Sequencing family DNA samples provides an attractive alternative to population based designs to identify rare variants associated with human disease due to the enrichment of causal variants in pedigrees. Previous studies showed that genotype calling accuracy can be improved by modeling family relatedness compared to standard calling algorithms. Current family-based variant calling methods use sequencing data on single variants and ignore the identity-by-descent (IBD) sharing along the genome. In this study we describe a new computational framework to accurately estimate the IBD sharing from the sequencing data, and to utilize the inferred IBD among family members to jointly call genotypes in pedigrees. Through simulations and application to real data, we showed that IBD can be reliably estimated across the genome, even at very low coverage (e.g. 2X), and genotype accuracy can be dramatically improved. Moreover, the improvement is more pronounced for variants with low frequencies, especially at low to intermediate coverage (e.g. 10X to 20X), making our approach effective in studying rare variants in cost-effective whole genome sequencing in pedigrees. We hope that our tool is useful to the research community for identifying rare variants for human disease through family-based sequencing. To identify disease variants that occur less frequently in population, sequencing families in which multiple individuals are affected is more powerful due to the enrichment of causal variants. An important step in such studies is to infer individual genotypes from sequencing data. Existing methods do not utilize full familial transmission information and therefore result in reduced accuracy of inferred genotypes. In this study we describe a new method that infers shared genetic materials among family members and then incorporate the shared genomic information in a novel algorithm that can accurately infer genotypes. Our method is particularly advantageous when inferring low frequency variants with fewer sequence data, making it effective in analyzing genome-wide sequence data. We implemented the algorithm in a computationally efficient tool to facilitate cost-effective sequencing in families for identifying disease genetic variants. DNA sequencing is being routinely carried out to identify genetic factors, rare variants in particular, associated with human disease. It has been successful in identifying causal variants for Mendelian disease ,2, and ca priori. Polymutt and FamSeq assume such a priori probabilities for all genomics regions and thus inefficiently model the data when the actual IBD can be inferred. As a concrete example, assuming we know that at a particular position the two siblings share 2 alleles IBD, then their genotypes are identical at this locus and can be inferred with improved accuracy by merging their sequencing data, essentially doubling the sequencing depth. In general, knowledge of IBD sharing helps confine genotypes to be compatible to the IBD patterns in pedigrees and a variant calling framework that models IBD is expected to deliver improved performance over existing methods. Such a framework makes it feasible to design studies with reduced coverage, since data from shared haplotypes in a pedigree are efficiently combined to make reliable genotype calls. This will be particularly beneficial for whole genome sequencing, which is still prohibitively expensive for large-scale sequencing studies. Linkage-disequilibrium (LD)-based methods such as Beagle4 [2) among rare variants as well as between rare and common variants, however, LD-based methods are expected to have reduced accuracy for rare than for common variants.A critical step in genetic analysis of family sequence data is to infer genotypes of individuals in pedigrees. For next-generation sequencing data, this is challenging due to base call error, alignment artifacts, possible allele dropout during library preparation and sequencing, especially at low coverage, among others. Although variant calling algorithms developed for unrelated individuals can be applied to family sequencing data, the accuracy is compromised due to the ignorance of family relatedness. Family-aware calling algorithms, e.g. Polymutt  and FamS Beagle4 , Thunder Beagle4  and SHAP Beagle4  have beeIn this study, we develop and implement a variant calling framework that infers the IBD sharing   file, whf founders and n non-founders, with sequencing data on M variants across a chromosome. Without loss of generality, we also arrange the pedigree such that the first f members in the pedigree are founders. Define a binary inheritance vector [j as Ij=  for the n non-founders in this pedigree. Each of the entries describes the transmission of the paternal (pi) or the maternal (mi) allele, with 0 (or 1) indicating the grand-paternal  allele being transmitted. Therefore an inheritance vector completely determines which of the 2f founder alleles were inherited by each nonfounder. There are N = 2n possibility inheritance vectors and let vk, k = 1,..,N, denote individual vectors. Let R denote data of all members in a family across all M variants, Rj be all reads at variant j, and Rij be the reads in family member i at variant j. Similarly, let Gj denote the vector of genotypes at variant j and its ith entry Gij =  be the ordered genotype of the ith member in the pedigree, where A1 and A2 represent the paternally and maternally transmitted alleles respectively. Assuming that recombination events are independent between all chromosome intervals, i.e. no crossover interference, the likelihood can be framed as a Hidden Markov Model [M variants in the pedigree can be calculated asP(I1), is assumed uniform across all N = 2n inheritance vectors. The transition between adjacent inheritance vectors, P(Ij|Ij-1), is calculated according to the recombination rate between the jth and j-1th variant, which can be calculated using the HapMap Phase II [P(Rj|Ij), which is the probability of reads in all family members at locus j given the inheritance vector Ij, can be calculated asP(Rj|Gj) can be factorized into the product of individual genotype likelihoods. Since an inheritance vector specifies precisely how the alleles were transmitted from founders to non-founders, the genotypes of the entire pedigree are determined by the ordered founder genotypes when the inheritance vector is known. Therefore the