile the PGL method presented has been successful at producing significant and meaningful results, there are drawbacks to using PGL risk score analysis. These drawbacks include the previously described risk for false negatives, the possibility that major contributing factors are outside the pathway chosen to be studied, and that considerable cross-talk is occurring between overlapping pathways, leading to confusing and difficult to confirm results. In addition, the selections of the target pathway and the set of SNPs are based on the information available at the time of the study which may not be complete enough to make accurate selections. To address this issue, we have used three different methods to develop our tiers aimed at maximizing the currently available knowledge base for CBE. Finally, the weighting method described by Huebinger et al. utilizes an adjusted odds ratio based on previously performed GWAS studies  and high (>25 mg/dL) peak TSB levels at birth. We acknowledge that it would be preferable to also investigate the free unbound bilirubin levels for these patients, but those data are rarely available. Because of the rarity of kernicterus in developed countries, 1.15:100,000 live births in an average of three studies from Denmark Ebbesen,  and 0.93We present a method for addressing the problems associated with identifying the genetic factors that influence both level of bilirubin and susceptibility to bilirubin encephalopathy (kernicterus). Because rare diseases by definition affect small numbers of people, it is impractical to use unbiased population-based GWAS studies. In this paper, we present an evidence-based candidate pathway approach in the form of the PGL risk score that will reduce the number of genes and variants investigated and thus reduce the need for overly large sample sizes. We propose new alternatives for selecting pathways and variants through the creation of custom gene lists and use of functional scoring methods. The logistic regression analysis proposed in Huebinger et al. will be used to determine whether the PGL score for patients with moderate and high TSB levels could successfully predict auditory or motor deficit outcomes. As this method is tested and refined, we believe it will lead to the creation of new hypotheses that will aid the investigation of the molecular mechanisms of bilirubin toxicity in newborns. This work could also potentially be used to develop a screening process for jaundiced infants that could inform physicians about whether more aggressive treatment is needed in infants with moderate TSB levels. Finally, this method could be adapted to other rare or complex diseases to address the challenge of missing heritability that exists despite GWAS.SR drafted the manuscript. SR, DB, JL, SG, CT, JW, RW, and SS contributed to the conception of the work and provided critical revision for important intellectual content.This work was supported by institutional startup funds from Children's Mercy Hospital.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.


Motivation: High-throughput sequencing technologies have impacted many areas of genetic research. One such area is the identification of relatives from genetic data. The standard approach for the identification of genetic relatives collects the genomic data of all individuals and stores it in a database. Then, each pair of individuals is compared to detect the set of genetic relatives, and the matched individuals are informed. The main drawback of this approach is the requirement of sharing your genetic data with a trusted third party to perform the relatedness test.Results: In this work, we propose a secure protocol to detect the genetic relatives from sequencing data while not exposing any information about their genomes. We assume that individuals have access to their genome sequences but do not want to share their genomes with anyone else. Unlike previous approaches, our approach uses both common and rare variants which provide the ability to detect much more distant relationships securely. We use a simulated data generated from the 1000 genomes data and illustrate that we can easily detect up to fifth degree cousins which was not possible using the existing methods. We also show in the 1000 genomes data with cryptic relationships that our method can detect these individuals.Availability: The software is freely available for download at http://genetics.cs.ucla.edu/crypto/.Contact:fhormoz@cs.ucla.edu or eeskin@cs.ucla.eduSupplementary information:Supplementary data are available at Bioinformatics online Detecting relatives from genetic data is one of the fundamental problems in genetics. As genotype-chip technologies reduce the cost of collecting genetic data for each individual, many personal genomic companies provide various services. One such service is the identification of relatives using genetic data. The underling idea of this service is to collect genotypes of different individuals and to store their data in a database. Then, the genotype for each pair of individuals is compared and any pair of individuals that appear to be genetically related are notified of a match.Unfortunately, the current version of this service provided by all companies requires individuals to share their genetic data with a trusted company.Recently, We propose a novel encoding mechanism that convert each individual’s haplotypes to a set of integer values such that the comparison between two sets approximate the genetic comparison between the two individuals where each individual has access only to its own variants list. The main innovations of our approach compared to We use both simulated and real data to show the utility of our method. We generated series of family relationships using the 1000 genomes data as the founder of the population. Then, we randomly generated offsprings for different generations. With the simulated data, we show that our secure protocol could detect up to fifth degree cousins. However, the previous method , 2012 tht’ as shown in t’ and it fails otherwise. Mostly, the keys used in ‘fuzzy’ encryption are in form of extremely long vectors which are sparse and the sparsity allows us to compute the Hamming distance efficiently using ‘fuzzy’ encryption.Our method uses the ‘fuzzy’ encryption, which is a new method in the field of cryptography  which is the basis of our approach to private relative identification. The secure comparison of sets works as follows. Each individual has a set of elements which is private to the individual. Using the cryptographic protocol based on fuzzy extractors, each individual is able to identify which other individuals have a set with at least ‘k elements, each of which is binary vectors of length m, then there are a total of 2m possible elements. The private keys are binary vectors of length 2m with k ‘1’s encoding which element exists in an individual’s set. We use fuzzy extractors to generate public keys for these private keys where the threshold for decryption is t’ elements in common. Any pair of private keys that have Hamming distance of t’ elements in common. Each individual can release their public keys and other individuals can detect if their sets have at least ‘t’ elements in common by attempting to decrypt the public key using their private key.The way secure set comparison is implemented using fuzzy extractors is that the private keys that are generated encode the membership of each element of the set. We consider all sets contain In this work similar to previous work . The entropy in ‘fuzzy’ encryption is bounded by There exist a series of methods to detect the relatedness among different individuals and even build the family tree using the Identity by descent (IBD) . In thisN individuals and we have access to each individual’s variants and the reference genome. In our method we only consider single-base variants which include both common and rare variants. Furthermore, we assume we have access to the phased haplotypes of each individual, in the case we have unphased haplotypes, we can phase them by using the existing methods . Moreover, j-th segment of the i-th individual’s binary haplotype. We use iS to indicate the set for i-th individual and ijs to indicate the j-th element of the set iS representing the j-th segment of genome.M denotes total number of base pair in each genome, in the case of human genome M = 3 billions.We assume that we have  methods , we phast’ we consider them as related individuals and if the distance score is >‘t’ we consider them as unrelated individuals. We assume the value of ‘t’ is computed using a training set where the true relationship between each pair of individuals is known.If the distance score between two individuals is <‘In order to compute the number of matched segments between two individuals, we count the number of shared haplotypes for each segment between the two individuals. There exist three possible values for each segment: zero, one and two. Zero indicates both haplotypes in that segment are different between the two individuals, two indicates both haplotypes in that segment are the same between the two individuals and one indicates only one of the haplotypes is the same between the two individuals.iS). Let iK indicates the sketch of i-th individual and ijk indicates the j-th element of the iK that is obtained by hashing the j-th element of the i-th individual genome set.r is a random binary number of size 100 that is referred to as the salt, and In order for individuals to securely compute the symmetric difference between their genomic sets, we define a sketch where we hash the value of each element in the genomic sets (f to be a one way function such that given x computing f(x) is easy. However, given the f(x) computing the x is hard. It is worth mentioning two segments obtained from the same genomic position in the genome for two different individuals that differ in one base pair have a different sketch element. Thus, reverse engineering the genome given the secure set is extremely hard based on the hardness of inverting one way functions.Collision-resistance hash function has two main properties: first, collision-resistance hash function is one-way function. Second, finding distinct values which have the same hashed value is hard. We consider function However, using the sketch for identification leaks information. We can compare the sketch of other individuals with our own sketch to detect which genome segments are similar. Thus, this results in the leak of information. We use the sketch as the private key and use the improved version of the Juels–Sudan construction . Then, for each variant in the