emission probability involves the summation of only the ordered founder genotypes, whose prior probabilities P(Gij) can be either obtained from the external sources, e.g. the 1000 Genome Project [Suppose we have a pedigree with e vector  at variaov Model , similarov Model . SpecifiPhase II  genetic  Project , or esti Project , assuminM variants; that is, we aim to calculate P(Ij|R). This can be achieved efficiently using the forward-backward procedure in HMM [αj(k) denote the forward variable at variant j for vk and βj(k) be the corresponding backward variable [vk at variant j isj, denoted as Ijmarg, can be used to represent the inferred inheritance vector for each variant; the IBD sharing can be directly derived from Ijmarg for any pair of family members. However, since Ijmarg only maximizes the likelihood marginally at variant j, we infer a global optimal path of inheritance vectors along the genome through the Viterbi algorithm [Ijbest to denote the optimal inheritance vector at variant j.Since the inheritance vectors usually cannot be determined unambiguously, the goal here is to infer the posterior distribution of the inheritance vectors at each variant using the sequencing data from all e in HMM . Let αjvariable . Then thlgorithm ; we use http://www.genome.ucsc.edu) and the 1000 Genomes Project. The final set of selected variants is used to contrast a sparse genetic map with high-quality variants for the inference of inheritance vectors, and the genetic distances of these variants are linearly extrapolated based on the HapMap Phase II genetic map [The Lander-Green algorithm requires that variants are independent, i.e. not in linkage disequilibrium (LD). For sequencing data variants are usually correlated. Since only a limited number of recombination events are expected in a pedigree, it is neither feasible nor necessary to use all data. We built a companion tool to automatically select a subset of independent variants by LD pruning, a similar approach used in Plink and others ,27. In aetic map . The oveP and P, representing the likelihood of polymorphism and monomorphism respectively given the data at the jth site and scaffold variants. We assume that for poly the two alleles are Aref and Aalt and for mono only Aref is present in the data. The posterior probability of polymorphism given the data is calculated asWe evaluate for each variant the evidence supporting the alternative allele in the data by calculating the posterior probability of being polymorphic. Specifically for each variant we calculate two probabilities, P is calculated based on P is simply the product of genotype likelihoods of homozygous reference allele across all family members at variant j. The prior probability of polymorphism, P(poly), is calculated as in Polymutt [P(mono) = 1-P(poly). Briefly, in a sample with N founders in the absence of natural selection, according to coalescent theory the prior probability that a site includes non-reference alleles is j is one of the scaffold variants, P = P(Ij | R), which was obtained in (2). Then the Phred-scaled variant quality is calculated as VQ = -10*log10). By construction, only a sparse subset of variants is included in the map file, and the vast majority of variants are located in the intervals of scaffold variants. In an interval within which a crossover occurred, the inheritance vectors on the two sides of the recombination point are different. Assigning wrong inheritance vectors to variants will not only produce wrong IBD sharing among family members but also greatly reduce variant calling accuracy. However it is unknown a priori in which intervals crossovers occurred and where exactly the breakpoint is if a crossover occurred. To address this issue, Polymutt2 calculates for each variant in scaffold intervals the posterior probabilities using the inheritance vectors on the left and right boundary separately, and takes the maximum value, Pmax, as the posterior probability of polymorphism. The Phred-scaled variant quality is calculated as VQ = -10*log10). The inheritance vectors are accordingly assigned to each of the variants in scaffold intervals. This assumes that there is at most one crossover event in any interval, which is reasonable given the limited number of expected recombination events per generation. As a result, the crossovers can be precisely located in intervals in which crossovers occurred.The term Polymutt  and P can be calculated using Gij = g. For variants in intervals of scaffold variants, P was obtained in calculating the variant quality as described in the previous section. The genotype with the maximum posterior probability Pmax is assigned to the individual, and the corresponding genotype quality is calculated as GQ = -10log10).After quantifying the variant quality as described above, the most likely inheritance vectors are assigned to each of the variants. The posterior probability of the genotypes for individual Ijbest or Ijmarg, can used to minimize the computation. Given the high accuracy of the inheritance vector inference . At the extreme, a single best inheritance vector, ence see , the incIjbest as the optimal inheritance vector for variant j inferred using the Viterbi algorithm as we described before. The posterior probability of each configuration of ordered genotypes at variant j given the sequencing data and Ijbest is calculated asP(Rij|Gij) is the genotype likelihood calculated before, and the term Ijbest. This is repeated for all positions and the haplotypes are automatically constructed by stitching the paternal and maternal alleles at each position along a chromosome. By construction, Mendelian error in haplotype calling is completely eliminated due to the Mendelian transmission dictated by the inheritance vector.When parental data available, we generate haplotypes along a chromosome by reconstructing the optimal ordered genotypes jointly for all family members at each position assuming that the inheritance vector is known. We use Note that the construction of haplotypes is based on the transmission of alleles from parents to offspring. When parental data are not available, such as in sibships, it is not possible to deduce the parental origin of the alleles and therefore haplotypes cannot be reconstructed.http://picard.sourceforge.net). The list of known Indels from the 1000 Genomes Project was provided to GATK for Indel re-alignment. We used