segment we consider the flanking sequence of length 500 bp around the variant. Virtually all common SNPs have been identified in the HapMap and 1000G projects. We concatenate all the flanking sequences around each variant in a segment to represent the segment uniquely. Then, the collision resistance hash function is applied as described above to generate elements of the set.In this encoding each segment is of size 30 000 bp and each segment starts from a known common SNP in the dbSNP  for each simulated individual and then each individual uses the secure sketch of another individuals and compare to its own sketch (private key). As expected, for each pair of individuals that are related, the program terminates successfully. However, for unrelated pairs of individuals the program fails.We use another population from the 1000 genomes to generate simulated data using the same process to make sure our results are not specific to only one population. We use the Mexican Ancestry in Los Angeles, California (MXL) population. The MXL consist of 69 individuals where nine individuals have cryptic relationships. We removed the cryptic-related individuals so that the founders are unrelated. We observe there exists a separation between the related and unrelated using our method of comparing sets. We can detect up to fifth-degree cousins using our method. The results are similar to the LWK population and for the sake of space we did not show the results.In order to assess the results of our method we used the 1000 genomes data. Although the 1000 genomes data consist of unrelated individuals, there exists three populations that contain cryptic (not known before sequencing) relationships. These three populations are African Ancestry in Southwest (ASW), and LWK. We used the final phase of data. The ASW population consists of 66 individuals where 10 individuals have cryptic relationships. The LWK population consists of 116 individuals where 19 individuals have cryptic relationships. The cryptic relationships in this data are parent–child, sibling or second-order relationships.In order to detect if two individuals are related or not there exist series of methods, the standard method is KING method (We run our method to generate the secure sketch (public key) for each individual in the 1000 genomes data. Then, each individual uses the secure sketches of other individuals and compare it with their own sketch (private key). As expected, for each pair of individuals that are related, the program terminates successfully. However, for unrelated pairs of individuals the program fails.In order to check if the new encoding mention in Section 2.4 works, we used the known list of SNPs from Hg18 and Hg19 obtained from the HapMap project. For each SNP we consider 500-bp sequence around the SNP in both builds of Hg18 and Hg19. Then, we used the SSHA-256 to hash each string (1000 bp) and compared the hash value for the same SNPs in the two different builds. In our experiment we observed only 0.002 fraction of the SNPs will not have the same hash value. Meaning only 0.002 of SNPs are not mapped to the right SNP position when two different genome builds are used. As a result, the majority of SNPs are mapped to the same flanking sequence when moving from Hg19 to Hg18. Thus, the encoding which utilizes the flanking sequence can easily use a different genome build to generate keys to be compared with the other individual’s public key that was generated using a different genome build.Sequencing technologies have made personal genomics possible and many companies are providing information about ancestry and health of individuals by utilizing genetic data. However, to obtain these information, each individual has to share their genomic data. The sharing of genomic data raises privacy issues.One solution to the privacy issue is to use a trusted third party for detecting relatedness, however, individuals may not feel comfortable to share their genetic data with a trusted party for detecting related individuals. In this article, we demonstrate detecting the relatedness between two individuals where both individuals have access to their genetic data and no third party is needed.Recently, In this work, we provide a secure method for individuals to detect the genetic relatives from sequencing data without exposing any information about their genomes that utilizes both common and rare variants and through simulated data, we demonstrate, we can detect up to fifth-degree cousins. We also show in two populations from the 1000 genomes data that contains cryptic relationships, our method can detect these individuals. Our method also utilized an encoding that allows us to compare individuals who utilized different genome builds for calling their variants. Thus, genomes encoded using today’s genome build can be used to detect relatives called using future builds.The input to our method is the phased haplotypes, in the case we have unpashed data, we phase our data using an existing method ; Stephen


K > 2 levels, and modeling of allele counts at two unlinked marker loci. Inference is based on within-family information to guard against potential bias due to population genetic structure. Score tests of the model coefficients taking into account the correlation between relatives in entire pedigrees are derived as an extension of the Generalized Disequilibrium Test (GDT). Simulations confirm that the tests have the expected statistical properties, and that their power exceeds that of the GDT under a favorable scenario. The score tests are illustrated with candidate genetic markers, a major psychosis phenotype and a cognitive endophenotype in large kindreds from Eastern Quebec.We extend the usual logistic model between a dichotomous phenotype and an allele count in two ways: a polytomous phenotype with  Studies of the association between a phenotype and genetic markers are commonly performed on the members of families of various sizes. While methods to estimate association parameters and test the null hypothesis of absence of association (possibly coupled with absence of genetic linkage) with dichotomous phenotypes in family samples are well developed  of Chen et al. .In previous work, we showed by simulation that conditioning on a marker at a known disease susceptibility locus increased power to detect linkage to new loci interacting with that disease susceptibility locus . Then we derive expressions for particular forms of terms in X.We extend the GDT of Chen et al.  in two wi with a general iX vector can be writtenThe polytomous model for subject kiX is the sub-vector of iX containing the allelic terms related to level (category) k and k the sub-vector of the full coefficient vector k .where n genotyped pedigree members with an observed phenotype are ordered such that the first n1 subjects are in outcome category Y = 1, the n2 following subjects are in outcome category Y = 2 and so on up to the last Kn subjects with Y = K.Without loss of generality, we assume that the K = 2 and a single X , Chen et al. , Kn−n + 1,···,n} and (h)aiX is the slice of aiX related to the coefficient βh. If βh is involved only in the logistic function between levels a and K, then the score statistic simplifies to:aE = {1n + ··· + na−1 + 1, ···, 1n+ ··· + an} for a > 1 and E1 = {1 ··· n1}.where (h)S and the covariance of (g)S and (h)S for coefficients βg and βh can be derived, following the steps of Chen et al. It is also easier to interpret. When the tested coefficient belongs to the logistic function attached to a single outcome category and the score statistic reduces to expression 4, it is a contrast of the value of the corresponding X term between subjects in the outcome category and subjects in all other categories.The advantage of expression 3 is that a closed-form expression for the variance of v[S] be an estimate of the variance-covariance matrix of S, the null hypothesis that Letting 2 distribution with degrees of freedom equal to the rank of which follows a χh1 = ··· = βmh = 0 for any subset of indices h1, ···, mh, the other coefficients are free to differ from 0 and the derivation in Supplementary Material no longer applies. We adopt here the approach Chen et al. X, c = {l : l ∉ } when the variability from estimating the where the weights  Stewart  S is 0. The weight definition will only have an impact on power. The joint null hypothesis βh1 = ··· = βmh = 0 for any subset of indices h1, ···, mh can be tested with the statisticwhich follows approximately a standard normal distribution under the null, when the weights are defined in such a way that the expectation of 2 distribution with m degrees of freedom under the null.which follows approximately a χ(h)S depends on whether the null hypothesis refers only to absence of association, or to absence of genetic linkage and association. In the first case, the null distribution of (h)S allows genetic linkage at the locus, and the identical-by-descent (IBD) sharing proportions in the variance estimate must be the actual IBD sharing proportions at the locus πhij S and covariance between (h)S and (g)S is given in Supplementary Material. When (h)S takes the form 4, (h)aiX is a main effect term, say X1, and the actual IBD sharing proportions πhij are used thenThe variance of X1, σ21, is estimated as described in Supplementary Material to obtain the estimate (h)]v[S of (h)]Var[S. With equal weights for all pairs, the computation involving the IBD sharing probabilities can be simplified as explained in Supplementary Material.The within-family variance of (h)aiX is instead a product term, say X12X, thenWhen X1X2, σ212, is estimated as described in Supplementary Material.where the within-family variance of the product term Y2 and a dichotomous endophenotype Y1, as defined in the introduction.The joint analysis of two dichotomous traits represents an important special case of a polytomous phenotype with four categories. We illustrate such a phenotype by referring to a dichotomous disease trait Y1 = 1 and possibly to the disease Y2 = 1 has already been established, and that we want to detect locus 2, which is undetectable in single-locus analyses, by conditioning on locus 1 with which it interacts. This leads to null hypotheses on a subset of coefficients tested with a statistic as defined in Equation 8.We consider here polytomous models for two markers at unlinked loci which may interact to cause the disease and endophenotype impairment. We assume that association of locus 1 to the endophenotype impairment A first option is to use the full model with distinct coefficients for each disease/endophenotype combination contrasted to the reference