GATK UnifiedGenotyper to infer variants and genotypes from sequencing. We then applied Polymutt, Polymutt2 and Beagle4 on the GATK-generated VCF files to refine the genotypes utilizing the GL values calculated by GATK and stored in the VCF file.We utilized the 1000 Genome Project  data to Pedigrees we investigated in this study include sibships of size 2 (Sib2), 4 (Sib4) and 6 (Sib6), nuclear families with 4 (Nuc4) and 6 (Nuc6) members, and an extended pedigree with 10 individuals, which is the same as the pedigree investigated in Polymutt . For eacWe used two metrics to measure the accuracy of genotype calling. The first is the false negative rate (FNR), defined as the percentage of true genotypes that are called into incorrect genotypes; this measures the sensitivity of the calling and is equal to 1-sensitivity. The second metric is the false discovery rate (FDR), defined as the percentage of called genotypes that are different from the true genotypes; this measures the specificity of the calling; this measures the specificity of the calling and corresponds to 1-precision. A good algorithm is expected to have low values of both FNR and FDR. We used GQ to filter low quality genotype calls and specifically we used GQ = 3 for Polymutt2 and Polymutt, GQ = 5 for Beagle4 and GQ = 10 for GATK; due to different calculations of GQ in these algorithms we found that these filtering criteria have reasonable FNR and FDR values. These criteria were used for all simulated data. Note that when no filtering is used FNR and FDR are the same for overall genotypes, and the difference is due to differential filtering based on GQ cutoffs. For heterozygotes, which are of particular interest in studying rare variants, however, both FNR and FDR are critical metrics to evaluate, as FNR can be made artificially low by aggressive calling of heterozygotes, which will results in high FDR, and conversely conservative calling of heterozygotes can lead to low FDR and high FNR.We derived the IBD sharing at each position between a pair of family members in a pedigree based on the inferred inheritance vector obtained via the Viterbi algorithm. We next investigated the accuracy of the heterozygous genotypes, which are of particular interest for rare variants. The major interest of sequencing studies, especially in family designs, is to identify rare variants associated with disease. Accurate heterozygote calling is of particular importance due to the challenges associated with rare variant inference from sequencing. We specifically investigated the heterozygote accuracy across different bins of alternative allele frequencies, in the range of  is similar to the unphased genotypes, although on average the error rates are slightly higher for phased genotypes. For example, for Nuc4 pedigrees at 15X, the FNR of overall genotypes is 0.30% for phased genotypes and is 0.28% for unphased genotypes; the corresponding FDR is 0.09% and 0.10% respectively. For heterozygotes, the FNR is 0.53% and 0.51% for phased and unphased genotypes respectively, with corresponding FDR values being 0.10% and 0.08%.–6 for all scenarios shown above, consistent with the previous report [We calculated the Mendelian inconsistency (MI) rate as the percentage of parent-offspring trios in which the genotypes violate the Mendelian transmission law. Pedigrees were divided into individual trios for the calculation. We used the minimum GQ of the genotypes in a trio as the filtering criteria to calculate MI rates on relatively high quality genotype calls. When either GQ 5 or 10 was used, both GATK and Beagle4 calls showed considerable Mendelian inconsistencies across various sequencing coverage . For exas report . Strikinhttp://www.illumina.com/platinumgenomes/). We selected a Nuc6 sub-pedigree for the analysis, which consists of four siblings  and their parents (NA12877 and NA12878). The sequencing coverage of these samples is ~50X. We followed the best-practice procedure for variant calling as we did for simulated data. Since there is only a single family with a few individuals, we used the 1000 Genomes Project reference panel when running Beagle4 (downloaded from Beagle4 website) on this pedigree to leverage the extensive LD in the panel. To have a fair comparison of Polymutt2 with Beagle4, we ran Polymutt2 using the allele frequencies derived from the same reference panel. Based on simulation results it is clear that at high coverage over 30X the accuracy measures of all callers are satisfactory. Our major goal here is to investigate to what extent genotype calls from various callers with a subset of data can recover the original high depth sequencing data. We first created a gold-standard callset from the original high-depth data by taking the consensus of genotype calls from GATK, Polymutt, Polymutt2 and Beagle4; this call set contains genotypes that are agreed by all 4 callers. GATK and Polymutt infer allele frequencies from the sequence data only, and due to the small sample size of the pedigree the estimates are not reliable. Here we focused only on the comparison of Polymutt2 and Beagle4, two competing methods based on simulated data. Specifically, we randomly extracted 30% and 15% of the reads from the original alignment, corresponding to ~15X and ~7.5X of coverage, and carried out variant calling using both Polymutt2 and Beagle4. For each of the two callers we calculated FNR and FDR using the gold-standard callset. We also compared their performance stratified by allele frequencies, which were calculated based on the same reference panel used in Beagle4. Since genotype filtering has a strong impact on FNR and FDR, e.g. aggressive filtering results in low FDR and high FNR and vice versa, we calculated the two measurements using GQ values from 3 to 30 and plotted them in FNR-FDR curves to represent genotype accuracy with a wide range of filtering. This is an objective way of comparing genotype accuracy and a curve completely underneath the other indicates consistent high accuracy of genotype calls for all GQ cutoffs in the range of 3 to 30.We downloaded the whole genome sequencing data in CEPH pedigree 1463 generated on the Illumina HiSeq platform , Polymutt2 calls achieve greater concordance with the gold standard callset than Beagle4, as manifested by the reduced error rates in the FNR-FDR curves . When weWhen we focused on heterozygotes, Polymutt2 and Beagle4 calls