category of absence of both the disease and endophenotype impairment. This model is:The null hypothesis of the conditional test of locus 2 given locus 1 under the full model is formulated as:Z statistics for each coefficient and the p-values associated to the tests of the subsets of coefficients , and .When the null is rejected, insights on the phenotype category driving the signal can be obtained by examining the Y1 = 1 and possibly to the disease Y2 = 1, and an allele at locus 2 increases susceptibility to the disease in carriers of gene 1 susceptibility genotypes (at higher risk of the endophenotype impairment). For that model we express allele counts as proportion of a given allele in a genotype, taking values 0, One can also postulate a model for a particular form of interaction between the two loci. We consider a model which we call the endophenotype-to-disease model where an allele at locus 1 increases susceptibility to the endophenotype impairment e, which represents the effect on the risk of the endophenotype impairment in non-carriers of the locus 2 tested allele. When the endophenotype-to-disease model holds, the coefficients β33 and βe are of the same sign. The marginal association of X2 to the endophenotype impairment under that model will typically be small. Its direction and magnitude depend on the values of β33 and βe and the distribution of X1.We keep the same notation for the coefficients as in the full model, except for the coefficient βThe null hypothesis of the conditional test of locus 2 given locus 1 under the above model is formulated as:The alternative hypothesis can be restricted toor a general alternative can be considered, but the alternative space then contains models outside of the conceptual model formulated above.X1 and X2, as in the context of a genetic analysis conditional on an environmental exposure  from input files in the Merlin/QTDT format (www.sph.umich.edu/csg/abecasis/Merlin/tour/input_files.html) and convert them into R objects. Alternatively, R objects made by the user in the same format can be provided as input. Functions are provided to setup design matrices for the full two-locus polytomous model, the one-locus polytomous model and the disease-to-endophenotype model. User-defined functions setting-up customized design matrices can be provided instead of these pre-defined functions.We have implemented the extension of the GDT to polytomous phenotypes and two loci in the R package Y1 and Y2 were generated in a two-step approach: we first simulated from the distribution of Yi1 for each subject i by summing over Yi2 in a polytomous model, then from the distribution of the vector Y2|Y1. In the model to simulate Yi2|Y1, Y1 is treated as a vector of fixed effect, with the effect of the endophenotype of subject h, Yh1, modulated by the kinship coefficient ϕih between i and h. An additive polygenic effect on the logit of Y2 was also included. The model can be written:The family structure used in the simulations is a 3-generation 16-member family depicted in Figure iX, Yi1) in an abbreviated expression of the model for the disease phenotype given the genotype at major loci and endophenotype status of subject i derived from a polytomous model and Φ is the kinship matrix between the family members. The parameter σ2 controls the degree of polygenic dependence between the disease status Y2 of the family members and the parameter α the degree of genetic dependance of Y2 on Y1 not captured by the genotype at the loci in the model. The parameter ν, between 0 and 1, determines the relative importance of the risk increase 1 − ν due to observing an endophenotype impairment and the risk decrease −ν due to observing the normal level of the endophenotype in a relative. We note this simulation scheme is meant to reproduce the association between disease phenotype and endophenotype status of relatives, not to represent a causal mechanism. Among the simulated families, we kept those with at least a cousin pair with Y2 = 1, i.e., affected by the disease to mimic the ascertainment process of families in a genetic study.where γ′(We simulated two scenarios of population origin of the sample: 1) homogeneity: the sample came from a single population where the phenotypes were generated under the polytomous model presented in Table  homogeneTo verify the Type I error of tests of association to locus 2 under the null hypothesis of no association to locus 2, but in presence of genetic linkage at that locus, we generated an additional biallelic variant at locus 2 independent from the causal variant at that locus, i.e., in linkage equilibrium with it. In the homogeneous population, the minor allele frequency of that marker was equal to the RAF of the causal variant, but in the mixture of two populations the minor allele frequency was 0.1 in population 1 and 0.5 in population 2, creating population structure at that locus. For the power evaluation, we tested association to the actual causal variant at locus 2.e, β33),” and β33 = 0. We also evaluated a single locus polytomous model (model 11 with X2 only). The coefficients in that model are labeled 3(1L) = 0. For the evaluation of the Type I error, Wald tests of the coefficients of the one locus model based on GEEs were also performed. However, these tests were not used for the power comparison, since they had inflated Type I error under our heterogeneity scenario where population stratification was present.The tests evaluated include the tests of the null hypotheses 11 which we denote “cpoly,” 13 which we denote “ consisting in testing association to the specific phenotype among subjects with a broader phenotype  , (2) the disease status Y2 in the subset of subjects with Y1 = 1 (endophenotype impairment), setting the phenotype of other subjects to unknown (GDTc), and (3) the endophenotype status Y1 (GDTe). We also compared our tests to score tests of coefficients of the usual two-locus logistic model for a dichotomous trait:In presence of population stratification, previously available valid tests are restricted to a dichotomous outcome and a single marker. Analysis options are then limited to testing association of a single marker to the dichotomous endophenotype 2 = η3 = 0 is denoted “cdisease” when the phenotype tested is Y2 and “cendo” when the phenotype tested is Y1.The 2 d.f. test of the null hypothesis ηThe Type I error was evaluated on 1000 replicate samples of 100 families. The results of the simulation under the null hypothesis in Table 33 = 0 (the interaction parameter for the combination of disease and endophenotype impairment) achieves the highest power among the tests considered  = 0 or the entire vector Under the simulated scenario the endophenotype-to-disease model holds. While the test of the null hypothesis 13 has some power, testing βd Figure . Using wSchizophrenia (SZ) and bipolar disorder (BP) are two forms of the spectrum of major psychosis (MP), which also includes schizo-affective disorder. SZ and BP co-aggregate in families  while it was positively associated to a lesser extent to MP without VisEM impairment with Z statistics of 2.54 for the X2 and 2.07 for the X1X2 terms (p = 0.005 for the test of the coefficients of both terms). The signal was thus driven by opposite associations to these two phenotypic categories. The signal at rs1087266 was detected by single locus tests with lower p-values than by tests conditioning on rs1156026. In that case, testing association with VisEM status was the key to detect the signal. Nonetheless, the conditional test of the polytomous phenotype provides a p-value similar to the standard GDT. Given the limited power of the analysis and the number of SNPs tested, these results cannot be considered statistically significant once multiple testing is taken into account.The results for rs7500550 illustrate that tests of the joint MP-VisEM phenotype conditional on the rs1156026 T allele count can detect associations to SNPs where the test of the MP or VisEM phenotype alone did not. In this case, the rare allele was negatively associated to MP with VisEM impairment with We have extended the GDT, a score test of genetic association applicable with extended families, to enable testing association with a polytomous phenotype. Another extension is the use of a model of association with two genetic loci, allowing to test association at a locus conditional on the genotype of a marker at a known risk locus, to exploit interaction between the two. A software implementation in the form of a R package has been made freely available. The within-family analysis framework that we adopted has the advantage of protecting against Type I error inflation due to population stratification. Polytomous phenotypes can be more informative than dichotomous ones to detect genetic associations, as illustrated in our simulation study.The proposed score tests also suffer from limitations. First, score tests provide no estimates of the regression parameters being tested. Conditional maximum likelihood estimation would be applicable only with exchangeable relatives, which is not required for the GDT as explained in Supplementary Material. We are exploring the robustness and power of conditional maximum likelihood estimation in sibships from extended families.Second, within-family analysis tends to be less powerful than population-level analysis which also exploits between family information. Furthermore, the Type I error of score tests for one locus conditionning on another tends to be conservative even with the weight definition 6 neglecting variability from estimating the Alexandre Bureau defined the research questions, derived the proposed statistical test, wrote part of the R implementation, conceived the simulation study, oversaw the analysis of the major psychosis data and drafted the manuscript. Jordie Croteau wrote part of the R implementation, performed the simulation study and the analysis of the major psychosis data, and created figures and tables. Yvon C. Chagnon oversaw the genotyping of the Eastern Quebec kindred study and contributed to the design of the genetic aspects of that study. Marc-André Roy contributed to the design of the genetic and clinical aspects of the Eastern Quebec kindred study, established diagnosis of patients and made substantial revisions to the manuscript. Michel Maziade designed the genetic and clinical aspects of the Eastern Quebec kindred study, oversaw clinical data collection and established diagnosis of patients. All authors approved the version submitted for publication and agree to be accountable for all aspects of the work.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.


Growth and carcass traits are very important traits for broiler chickens. However, carcass traits can only be measured postmortem. Genomic selection may be a powerful tool for such traits because of its accurate prediction of breeding values of animals without own phenotypic information. This study investigated the efficiency of genomic prediction in Chinese triple-yellow chickens. As a new line, Chinese triple-yellow chicken was developed by cross-breeding and had a small effective population. Two growth traits and three carcass traits were analyzed: body weight at 6 weeks, body weight at 12 weeks, eviscerating percentage, breast muscle percentage and leg muscle percentage.Genomic prediction was assessed using a 4-fold cross-validation procedure for two validation scenarios. In the first scenario, each test data set comprised two half-sib families (family sample) and the rest represented the reference data. In the second scenario, the whole data were randomly divided into four subsets (random sample). In each fold of validation, one subset was used as the test data and the others as the reference data in each single validation. Genomic breeding values were predicted using a genomic best linear unbiased prediction model, a Bayesian least absolute shrinkage and selection operator model, and a Bayesian mixture model with four distributions. The accuracy of genomic estimated breeding value (GEBV) was measured as the correlation between GEBV and the corrected phenotypic value. Using the three models, the correlations ranged from 0.448 to 0.468 for the two growth traits and from 0.176 to 0.255 for the three carcass traits in the family sample scenario, and were between 0.487 and 0.536 for growth traits and between 0.312 and 0.430 for carcass traits in the random sample scenario. The differences in the prediction accuracies between the three models were very small; the Bayesian mixture model was slightly more accurate. According to the results from the random sample scenario, the accuracy of GEBV was 0.197 higher than the conventional pedigree index, averaged over the five traits.The results indicated that genomic selection could greatly improve the accuracy of selection in chickens, compared with conventional selection. Genomic selection for growth and carcass traits in broiler chickens is promising.The online version of this article (doi:10.1186/s12863-014-0110-y) contains supplementary material, which is available to authorized users. Genomic selection has been widely applied in dairy cattle breeding -5 and haCarcass traits are very important traits for broiler chickens. However, carcass traits cannot be directly measured from breeding candidates. Therefore, indirect measures are usually used as indicator traits, for example, using ultrasound measurement of breast meat to predict actual weight of breast meat. Breeding values of carcass traits predicted using the indirect measurements could be inaccurate. With genome-wide dense markers, it is possible to predict breeding values accurately, based on direct measurements of carcass traits from a reference population. Recently, some studies on genomic selection in chickens have been carried out -13; howeIn general, Chinese local breeds, are characterized by high meat quality and rich flavor, which meet popular demand in China. Major breeds of Chinese local chickens have yellow beak, yellow feather and yellow claw, and therefore they are named Chinese triple-yellow chickens. However, slow growth is another characteristic of Chinese local breeds. Cross-breeding is often used to breed synthetic lines in chickens ,15. In tThe accuracy of genomic prediction is key to the successful application of genomic selection. A number of statistical models have been proposed to predict genomic values -21, amonAccuracy of genomic prediction is greatly dependent on the size of reference population and effective population size. Larger reference population provides more information of phenotypic records , and smaller effective population size leads to smaller effective number of loci . Therefo2 generation.The main objective of this study was to investigate the accuracy of genomic selection for a population with small effective population size but also small reference population. Genomic prediction was performed for two growth traits and three carcass traits, using GBLUP, BayesLASSO and Bayesian mixture models, based on data from a Chinese triple-yellow chicken population, which had a small number of foundation animals and only had records from the Fth week (BW6) and at the 12th week (BW12), and were 0.44, 0.39 and 0.39 for eviscerating percentage (EP), breast muscle percentage (BMP) and leg muscle percentage (LMP), respectively.Estimates of genetic parameters based on the full phenotypic data  are presented in Table Table As shown in Table In general, GEBV predicted by GBLUP and BayesLASSO had similar accuracies Table , while BThe statistic power of the accuracies from the three genomic prediction models were acceptable (P > 0.85) for all five traits in both validation scenarios. But the statistic powers of the accuracies from the conventional model were unacceptable (P < 0.85) for all traits in the ValFamily scenario. The differences between the three genomic prediction models and conventional model were significant (P < 0.05) for all traits in the ValRandom scenario, and were significant for BW6, BW12 and EP in the ValFamily scenario. Although the differences between accuracies of predictions from conventional and genomic prediction models were larger in ValFamily scenario than in ValRandom scenario, the differences for BMP and LMP were not statistically significant in ValFamily scenario. This could be resulted from larger sampling error in ValFamily scenario. In this scenario, the individual within a fold are strongly related, consequently reducing effective sample size and increasing sampling error. It was also reflected by a large variation in correlations between folds in ValFamily scenario , the results showed that the accuracies of the predictions were relatively high, considering the size of the training data. This could be attributed to the small effective population size in this line. If the effective population size is small, it is expected that animals will share larger chromosome segments and the genomic predictions will be more accurate. The influence of the effective population size on the accuracy of genomic prediction has been demonstrated in some studies [The current study was based on the data from F studies ,26. In aGenomic selection greatly benefits the traits that are difficult to be measured or cannot be directly measured when the animals are selected. As shown in this study, the gain from genomic prediction was relatively small when the animal had own records Table , while rAlmost all the regression coefficients of corrected phenotypic values on GEBV were close to one in both ValFamily and ValRandom, except the ones for LMP in ValFamily which were far from one for all models, indicating a serious inflation of GEBV for LMP in this scenario. The reason for this unexpected regression coefficient is not clear. One possible reason could be that markers may fit part of noise, consequently reducing accuracy of GEBV  and regression coefficient (inflating variance of GEBV). An inflation of GEBV is common phenomenon in genomic prediction ,35 causeOne of the factors influencing the accuracy of genomic prediction is the relatedness between the predicted animals and the training animals. In most studies ,7,12,36 A number of previous studies have been carried out that compared statistical models for genomic prediction. In general, simulation studies with the assumption that few QTLs account for a large proportion of the additive genetic variance have shown that the predictive ability of Bayesian variable shrinkage and variable selection models are superior to linear BLUP models ,40,41. HIn the current study, GBLUP and the BayesLASSO produced genomic predictions of similar accuracies. None of these three models showed a consistently better performance for carcass traits; however, the differences among these models were very small (less than 0.01). BayesMix4 performed slightly better than the other models for growth traits. The results were similar to those obtained in other farm animals. For example, Ostersen et al.  comparedSome studies -44 reporThe results of this study show that in a breed with small effective population size, accurate GEBV can be obtained from a relatively small reference population. Moreover genomic prediction is a feasible approach for accurate selection in chicken breeding programs, especially for the traits which are difficult to be measured such as carcass traits.The Animal Care Committee of the Institute of Animal Science, Guangdong Academy of Agricultural Sciences  approved the current study .0 individuals, 51 F1 birds, and 511 F2 birds, which came from 8 half-sib families.The birds in this study came from a population of a three-generation intercross between the “High Quality chicken LineA” (HQLA) and the Huiyang Beard chicken (HB), as described in Sheng et al. . The HQLThe birds were genotyped using the Illumina Chicken 60K SNP Beadchip  by DNA LDuring the first 5 weeks of life, the birds were kept with group cages by hatch, and were provided with a starter feed . From 6th to 13th week, all birds were housed in single cages, and provided with a grower feed . The birds had free access to feed and water. The breeding facility supplied 24-hour lighting. A water curtain system was used to adjust the temperature.2 animals.Traits measured in the analysis included BW6, BW12, EP, BMP, and LMP. Table Conventional EBV was predicted using a BLUP model. Genomic breeding values were predicted using a GBLUP model, a Bayesian Lasso model and a Bayesian mixture model.The BLUP model  to prediwhere y is the vector of the observations, b is the vector of the fixed effect (sex and hatch), X is the incidence matrix of b, a is the vector of additive genetic effects of the birds in the pedigree, Z is the incidence matrix of a, and e is the vector of the residuals. It was assumed that a ~ N The GBLUP model  used to where the definitions of y, b, X, and e are the same as those in the BLUP model, u was the vector of additive genetic effects of genotyped individuals and Z was the incidence matrix of u. It was assumed that u ~ N ormation  and \docIn the Bayesian analysis, the effects of SNPs were estimated using the following model:where q was the vector of random SNP effects, M was the matrix of genotype indicators, and y and e are the same as in the GBLUP model. The difference between BayesLASSO  and the where k was the number of markers, λ was a rate parameter that was sampled from a uniform distribution.1 = 0.889, π2 = 0.1, π3 = 0.01 and π4 = 0.001, where π1 was the proportion of the distribution with the smallest variance, and π4 was the proportion of the distribution with the largest variance [BayesMix4 assumes that the distribution of marker effects is a mixture of four normal distributions. In the current study, mixing proportions in this distribution were taken as known and set to πvariance .ij was the genotype of marker j for individual i, and k was the number of markers. The DMU package [th sample of the remaining 30,000 samples was saved for posterior analysis. The BayZ package (http://www.bayz.biz/) performed the analysis of the Bayesian models.GEBV of individual i was defined as  package  was used package , using aTwo scenarios of 4-fold cross-validation were used to evaluate the accuracy of the genomic predictions. In the first scenario, the 8 half-sib families were divided into four subsets of similar sizes, i.e., a family sample, such that individuals in one subset did not have any half-sibs or full-sibs in the other subsets. In each fold of cross-validation, one of the four subsets was used as the test data, where the phenotypic values were masked during genomic prediction; the remaining three subsets were used as the training data. In the second scenario, 511 individuals were randomly split into four subsets, i.e., a random sample. As in the scenario of the family sample, in each fold of validation, one subset was used as the test data and the other three subsets were the training data. The numbers of birds in the test and training data sets for each fold of validation are shown in Table c), where yc was defined as the original phenotypic value corrected for fixed effects (sex and batch effects) which were estimated using the conventional BLUP model based on the full dataset, i.e., yc = y – sex effect – batch effect.The accuracy of GEBV was assessed by the correlation between GEBV and corrected phenotypic value .Regression of yng value . The ana