have similar accuracy when all variants were considered with both 30% and 15% of the data  Fig. WheWe observed considerable MI rates in Beagle4 calls with both ~15X and ~7.5X data. For example, at ~15X the MI rates are 0.14% and 0.09% when the minimum GQ was set to 5 and 10, respectively. The corresponding MI rates at ~7.5X are 0.15% and 0.1%. When we focused on low frequency variants, the MI rates in Beagle4 calls are noticeably increased. For example, for variants with allele frequency <0.1 at ~15X, the MI rates are 0.27% and 0.21% for GQ cutoffs of 5 and 10, respectively, indicating that increased genotype error rates associated with low allele frequencies in Beagle4 calls resulted in higher MI rates. On the other hand, as a direct comparison, we did not observe Mendelian error in Polymutt2 calls in all of these scenarios investigated, indicating the extremely low Mendelian error rate in Polymutt2 calling in real data.Sequencing pedigrees has shown its effectiveness in identifying rare variants associated with human disease, and is expected to continue in gene mapping for complex traits in complement to population-based designs. In addition, family designs are not prone to population stratification, which may be more challenging to control for rare variants . In this2 in this context) between rare variants and between rare and common variants is low, the effectiveness of LD-based calling for rare variants is reduced. Although for pedigrees with limited IBD sharing (e.g. sibpairs) Beagle4 outperformed Polymutt2 when considering all genotypes, Polymutt2 still achieved increased accuracy in calling rare variants. In addition, Mendelian inconsistency in LD-based calls, especially for rare variants, which are usually analyzed in groups, may have inadvertently impact on association analysis since the effect of Mendelian error in individual variants may be aggregated and amplified. As the major focus in sequencing is to identify rare variants we hope that Polymutt2 is useful for gene mapping of rare variants for complex disease.Compared to Polymutt and GATK, Polymutt2 has increased accuracy of genotype calling from all aspects. This is rather unsurprising given that Polymutt2 uses extra information than the other two callers. On the other hand, Polymutt2 and Beagle4 use orthogonal information, i.e. the explicit modeling of IBD sharing in Polymutt2 vs. the utilization of LD among variants in Beagle4 for variant calling. Since the LD  to O(NlogN)in the HMM, where N is the number of inheritance vectors. Even with these speedup techniques, however, the computation can be still very challenging. To further mitigate the problem, we implemented the software using multi-threads so that the computation can be parallelized when possible. The current implementation can handle simple pedigrees efficiently. For example, for sibpairs and sibships of size 4, and nuclear families of size 4 and 6, the average time per family using 8 threads for chromosome 1 whole genome sequencing is on the scale of minutes. For sibships of size 6 the time is significant increased and it took over an hour to finish variant calling per family. For pedigree of Ext10 the time is even further increased to over 10 hours to get marginal calls. If computing is limited an option is to use only inheritance vectors with highest posterior probabilities for such pedigrees; for example using the single best inheritance vector the computing is a few minutes. For pedigrees beyond the exact calculation of the likelihoods, Monte Carlo approaches [Since the Lander-Green algorithm is the major component for the inference of the inheritance vectors, the computation is linear with respect to the number of variants but can be explosive when pedigrees get large. For a pedigree with  storage . Further storage , which rproaches –35 are n2 = 0.2. We also investigated other thresholds to evaluate the sensitivity of the results to the LD pruning. Specifically we used cutoffs of 0.1 and 0.5 and observed similar results as 0.2, with the difference below 0.01% for most of pedigrees and coverage investigated in Figs In the inference of inheritance vectors, we selected the scaffold variants by LD pruning. The results reported in the article were based on the maximum correlation coefficient of RWith the comprehensive catalog generated by the 1000 Genomes Project, identifying known variants in study sample is generally very accurate. However calling novel variants for pedigrees is usually of particular interest. This remains challenging due to potential alignment artifacts. Unannotated structural variants are a major source of alignment artifacts, and when such artifacts do not follow Mendelian transmission laws the variant quality is expected to be dramatically reduced for such sites when the IBD sharing is imposed in the calculation of the likelihood. We believe that Polymutt2 is effective in filtering false novel variant candidates given its efficient use of allele sharing.De novo mutations, however, violate the rule and make the inference of inheritance vector inaccurate. Although it is unlikely to include de novo mutations in scaffold variants, accidental inclusion of such variants makes the results not reliable. To avoid this situation, Polymutt2 internally checks the likelihood of de novo mutations during the calculation and if a strong violation of Mendelian inheritance is detected the algorithm ignores these variants so that the inheritance vectors can be robustly inferred. The current version of Polymutt2 is not designed to call de novo mutations and other methods  should https://medschool.vanderbilt.edu/cgg). We hope that our user-friendly software packages are useful to the research community for pedigree sequencing studies to facilitate the identification of rare variants for human disease.Our tools were implemented in C++. The source code and company resources can be downloaded from the authors’ website  for sequencing coverage of 10X and 20X, and panels C and D show the FDR (%) for the same set of coverage.(TIF)Click here for additional data file.S2 FigResults of different pedigrees are shown in panel A) for Sib2, B) for Sib4, C) for Sib6, D) for Nuc4, E) for Nuc6 and F) for Ext10.(TIF)Click here for additional data file.S3 FigApplication to real data for the details on the pedigree and the calculation of error rates.See (TIF)Click here for additional data file.