Statistics in Medicine published by John Wiley & Sons Ltd.Instrumental variable estimates of causal effects can be biased when using many instruments that are only weakly associated with the exposure. We describe several techniques to reduce this bias and estimate corrected standard errors. We present our findings using a simulation study and an empirical application. For the latter, we estimate the effect of height on lung function, using genetic variants as instruments for height. Our simulation study demonstrates that, using many weak individual variants, two-stage least squares (2SLS) is biased, whereas the limited information maximum likelihood (LIML) and the continuously updating estimator (CUE) are unbiased and have accurate rejection frequencies when standard errors are corrected for the presence of many weak instruments. Our illustrative empirical example uses data on 3631 children from England. We used 180 genetic variants as instruments and compared conventional ordinary least squares estimates with results for the 2SLS, LIML, and CUE instrumental variable estimators using the individual height variants. We further compare these with instrumental variable estimates using an unweighted or weighted allele score as single instruments. In conclusion, the allele scores and CUE gave consistent estimates of the causal effect. In our empirical example, estimates using the allele score were more efficient. CUE with corrected standard errors, however, provides a useful additional statistical tool in applications with many weak instruments. The CUE may be preferred over an allele score if the population weights for the allele score are unknown or when the causal effects of multiple risk factors are estimated jointly. © 2014 The Authors.  Mendelian randomization uses genetic variants as instrumental variables to investigate the effects of modifiable risk factors for disease such as weight, blood pressure, cholesterol, alcohol, and tobacco consumption on different outcomes of interest –9. An inA weak instrumental variable is one that explains only a small proportion of the variation in the exposure. Studies using a single weak instrument will have low power to reject the null hypothesis. In addition, any minor violation in the ‘exclusion restriction’ (i.e. the assumption that the instrument is unrelated to any confounders and does not directly affect the outcome of interest) can cause large biases .Studies using many instruments that are each only weakly associated with the exposure can suffer from a further distinct bias: a many weak instruments bias. This implies that, even if a set of multiple instruments is valid,  the two-stage least squares estimator can still be biased towards the conventional regression estimate ,12. ThisR2=0.00012). In order to increase the precision of their estimates, the authors included the interaction of length of schooling and year of birth, which resulted in 180 instruments. This increased the partial R2 to 0.00043 and reduced the standard errors on the effect of schooling by over half. However, Bound et al.  = σ2(zi), two-stage least squares is no longer efficient, but the two-step GMM estimator, as described later, is.where β, denoted Hansen described the two-step GMM estimator . The twowhere et al. simultaneously minimizes over β in the moment conditions and the weighting matrix [The CUE proposed by Hansen g matrix . The CUEβ. Imposing conditional homoskedasticity, the CUE objective function simplifies towhere where Theoretical and simulation studies such as Newey and Windmeijer and Burgess and Thompson have demonstrated that LIML and CUE are less biased than two-stage least squares (2SLS) when using many weak instruments –19. Undex, σuv is the covariance of the error terms ui and vi. In the sample, the concentration parameter evaluated at the OLS estimates for π and J is equal to the F-statistic for testing the null hypothesis that π = 0. Thus, the 2SLS bias shown in Equation J, the bias will only fall if it explains a sufficient additional amount of the variance in the exposure . There is, however, a positive correlation between ui and vi because of the presence of the unobserved confounder wi in the models for both the risk factor and the outcome. We used this data generating process to simulate 10,000 datasets with 3000 observations each and report median bias and rejection proportions of Wald tests for the null hypothesis H0: β = 0. To avoid local optima, we estimated the CUE by taking the minimum of We set Using the bias shown in Equations et al., [F-statistic minus one approximately equals the concentration parameter divided by the number of instruments or E(F) ≅ μ2/J + 1. Thus, solely based on the parameters of the data generating process, we know the concentration parameter, the approximate expectation of the F-statistic, and the approximate bias of 2SLS and LIML estimators. We report these theoretical results together with the corresponding results from the simulation study in Table π. The allele score is constructed as the unweighted sum of the instruments, which in this case is the sum of the risk alleles (10).According to Stock et al., , the expTable We illustrate the many weak instrument bias and its different estimators in an empirical application, investigating the relationship between height and lung function. We chose this example, because we know that there is a mechanical relationship between the two variables, with lung volume increasing with height. Therefore, we can use this example to illustrate how height variants can estimate the causal effect of height independent of a confounding factor – gender. Gender confounds the raw association of lung function and height because boys are both taller and have higher lung function. We used data from Avon Longitudinal Study of Parents and Children (ALSPAC), a cohort study of 15,247 pregnancies delivered between 1 April 1991 and 31 December 1992 in the South West of England, which has been described in detail elsewhere ,36. Our Lung function was measured using forced vital capacity derived from a lung spirometry test. This measure has been described in detail elsewhere ,39. We sIndividuals' height was measured in millimeters using the Harpenden stadiometer, when the individuals were aged 15 and a half . We stanWe derived the following covariates: age at measurement (in months); birth weight; number of younger and older siblings; log weekly household income adjusted for inflation, household size, and composition; parents' education; and social class and employment status. Individuals whose fathers were in the military were coded as social class 3. The derivation of these covariates has been described elsewhere .et al. reported 180 independent genetic variants associated with height [et al., our results will not suffer from bias due to selecting variants based on their observed association within our data [et al., as well as in our ALSPAC sample. In addition, Figure et al. The protocols for cleaning the genome-wide data have been described in detail elsewhere [In a genome-wide study of 183,727 people, Lango h height . Becauseour data . We use lsewhere ,44.We used the 180 height variants as 180 individual instruments. Each variant was coded 0, 1, or 2 depending on the combination of height-increasing alleles the individual had. To further explore alternative definitions, we also consider two additional versions of the instrument. First, a simple count of the number of height-increasing allelesGij indicates the jth genetic variant. Second, a weighted allele score, where the weights, j and height, as reported by Lango et al.where To simplify the interpretation of the results, we normalized the unweighted and weighted allele scores to have mean zero and standard deviation one.α = 0.05, 0.01, and 0.001) that occurred to the number that would be expected if all the variables were uncorrelated. Finally, we tested the strength of the association of the instruments and height using linear regression and report the F-statistics for this association. We further report R-squared values as measures of the proportion of the variance in height explained by each definition of the instruments.We tested whether the height, the height variants, and the allele scores were associated with the covariates using robust linear regression. Furthermore, we used linear regression to estimate the associations of 153 pairwise correlations of the 18 nongenetic covariates, and the 3240 pairwise associations of the 180 genetic variants and the 18 nongenetic covariates. We compared the number of significant associations .To illustrate how the many weak instrument bias affects the results in the analysis that includes the individual variants, we sorted the height variants in order of effect size and repeated the analysis adding one variant at a time, starting with the variant with the biggest effect and ending with the weakest variant. We report the estimates and standard errors for each of the regressions using 2SLS and the CUE and also report p < 0.05). Taller individuals were more likely to be from a higher-income household, have more educated parents and grandparents, have been breast-fed, and have an older mother. In contrast, there was little evidence of associations between the allele scores and the covariates   standard deviation increase in lung function Table . After wThe instrumental variable results using an unweighted allele score were close to the LIML and CUE results, but the latter's uncorrected standard errors were 8.3% smaller and 36.2% smaller, respectively. The weighted allele score results were almost identical to the unweighted allele score, but the standard error was reduced by an additional of 7.9%. The standard errors of the weighted allele score estimates are 48% smaller than those from the corrected CUE or the corrected LIML analyses. As shown by the Hausman test, the allele score specifications found strong evidence of differences between the OLS and instrumental variable estimates.x-axis and add more variants, the 2SLS estimates trend upwards, becoming more biased towards the OLS estimate, whilst the CUE remains relatively stable.As we have shown earlier, the 2SLS estimate using all variants as instruments is relatively close to the OLS estimate. This is likely to be because 2SLS is biased towards OLS when using many weak instruments . We illuWhen using many weak instruments in Mendelian randomization studies, researchers should consider the fact that the routinely used 2SLS estimator is biased. So far, two methods have been proposed in the epidemiology and econometric literature to account for this problem. First, constructing a weighted or unweighted allele score and using 2SLS with only one instrument. Second, using the full set of instruments together with an estimation method that is robust to using many weak instruments. In the latter case, only LIML has been discussed in the literature . HoweverThe LIML has recently been shown to be biased with many weak instruments when the errors are conditionally heteroskedastic . The CUEet al., [Using a single allele score as instrument can be a useful and appropriate way to get around the many weak instruments problem. In contrast, the CUE will be useful in situations when there is no clear way to aggregate a set of instruments. For example, consider a researcher who is interested in the relative contributions of body mass index (BMI), fat mass and lean mass to asthma . Whilst et al.,  used theThe CUE may be particularly useful in cases where there are multiple risk factors of interest and many variants, as it may be difficult then to construct different allele scores for each of the risk factors. Indeed, in the example earlier, one could use the CUE to estimate the causal effects of lean and fat mass jointly. Outside the world of Mendelian randomization, recent pharmaco-epidemiological studies have found that including multiple physicians' previous prescriptions as instruments for their prescribing behavior increases the precision of estimates –59. ThesIn this proof of principle study, we showed how to apply these methods using the illustrative example of the effect of height on lung function. We found that the height variants and allele scores were associated with height and that the genetic variants were no more associated with the observed covariates than would be expected by chance. Our results suggest that, compared with the causal effects identified by the genetic variants, the observational association may suffer from a slight upward bias. We demonstrated that the 2SLS estimates suffered from many weak instruments bias when we used all the individual variants. In contrast, the results using LIML, CUE, and the weighted or unweighted allele scores instrumental variable estimators were mutually in concordance, and all suggested a weaker underlying causal relationship between height and lung function. As with the simulated results, in the empirical example, the corrected standard errors for LIML were almost identical to the corrected CUE standard errors but considerably larger than those for the weighted allele score instrumental variable estimates. This is likely to reflect the relative efficiency of these approaches in many applied examples. Nevertheless, by holding the number of instruments constant, as the sample size increases, the difference in efficiency between these approaches will reduce.In conclusion, when using many weak instruments, 2SLS estimates can be biased. We demonstrated that, under homoskedasticity, the allele score instrumental variable estimators, CUE, and LIML with corrected standard errors provide accurate inferences. If homoskedasticity holds, the LIML is likely to be slightly more efficient than the CUE. In small samples, both estimators are likely to be less efficient than the allele score. However, if there is conditional heteroskedasticity, LIML can be inconsistent when using many weak instruments and researchers should use the CUE instead. However, both methods are likely to be less efficient than using allele scores when there are many instruments and modest sample sizes. Using multiple variants as instruments can increase precision of the results over using single variants, but researchers must report corrected standard errors.


NFXL1 gene that confers a nonsynonymous change (N150K) and is significantly associated with language impairment in the Robinson Crusoe population . Subsequent sequencing of NFXL1 in 117 UK SLI cases identified four individuals with heterozygous variants predicted to be of functional consequence. We conclude that coding variants within NFXL1 confer an increased risk of SLI within a complex genetic model.Children affected by Specific Language Impairment (SLI) fail to acquire age appropriate language skills despite adequate intelligence and opportunity. SLI is highly heritable, but the understanding of underlying genetic mechanisms has proved challenging. In this study, we use molecular genetic techniques to investigate an admixed isolated founder population from the Robinson Crusoe Island (Chile), who are affected by a high incidence of SLI, increasing the power to discover contributory genetic factors. We utilize exome sequencing in selected individuals from this population to identify eight coding variants that are of putative significance. We then apply association analyses across the wider population to highlight a single rare coding variant  in the  NFXL1 gene and the protein it encodes might be important in risk of SLI.Children affected by Specific Language Impairment (SLI) have unexpected problems learning to talk and understand language, despite developing normally in all other areas. This disorder runs in families but we do not understand how the genetic contributions work, or which genetic mechanisms might be important. In this paper, we study a Chilean population who are affected by a high incidence of SLI. Such populations may provide increased power to discover contributory genetic factors, under appropriate conditions. We identify a genetic change in the population that causes a change to a protein called NFXL1. This change is usually very rare but is found at a higher frequency than expected in our population, particularly in those people affected by SLI. We then looked at this gene in over 100 individuals from the UK affected by SLI and found four more changes that probably affect the protein. This is a higher number than we would expect by chance. We therefore propose that the  Language deficits form a central feature of many developmental disorders and account for a high number of pediatric referrals and statements of special educational need . These lATP2C2 (OMIM#613082), CMIP (OMIM#610112) [ABCC13 (OMIM#608835) [FLNC (OMIM#102565), RBFOX2 (OMIM#612149) [ROBO2 (OMIM#602431) [NDST4 (OMIM#615039), ZNF385D, COL4A2 (OMIM#120090)  and NOP9 . Other studies implicate rare genetic events which may have higher penetrance [SLI affects between 5 and 7% of children in the UK  and signOMIM#61302, CMIP , a forkhead/winged-helix transcription factor [FOXP2, caused by mutation or chromosomal rearrangements, leads to characteristic deficits in coordinating sequences of orofacial movements, impairing speech, producing a disorder known as developmental verbal dyspraxia (DVD) or childhood apraxia of speech (CAS) [FOXP2 mutation cases are accompanied by wide-ranging problems with spoken and written language [FOXP2 disruptions are rare and account for only a small proportion of DVD/CAS cases, the investigation of this gene, its expression patterns and interactions, have led to the elucidation of genetic networks that are important to language development and contribute to more common forms of language impairment [CNTNAP2 (OMIM#604569), a member of the neurexin family which mediates interactions between neurons and glia during nervous system development [CNTNAP2 has been associated both with language deficits [Clearer links have been made between the presence of language deficits and disruption of the OMIM#6053, a forkhn factor . Reducedch (CAS) –22. Typilanguage . Whilst pairment –25. One elopment . Geneticdeficits ,27–29 andeficits –32. Varideficits , indicatFOXP2 and CNTNAP2 [In 2008, Villanueva et al described a population who are affected by an unusually high prevalence of language impairment . This ad CNTNAP2 . HoweverIn this study, we make use of this admixed isolated population and assess the possibility of a founder mutation, by completing exome sequencing of five individuals from the Robinson Crusoe population affected by SLI. We substantiate the findings of the exome screen by performing association analyses of selected putative functional variants in the wider Robinson Crusoe population. The contribution of identified risk variants is subsequently validated by performing targeted sequencing of candidate genes in a UK-based cohort of individuals affected by SLI.We selected five related individuals with SLI from the Robinson Crusoe cohort for exome sequencing . From th−4, chromosomes 2, 6, 7, 8, 9, 12, 13 and 17, as listed in On average, 47,276  genic variants were identified in each of the five exomes. This included an average of 17,405  exonic variants, 8,379  missense variants and 106  nonsense (including indels) variants per individual. Across all five samples, 90.0% of targeted exome sequencing had coverage of at least 10-fold. The average coverage of targeted sequence was 56.5-fold and 21% of the reads reached this level. Sequencing metrics can be found in −4) . This validation cohort was ascertained via 35 children living on the Robinson Crusoe Island who had been diagnosed with SLI or who showed typical language development (as described in methods) and included the five children used in the exome sequencing. All children were descendants of the founder families of the Robinson Crusoe Island and, as such, the cases and controls used in these association analyses were inter-related . We ther−4) . Across −4) .Homo sapiens nuclear transcription factor, X-box binding-like 1 (NFXL1) gene  falls in exon 4 of the L1) gene . The varL1) gene .The variant at chr4:47,907,320 was not observed in 127 independent European population controls that were genotyped . We therNFXL1 region of chromosome 4  within seven extended pedigrees from the Robinson Crusoe validation cohort  cohort [NFXL1 in SLI etiology. In total, we identified 166 high-quality sequence variants across the NFXL1 gene. 155 of the variants detected were intronic, 4 were in the 3’UTR and 7 affected the coding region. Of the coding variants, three were nonsynonymous and four were synonymous substitutions (We sequenced the entire coding region of the ) cohort –39), to itutions .Nonsynonymous variants and those with estimated allele frequencies of <5% were verified across all the pools of DNA in which they were observed using Sanger sequencing. This allowed the derivation of accurate allele frequencies within the SLIC cohort.P-value of 0.0244. Intriguingly, although it is synonymous, this variant was predicted to be “disease-causing” by MutationTaster with a confidence probability of 0.98 (SIFT = 1.0). This variant falls in the most 5’ coding exon of NFXL1 and is part of a CpG island, indicating that it may be important for the regulation of gene expression. Furthermore, ENCODE data shows that it is part of a H3K4Me3 mark (which is often associated with promoters) and binds multiple transcription factors, particularly POLR2A c-MYC and PHF8 .One of the synonymous variants  was found in a heterozygous state in one SLIC proband  but had not been documented in any European individuals in the 1000 genomes project  or the NThe remaining three synonymous variants  found in SLIC probands were also found at similar frequencies in control databases. All had allele frequencies of >5% and are therefore thought to represent common polymorphisms .P-value of 0.024 (1 of 234 SLIC chromosomes tested vs 0 of 9358 control chromosomes tested). Further investigations found that this variant had been observed in a heterozygous state in a single African American individual from the EVS. Principal components analysis of genome-wide SNP data in the SLIC proband against the hapmap-3 populations did not detect any African ancestry. The rarity of the rs151113647 variant and its position within a zinc-finger motif  was found in a heterozygous state in a single SLIC proband  and again, was not observed in 4679 independent European individuals in the control public databases , yieldiner motif  indicateer motif .A second nonsynonymous substitution  was observed in a heterozygous state in two independent SLIC probands . This variant was also found in 44 of 4679 independent European control individuals from public databases  was observed to occur across all the sequence pools with an estimated allele frequency of 32% . This coThe three rare variants identified  were sequenced in all available family members of the SLIC proband in whom they were observed . The chrNFXL1 gene that is shared by three of the five individuals sequenced. Association analyses within a larger Robinson Crusoe validation cohort, demonstrated that this variant occurred at a significantly increased frequency in Islanders with language impairment than those with typical language development (P = 0.0002) and is predicted to be “disease-causing”. Subsequent sequencing of NFXL1 in a cohort consisting of 117 independent UK probands (SLIC) with SLI identified four individuals with putative high-risk variants in the heterozygous state; three SLIC individuals carried rare nonsynonymous changes and one SLIC individual carried a novel variant that falls within a regulatory motif. Given the above evidence, we postulate that variants within NFXL1 may contribute to genetic risk of language impairment. We propose that such changes are likely to function as—risk variants with a complex model of inheritance.In this paper, we report results from the whole exome sequencing of five individuals from an isolated Chilean island population affected by a high incidence of SLI. We identify a heterozygous nonsynonymous coding variant in the We used