Recent studies have implicated the role of differential co-expression or correlation structure in gene expression data to help explain phenotypic differences. However, few attempts have been made to characterize the function of variants based on their role in regulating differential co-expression. Here, we describe a statistical methodology that identifies pairs of transcripts that display differential correlation structure conditioned on genotypes of variants that regulate co-expression. Additionally, we present a user-friendly, computationally efficient tool, dcVar, that can be applied to expression quantitative trait loci (eQTL) or RNA-Seq datasets to infer differential co-expression variants (dcVars). We apply dcVar to the HapMap3 eQTL dataset and demonstrate the utility of this methodology at uncovering novel function of variants of interest with examples from a height genome-wide association and cancer drug resistance. We provide evidence that differential correlation structure is a valuable intermediate molecular phenotype for further characterizing the function of variants identified in GWAS and related studies. Recent advances in DNA and RNA sequencing technology have afforded the ability to interrogate variance in gene expression and allele frequency distributions to determine associations with phenotypic variance, including disease. However, many of the variants uncovered in the genome-wide association study (GWAS) era have yielded few functional characterizations for particular phenotypic associations . MoreoveIn transcriptomic analyses, a strong co-expression or correlation between a pair of expression probes is used to infer a shared biological function or pathway. In these co-expression studies, the correlation between pairs of genes is typically assumed to be uniform across all samples, even in datasets designed to examine phenotypic differences. However, the inter-group (phenotypic) differences in correlated expression data may provide more powerful insights into phenotypic variance than a uniform correlation measure. For example, R package but were not designed for variants to define group inclusion  can potentially functionalize variants identified in GWAS and related association studies. To demonstrate this, we implement our methodology in a computationally efficient tool called dcVar and apply this tool to the HapMap3 eQTL dataset. We discuss two of the significant results that demonstrate added functionality to previously implicated variants in phenotypic variance. Our results suggest that the examination of variants that induce differential correlation structure in expression levels provides a powerful intermediate molecular phenotype that can be readily examined in parallel with existing eQTL as well as RNA-Seq analyses.Z-test discussed in the following equations. First, the Pearson correlation of expression E is calculated for pairs of genes i and j for subjects within each of the two genotype groups, G = 1G or 2G:To model differential co-expression of two genes between two groups of subjects separated by the genotype of a variant based on a given genetic model, we use the Fisher’s 1G and 2G:The within-group correlation values are then Fisher z-transformed for each group G1 of sample size 1m and G2 of sample size 2m are computed for genes i and j:The difference of the z-transformed correlation values between groups p-value associated with the difference in within-group correlation can be determined from the Z score (The resulting statistic produced by Eq. (3) is assumed to be normally distributed, where the  Z score . More ro1G or 2G on the basis of genotype, we propose three different models. For a hypothetical single nucleotide polymorphism (SNP) with a major allele A and minor allele T, three possible separations are implemented in our algorithm. First, a dominant encoding model where the presence of one or more minor alleles results in individuals with an AA genotype comprising group 1G while group 2G is composed of individuals with either an AT or TT genotype. Conversely, one can impose a recessive model where individuals with either the AA or AT genotype are assigned to 1G whereas only subjects with both minor alleles (TT) constitute group 2G. Finally, we implemented a model denoted “homozygous,” such that group 1G is composed of only subjects with both major alleles (AA) whereas group 2G individuals have both minor alleles (TT). Thus, the heterozygotes for the particular variant (AT) are excluded from the analysis. In the conclusions, we discuss additional genotype encodings that may be combined with a linear model of co-expression.In order to separate individuals into groups Figure 1), which is an important consideration when developing bioinformatics software for very large data sets . As the computational scale of a dcVar analysis is order (Number of Transcripts2 × Number of SNPs), we emphasize the enhanced utility of dcVar over existing tools to efficiently compute differential correlation especially on a genome-wide scale. The C++ and R implementation of dcVar and a tutorial are available for download and installation at http://insilico.utulsa.edu/dcVar.php.We implemented the described statistical framework as a C++ tool called dcVar based on the PLINK source code . To compata sets . While sata sets , which iTo assess the utility of the proposed method in terms of biological relevance and computational performance, we applied dcVar to an eQTL dataset of 491 HapMap3 individuals from six different ethnicities . After pp > 1.41 × 10-14), which was computed by dividing 0.05 by the number of tests performed  × 9,999 × 70,716). Additionally, to estimate the type-I error of dcVar, we permuted the same HapMap3 dataset by randomizing the genotypes for each variant while fixing the expression values for each individual. The same dominant model was applied as described in our regular analysis, and the number of significant probes against our corrected threshold were counted as false positives.The number of transcripts was filtered by selecting the top 10,000 transcripts using a total variance filter after quantile normalization  was applFigure 1 shows the benchmarking results of executing dcVar on a Linux desktop with an AMD FX(tm)-4100 Quad-Core Processor with a 3.6 GHz CPU and 8 GB RAM. Of the four example benchmarks computed, the C++ version of dcVar outperformed an identical R implementation by an average of 21× or 15× in scenarios with larger numbers of tests. The order of magnitude difference in performance between these implementations becomes more pronounced as the number of tests approaches a genome-wide analysis . Our implementation of a framework to compute differential correlation from variants in C++ provides a tool for researchers to uncover these effects in a genome-wide eQTL or RNA-Seq analysis. While benchmarking was performed on a desktop machine, the analysis performed on the HapMap dataset was executed on a computing cluster available at Oklahoma Medical Research Foundation. We note that similar genome-wide analyses using dcVar would be best performed on a similar local computing cluster or through the NIH biowulf cluster.To assess the performance of our R and C++ implementations