the Robinson Crusoe ancestry to trace back the relationships between individuals carrying the associated rs144169475 variant. The only common ancestors to the carriers were two founder brothers who had previously been reported to head the SLI lineage on the Island . These bNFXL1 may extend to the etiology of SLI in other populations. In a screen of the NFXL1 coding regions in 117 independent UK probands affected by SLI, we observed four individuals who carried rare coding changes generating a combined high risk allele frequency of 1.71%. By contrast, the combined allele frequency of these three variants in 4679 independent European controls (from the 1000 genomes and EVS public databases) is 0.47%, a difference that yields a marginally significant P-value of 0.029 (4 of 234 SLIC chromosomes vs 44 of 9358 control chromosomes). Extending our investigations to include all private coding mutations  across the entire NFXL1 transcript, as opposed to the consideration of the three specific mutations considered above, we again observed a marginally increased frequency in the SLIC cohort  above that expected given the data reported in public European databases . Broadening our investigation to include all rare coding changes (<1%) across the entire NFXL1 transcript, revealed a similar trend (1.71% (4 of 234 chromosomes sequenced) in the SLIC cohort, compared to 1.36% (127 of 9358 chromosome sequenced) in public European databases) but this did not reach significance (P = 0.3821).Our data further suggest that the effects of rare mutations in NFXL1 may represent genetic risk factors with incomplete penetrance. Given our data, it is likely that these putative risk factors are modulated by other genetic variations and/or environmental factors [NFXL1 variants and the presence of SLI in either the Robinson Crusoe validation population or the UK SLIC cohort. Thirty nine percent of the Robinson Crusoe validation cohort affected by language impairment carried the rs144169475 variant, as did ten percent of the Robinson Crusoe validation cohort with typical language ability. Similarly, one of the variants observed in the SLIC probands was inherited by a child with typical language development and two children affected by language impairment did not inherit the observed variant. In addition, we observed a high phenocopy rate in the Robinson Crusoe cohort; only 39% of individuals affected by language impairment carried the rs144169475 variant. Incomplete segregation is commonly described in neurodevelopmental disorders such as autism [Given our consistent findings across cohorts, and in line with the data arising from other neurodevelopmental disorders, we suggest that rare variants in  factors –43. We cs autism ,43 and is autism  and reprs autism .NFXL1 gene encodes a NFX-1-type nuclear zinc-finger transcriptional repressor that is expressed at the cytoplasm [www.brainmap.org). NFXL1 is so-called because it is a paralogue of the NF-X1 transcription factor which binds the X-box sequence of class II MHC genes [NF-X1 isoform functions in the regulation of the NFĸB pathway [CMIP, a gene implicated in the etiology of SLI in UK populations [The ytoplasm . Little ytoplasm . This trytoplasm  and showHC genes . This feHC genes . Similar pathway , as doesulations ,53.NFXL1 coding variants in SLI susceptibility.A natural limitation of all studies of founder or isolated populations is the restricted size of the cohort. Although our study represents a comprehensive profiling of the Robinson Crusoe child population, the total sample consisted of only 111 individuals, 100 of whom were founder-related and 49 of whom had language impairment. Although it should be noted that the power of this particular sample lies in the close relationships between individuals rather than the absolute number of samples, the issue of sample sizes is especially pertinent when one is considering rare variations. Thus it is of particular importance that we observed independent evidence implicating NFXL1 rare variants in another cohort. However, in the absence of a large South American cohort of language-impaired individuals, we were unable to include the rs144169475 variant in our replication investigations (since this SNP is particular to South American populations). Thus, further studies of larger sample sizes that include language-selected controls and South American individuals will be required to fully evaluate the role of rs144169475 and rare NFXL1 region of chromosome 4  in combination with evidence of a high phenocopy rate in our cohort . In combination, these factors break down the correspondence between genotype and phenotype, compromising the ability to detect linkage [Of note, none of the shared variants identified through exome sequencing co-incided with regions of suggestive linkage reported in a previous genomewide linkage study of the Robinson Crusoe population  Tables . Nor didmosome 4 . We must linkage .NFXL1 gene at a highly conserved residue. Subsequent sequencing of the NFXL1 coding regions in 117 independent UK SLI cases identified four individuals with rare heterozygous variants predicted to be of functional consequence. We conclude that coding variants within NFXL1 confer an increased risk of SLI within a complex genetic model.In summary, the Robinson Crusoe admixed founder population represents a rare resource which may assist in the identification of genetic variants that contribute to SLI susceptibility. Exome sequencing of five individuals from this population identified eight shared coding variants. One of these variants (rs144169475) was found to be significantly associated (P = 0.0002) with language impairment in the wider Robinson Crusoe population. rs144169475 confers a nonsynonymous change (N150K) in the The work on the Robinson Crusoe Island was approved by the ethics department of the University of Chile. Ethical permission for each SLIC collection was granted by local ethics committees. Guys Hospital Research Ethics Committee approved the collection of families from the Newcomen Centre to identify families from the South East of England with specific language disorder. Ref No. 96/7/11. Cambridge Local Research Ethics Committee approved the CLASP project “Genome Search for susceptibility loci to language disorders” Ref No. LREC96/212. Ethical approval for the Manchester Language Study was given by the University of Manchester Committee on the Ethics of Research on Human Beings. Ref No. 03061 The Lothian Research Ethics Committee approved the project “Genetics of specific language impairment in children in Scotland” for the use of the Edinburgh samples. Ref. No. LREC/1999/6/20. The ethics department of the University of Chile approved the project “Genetic analysis of language-impaired individuals from the Robinson Crusoe Island”. Project Number 001-2010. Informed consent was given by all participants and/or, where applicable, their parents.The Robinson Crusoe cohort was ascertained on the basis of phenotypic data from 61 children, between the ages of 3 years and 8 years, 11 months  all of whom were descendants of the founder families and represents an extended cohort (including children who have turned 3 years of age since 2008) of that described in . First-dth percentile on either the receptive or expressive scales of the TEGE, (ii) nonverbal IQ not below the 10th percentile, (iii) normal hearing, oral motor skills and neurological development.“Specific Language Impairment)”  defined as (i) performance >2SD below expected on TEPROSIF (for children aged 6 years or less) or performance >2 years below expected for chronological age on TEPROSIF (for children aged over 6 years) and/or performance below the 10th percentile on both the receptive and expressive scales of the TEGE.“Typical language development”  defined as (i) performance not >2SD below expected on TEPROSIF or performance >2 years below expected for chronological age on TEPROSIF (for children aged over 6 years) and performance above the 10th percentile on either the receptive or expressive scales of the TEGE, and (ii) nonverbal IQ >1SD below age-expected, and/or (iii) evidence of hearing loss or oral motor disability (e.g cleft lip) or abnormal neurological development.“Nonspecific language impairment”  defined as (i) performance >2SD below expected on TEPROSIF or performance >2 years below expected for chronological age on TEPROSIF (for children aged over 6 years) and/or performance below the 10The language ability of 61 children, all of whom were related to a founder individual, was assessed by tests of expressive and receptive language  and phoThe observed language deficits in the individuals diagnosed with SLI were typical of those described in other SLI cohorts and involved varied deficits across grammatical, morphosyntactical and receptive aspects of language, but not dialectic variations in intonation, vocabulary or phonology.th percentile on either the Barcelona test or the token test or they self-reported a need for writing or reading support at school or a history of language support in the family history questionnaire.“Language-impaired”  if they scored below the 10th percentile on both the Barcelona test and the token test and they indicated no requirement for writing, reading or language support in the family history questionnaire.