of dcVar, we analyzed random subsets of the full  HapMap3 eQTL dataset using the dominant encoding model. NUCKS1), has previously been associated with pubertal height growth  gene (pdom = 1.69 × 10-15). As WSB1 modulates thyroid hormone activation and parathyroid hormone-related peptide secretion in developing growth plate  under all three models for stratifying groups: dominant (A), homozygous (B), and recessive (C). Like eQTL analyses that use transcriptomic markers to bridge the gap between SNP associations and phenotypic variance, dcVar uncovers additional transcriptomic markers that interact in the functional network.After executing dcVar on our HapMap eQTL dataset, we observed a significant differential correlation structure between this height-associated variant, rs823094, its corresponding gene, th plate , a commoNUCKS1, which has a similar biological role as WSB1 in promoting growth, a direct interaction between the products of these genes has not been observed. However, we note two pieces of evidence that point to a plausible connection between NUCKS1 and WSB1 and a possible biological explanation for the genotype-specific differential correlation structure observed. First, a remarkable number (107) of transcription factors (45.5% of factors in EncodeQT) regulate both of these genes within 500 bp of their transcription start sites as determined by ChIP-Seq signals generated from the ENCODE Project  and TPR (translocated promoter region), as shown in Figure 3. While a specific mechanism of activity leading to phenotypic variance in height is unclear, the likely interaction between NUCKS1 and WSB1 through a degree of separation as predicted by IMP suggests a high level biological interaction. Thus, at both the regulatory level via transcription factors and the interaction level via intermediate genes, some interaction exists between NUCKS1 and WSB1, demonstrating the plausibility of a differential correlation existing between these two genes that better characterizes the association of rs823094. We illustrate this differential correlation process using the homozygous model . The left  depicts the emergence of a strong correlation structure (r = 0.715) for individuals with a GG genotype for rs823094, and the right panel shows a weaker correlation (r = 0.219) for those with both major alleles, noting that a strong correlation (r = 0.775) is present for the heterozygotes (GT genotype).Though the variant modulating the differential correlation in this example is encoded in an intron in  Project . As thes Project , we noteATF4) and circadian locomotor output cycles kaput (CLOCK) genes regulated by rs12624829 (pdom = 8.25 × 10-19). As the protein interactions between these two genes has been well-characterized in the transcription regulation system, the CLOCK and ATF4 interaction has also been implicated in regulating drug resistance in the A549 cancer cells . However, the minor alleles in this variant cause this correlation to decrease. As the synergistic effect of CLOCK and ATF4 has been implicated in multidrug resistance through glutathione-dependent redox system, a breakdown in this correlation could lead to differential drug response in human cancer , in the same A549 cell line  and 1,237,788 unique gene pairs. These relatively high percentages likely indicate inflated statistics for a few reasons. First, variants in strong LD that fall outside the 50 kb region from the PLINK LD pruning flag would inflate the number of observations while representing only one true effect. In addition, transcripts that exhibit strong covariance would also inflate the number of positive associations.Using the dominant model, our methodology computed a significant differential correlation structure for 47.1% of the 10,000 expression probes and 13.7% of the 70,716 common variants included for analysis using the p = 0.9969; ATF4/CLOCK: p = 0.1826) (The two cases highlighted in the manuscript were selected based on the strength of the association (1–4 orders of magnitude greater significance than the threshold) and biological relevance. In particular, we used two approaches to prioritize the hits using biological knowledge. First, we annotated the pairs of gene expression probes with interaction scores from STRING-DB. The ATF4-CLOCK example represented 1 of 180 gene pairs that had a STRING interaction score >800. Second, we enriched 40 SNPs for known genome-wide association terms from general population phenotypes  using the NHGRI database. The NUCKS1-WSB1 variant (rs823094) represented one of 40 of these enriched variants. Additionally, we note that other multiple phenotype regression models did not uncover these effects identified by dcVar. Notably, the two examples that we highlight in this manuscript were not significant using the Plink.multivariate association model (NUCKS1/WSB1:  0.1826) . Though p < 0.05 significance threshold, only 1.84% of SNP-gene pairs significant in our dcVar computation were significant. When further requiring both gene expression probes to be significant for the SNP × gene × gene trios uncovered by dcVar, only 0.29% of our uncovered effects were significant in standard eQTL models. In the two cases highlighted above, the univariant eQTLs were not significant for either rs823094  or rs12624829 . As eQTL studies often employ more stringent p-value thresholds for discovery, few significant results uncovered by the dcVar approach would be represented in a typical eQTL computation.As dcVar computes the effect of variant alleles on pairs of expression values for genes through differential correlation, we sought to determine if these effects were captured under standard linear regression as used in most eQTL analyses. Using a nominal ∗10,000∗9,999/2) = 1.41 × 10-14), only a single trio in the permutation simulation survived the threshold. We used this strict threshold in the current application of dcVar to the HapMap3 data. As a side note, if one were to use a per-variant corrected threshold of 1x10-9 ), 15,699 SNP-probe-probe trio statistical tests would be significant in the permuted data.To estimate the false positive rate (FPR) of dcVar, we performed a permutation-based analysis on the HapMap3 eQTL data. While maintaining the order of the 10,000 expression probes, we permuted the genotypes of a given variant and applied dcVar to test differential co-expression for all pairs of probes. We repeated this for all 70,716 SNPs that passed the pruning process. When we use the Bonferroni threshold based on all SNP-probe-probe trios  may do so with the dcVar tool. Future applications of dcVar to genome-wide eQTL datasets will further characterize the highly interconnected network of possible regulatory variants involving the dcVar intermediate molecular phenotype.The computational efficiency of dcVar enables users to incorporate information from variants that modulate differential correlation structure through a variety of means. In the analysis described in this study, we tested our approach on the HapMap eQTL data, so there was not an A limitation of our approach is the modeling of changes in co-expression between subjects conditioned on only two genotype groups. Specifically, we compute the differential co-expression between subjects grouped by a recessive or dominant encoding, which may not properly model the co-expression variation in the heterozygous group. A potentially more powerful approach would be to estimate a linear model of the co-expression using an additive encoding, which has been more popular in most GWAS and other genomics studies , althougAnother limitation of the dcVar approach is the potential for increased type-II error. In order to limit type-I errors associated with the very large number of dcVar hypotheses, we used a strict Bonferroni correction. The dcVar tool includes a Benjamini–Hochberg FDR option, which gives the user one way to decrease the type-I error. Our use of Pearson correlation to compute co-expression in genotype groups also increases the risk of type-II error and sensitivity to outliers. More robust statistics such as Spearman and bootstrapping methods may decrease sensitivity to outliers and deviations from normality (Fisher’s z-transform notwithstanding) and thereby decrease type-II error. Future studies are needed to demonstrate the extent to which robust statistics may improve dcVar effect detection. Finally, we note that our previous study employing differential co-expression between case-control status identified hub determinants of phenotypic variation by integrating information from the broader differential co-expression network . While tCL and BW wrote the software and analyzed the data. CL, CM, and BM wrote the manuscript. All authors have read and approved of the final version of the draft.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.


Motivated by the challenges associated with accounting for the ascertainment when analyzing secondary phenotypes that are correlated with case-control status, Lin and Zeng have proposed a method that properly reflects the case-control sampling (Lin and Zeng,  For the analysis of secondary phenotype data collected in a case-control study, Lin and Zeng have proposed a method that properly reflects the case-control sampling , Y denotes the secondary phenotype, n denotes the total number of subjects, and X denotes the genotype of interest.When the secondary phenotype is normally distributed, Lin and Zeng propose an adjusted score test that incorporates genetic associations with affection status into the test statistic and models the likelihood function as follows  is defined as a logistic regression model. They model P(Y|X) as a logistic regression for dichotomous Y or a linear regression for normally distributed Y. They maximize the likelihood with respect to P(X) by the Newton Raphson algorithm. In this framework, likelihood based statistics  can be used to make inference.Lin and Zeng calculate The Lin and Zeng approach requires the secondary phenotype to be normally distributed and the method can be problematic under the null hypothesis since the likelihood surface that needs to be maximized can be relatively flat. Since Lin and Zeng's method estimates the parameters in the model by maximizing the likelihood given in Equation (1), the approach is numerically exhaustive when testing a large number of SNPs where a majority of the SNPs are under the null hypothesis. This is a result of the maximization of the likelihood function being difficult under the null hypothesis, since the surface can be flat due to the ascertainment condition.If the primary goal of the secondary phenotype analysis is hypothesis testing as opposed to estimation of disease-association parameters, an alternative approach is to use the following likelihood composition, which ultimately does not require maximizing a relatively flat likelihood surface. Therefore, for the association testing of secondary phenotypes in case-control studies, we propose using a simpler break down of the likelihood that requires few assumptions.P(X|D) and P. For an additive genetic model, i.e., X = 0, 1, 2, corresponding to allele counts, instead of modeling the likelihood function, one can use a cumulative logistic regression model with proportional odds proportional for P(X|D) and the P such thatj = 0, 1. To control for any known confounders, these covariates can be added to Equation (4). This model assumes the same effect for different cumulative logits , γ1 varies from 0 to log(1.5), and γ0 was chosen such that the disease rate is 1% or 5%. For each combination of simulation parameters, we generated 1000 data sets with 500 cases and 500 controls.To assess the performance of this approach and compare it to Lin and Zeng's method, we conducted simulation studies following Lin and Zeng's manuscript with a MAF of 0.3, an additive mode of inheritance, and α = 0.01 level of significance  and the disease rate equal 5%. The plot on the right is the log Likelihood specified by Lin and Zeng for varying values of γ1 and γ2 with all other parameters fixed at their true values, and for data generated under the null hypothesis with γ1 = log(1.5) and the disease rate equals 5%. The red dots on the plots represent the true maximum. The surface for β0 and β1 has a clear maximum whereas the surface for γ1 and γ0 is relatively flat, demonstrating the difficulty in maximizing the likelihood surface defined by Lin and Zeng under the null hypothesis.Figure While the power of the proposed method is comparable to the method of Lin and Zeng, the proposed approach does not have the issue of maximizing a flat likelihood surface under the hull hypothesis that can be computationally intensive. Since the proposed approach is limited in it's ability to accurately estimate effect sizes while the approach by Lin and Zeng has the advantage that effect sizes can be accurately estimated, we recommend the following work-flow for the analysis of secondary phenotypes.Test all SNPs with the proposed approach using proportional odds logistic regression since the vast majority of SNPs will be under the null hypothesis.For the significant SNPs, apply Lin and Zeng's method to obtain parameter estimates and confidence intervals.By using our approach to test all the SNPs in the GWAS, the hypothesis testing can be done quickly and efficiently since our approach does not suffer from this issue of maximizing a flat likelihood surface under the null hypothesis. By obtaining parameter estimates for only the significant SNPs with Lin and Zeng's method, one can make sure that the likelihood is properly maximized which is too computational exhaustive to apply to the entire GWAS.There are potential limitations associated with this strategy of combining two methodological approaches to reduce the computational burden while still being able to estimate the parameters of interest. While the two approaches have comparable power, a relatively small number of SNPs that are significant from the new approach may not be significant in the Lin and Zeng's method and vice versa. Also both approaches may have issues if the case control status is extremely correlated with the secondary phenotype. In this case, the secondary phenotype is not providing new information compared to the case-control status and these methods for testing secondary phenotypes in case-control genetic association studies are not applicable.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.