“Typical language ability”  if they scored above the 10Since we were particularly interested in genetic contributions to SLI, our family cohort consisted of the first-degree relatives of the 39 founder-related children presenting with SLI or typical language development. All available first-degree family members  were assessed for language difficulties using tests of verbal fluency (Barcelona test ) and verFive Islanders  from the child cohort who had been diagnosed with SLI were selected for exome sequencing. The selection of individuals for sequencing was based upon the amount and quality of DNA available, the severity of observed language impairment and their known relationships with other affected individuals. The five children were selected to cover the different branches of the founder pedigree and were descendants of the founder families .Exome capture was performed using 10μg of genomic DNA with a first generation (v1) Agilent SureSelect human exome kit , which provide an average target coverage of 80% of the exome at 56-fold across all samples. Sequencing of the generated fragments was performed on the SOLiD 4 sequencer . Color space reads were mapped to the human reference genome (hg18) in the SOLiD bioscope software (v1.2), which applies an iterative mapping approach. Variants were called using a diBayes algorithm  using hiTo test the hypothesis that the founder brothers carried a rare causative genetic mutation, for our downstream analyses, we focused upon novel variants that were potentially deleterious. Each exome file was individually filtered to exclude nongenic, intronic  and synonymous variants. The remaining nonsynonymous and splice-site mutations were further filtered to exclude known sites of variation , publically available genome sequences and an in-house sequencing database). The remaining variants were then compared across exome samples to allow the selection of variants that occurred in 3 or more of the 5 children sequenced. A flow diagram of the methodology can be found in All novel nonsynonymous or canonical splice-site variants found to occur in 3 or more of the 5 exome samples were also genotyped in the wider child and family cohorts from the Robinson Crusoe population. We were able to obtain DNA samples for 35 founder-related children  and their family members (from the family cohort described above). Forty nine of these individuals , 7 siblings and 4 half-siblings) were language impaired and 62 , 9 siblings and 2 half-siblings) had language ability in the normal range. These families included the five children used in the exome sequencing. DNA was extracted from EDTA whole blood samples using a standard chloroform extraction protocol. All novel nonsynonymous or canonical splice-site variants identified from the exome screen were sequenced using a standard Sanger protocol in these 111 individuals.The resultant genotype data were used to perform a family-based test of association within the MQLS-XM package ,67. ThisA full pedigree structure was generated that accounted for all known relationships between 111 individuals from the child and family cohorts and the two identified, shared, founder brothers. This pedigree included 288 individuals , 203 non-founders) over 5 generations. As described above, 111 individuals (including 11 non-founder-related parents) had full genotype and phenotype data, 11 individuals were also included who had phenotype data but no genotype data and the remaining 166 individuals had no phenotype or genotype data but defined relationships between the 111 genotyped individuals and the founder brothers. In the MQLS-XM analyses, the expected prevalence of SLI was set at 0.25 for males and 0.27 for females. These figures were derived from the child cohort described above.Any variant that was significantly associated with language impairment in the population cohort was genotyped in 127 independent European population controls ,441 independent South American controls; 320 individuals of Colombian descent and 121 individuals of Chilean origin. The Colombian controls were collected as part of a genetic demography study in the Colombian population, where all participants had to have four grandparents of local origin . The Chilean controls were ascertained from the Santiago area and consisted of DNA from 30 male Chilean students (provided by P Villanueva) and from 91 female adult controls from a breast cancer study . Genome-wide SNP data indicated that these samples were of Amerindian and European ancestry. Note that both the European and South American control populations were unselected and, as such, were not screened for language ability.−4) between SLI and chromosomes 2, 6, 7, 8, 9, 12, 13 and 17. In the current study, we had access to a new set of denser genotypes from the Robinson Crusoe population, generated with the Affymetrix Axiom GW-LAT 1 array , supplemented with a custom array designed to cover South American-specific variants which together included 1,141,741 SNPs.Genome-wide linkage data for the Robinson Crusoe validation cohort have previously been reported . These pNFXL1 gene . SNP data were filtered within PLINK [2>0.5) resulting in a linkage dataset of 54 independent SNPs that were appended with rs144169475 genotype data and analysed for linkage in MERLIN [929 SNPs across chromosome region chr4:46,000,000–49,000,000 (hg19) were selected to cover the chromosome region surrounding the in PLINK  to removn MERLIN . LinkageSince linkage packages were unable to analyse genome-wide data for the 321-bit Robinson Crusoe validation pedigree as a whole, it was broken into sub-pedigrees manually selected on the basis of closest shared ancestor. We employed linkage sub-pedigrees and linkage methods analogous to those described in the previous linage study ; Seven ePutative functional effects of associated variants were evaluated using MutationTaster . MutatioFor each of the variants highlighted, we also present the SIFT and polyphen-2 scores. In contrast to MutationTaster, the SIFT and PolyPhen algorithms primarily consider protein sequences, motifs and structures to assign pathogenicity and therefore can only be applied to coding changes. SIFT performs a multiple alignment of closely related protein sequences to identify conserved motifs and assign a probability that a given amino acid substitution is pathogenic . PolyPheNFXL1 gene were subsequently sequenced in 117 unrelated British children affected by SLI. These children formed part of the SLI Consortium (SLIC) collection, which has previously been described in detail [In order to further investigate the role of NFXL1 variants in SLI, the coding regions of the n detail ,39. In sn detail , the Chin detail  and the n detail ). All prn detail ) more thn detail ) in the www.illumina.com). Sequences were aligned against human reference sequence (37d5) using STAMPY [The concentration of genomic DNA samples from 117 independent SLIC probands was quantified by picogreen and each sample normalized to 10ng/μl. Individual DNAs were pooled prior to PCR amplification. Following PCR, the amplicons were fragmented, end-repaired and adapter-ligated. The prepared and tagged libraries were then multiplexed before paired-end sequencing in a single lane of flow-cell on an Illumina HiSeq 2000  which includes data from 4300 independent individuals of European American ancestry. The 1000 genomes samples are unselected controls while the EVS samples are selected to include controls, extremes of specific traits (LDL and blood pressure) and specific diseases . Allele frequencies were compared between SLIC probands and controls using a two-tailed Fisher’s exact test with 1 degree of freedom. Calculations were performed in the graphpad online calculator (http://www.graphpad.com/). Where given variants were observed in alternative populations, these data are reported but were not included in the statistical analyses since population admixture and stratification can lead to false positives, especially when investigating rare variants [The allele frequencies of coding variants discovered in SLIC probands were compared to those observed in 4679 individuals of European ancestry across publically available control databases; the 1000 genomes project (the European (EUR) super-population from integrated phase 1, accessed March 2014)  which invariants .S1 FigBlue boxes show each filter step and red boxes describe exclusion criteria involved in each step(PDF)Click here for additional data file.S2 FigSeven pedigrees of no more than 24-bits were used for linkage analyses. Individuals with language impairment are colored in black. Individuals with typical language are denoted in white. Individuals with unknown phenotype are shaded grey.(PDF)Click here for additional data file.S3 Fig2>0.5. Position of NFXL1 gene is shown by red box. Plots were generated in haploview  using linkage pedigrees  across chr4:46–49Mb (hg19). b—Linkage disequilibrium between all analyzed markers (n = 55) across chr4:46–49Mb (hg19), after pruning for r(PDF)Click here for additional data file.S4 FigNFXL1 gene is indicated by the red box on the X axis.No linkage was observed to the NFXL1 region of chromosome 4 under parametric and non-parametric models using a dense SNP array. The approximate position of the (PDF)Click here for additional data file.S1 Table(PDF)Click here for additional data file.S2 Table(PDF)Click here for additional data file.S3 Table(PDF)Click here for additional data file.S4 TableNFXL1 variant has an expected population frequency of between 0.033 (1000 genomes CLM) and 0.09 (1000 genomes PUR) and is predicted to be present in both founder brothers (frequency in founder brothers of 0.5). Given the population structure, it would therefore be expected to be present in the current population at a frequency of between 0.08 (MAF = 0.03) and 0.14 (MAF = 0.10). Although the frequency of the NFXL1 variant in the founder-related individuals of the Robinson Crusoe validation cohort was at this expected level (0.125), the variant allele was found to cosegregate with language impairment; the frequency of the NFXL1 variant in the founder-related individuals with SLI was above expected (0.194) while that of founder-related individuals with typical language was below expected (0.048), supporting a pathogenic role for this allele.The (PDF)Click here for additional data file.S1 Text(PDF)Click here for additional data file.