Canine behaviours that are both desirable and undesirable to owners have a demonstrable genetic component. Some behaviours are breed-specific, such as the livestock guarding by maremmas and flank sucking seen in Dobermanns. While the identification of genes responsible for common canine diseases is rapidly advancing, those genes underlying behaviours remain elusive. The challenges of accurately defining and measuring behavioural phenotypes remain an obstacle, and the use of variable phenotyping methods has prevented meta-analysis of behavioural studies. International standardised testing protocols and terminology in canine behavioural evaluations should facilitate selection against behavioural disorders in the modern dog and optimise breeding success and performance in working dogs. This review examines the common hurdles faced by researchers of behavioural genetics and the current state of knowledge. All canine behaviour, whether desirable or undesirable to owners, has a genetic component. Studies of “showing eye” and “bark” which compared the behaviour of offspring with parents concluded that behaviour does not follow simple Mendelian inheritance. Some behaviours are breed-specific, such as “livestock guarding” by maremmas and “flank sucking” seen in Dobermanns.Identification of genes responsible for canine monogenic diseases (caused by one gene) is advancing rapidly, but the genes underlying behaviours remain elusive. This is because canine behaviours are similar to complex diseases such as Hypothyroidism, where there are both environmental and multiple genetic components.A major obstacle in behavioural studies has been the challenge of accurately defining and measuring behaviours, and how these are expressed . As researchers have used a variety of different ways to measure behaviour, data from multiple behavioural studies cannot be combined. International standardised testing protocols and terminology (definitions) in canine behavioural evaluations should help selection against behavioural disorders in the dog, and optimise breeding success and performance in working dogs.This review examines the common hurdles faced by researchers of behavioural genetics and the current state of knowledge.In the space of 30,000 years, dogs have moved from camp-side scavengers to being considered ‘man’s best friend’. Current statistics on pet ownership show that 36% of both Australian and U.S.th century, extensive record keeping began to trace the lineages of dogs bred for purpose. The domesticated dog became refined into breeds with closed studbooks and written breed standards. As leisure time and wealth increased, the objectives of selection altered from being purpose-driven to fashion-driven. Although some working breeds are still in demand, and some utilise their original working traits in contemporary canine sporting activities such as agility trials, numerous breeds have been selected for purposes unrelated to practical work. In the role of companions, modern dogs may require higher tolerance than their ancestors for the frustration of inactivity, social isolation and unstimulating environments[Since their domestication, dogs have played many roles in their association with humans. For hundreds of years they have been both companions and valuable working colleagues, assisting us with protection, transport, agricultural production and hunting. While domestic dogs retain many of the behavioural vestiges of their wolf ancestors, both their morphology and behaviour have been greatly altered by artificial selection. These changes were often distilled by geographic isolation. In the 19ronments. In thisronments, provingThe formation of dog breeds has created a genome that is extremely well suited to genetic research. There is large genetic variation between breeds and small variation within breeds. Linkagehttp://www.caninehealthfoundation.org). It is worth asking why so much progress has been made in canine inherited diseases and so little in the genetics of canine behaviours. Improved understanding of canine behavioural genetics has the potential to benefit the dogs themselves and provide useful models for several human psychiatric disorders.The sequencing of the canine genome in 2005 heralded an escalation in the development of genetic tests. The Canine Health Foundation website currently lists 102 genetic tests. Of these, 97 are tests for inherited diseases and five are concerned with coat characteristics  of also demonstrating separation anxiety. There iPhenotyping must be valid, reliable, sensitive and as objective as possible to be useful for genetic analysis. Unlike most diseases studied, there are no specific physical characteristics or blood tests for behavioural conditions. Clinical criteria used for phenotyping may overlap or be either more restrictive or broader than the criteria used for diagnosis. Methods of phenotyping used in behavioural studies include battery testing, owner questionnaires and observational study. The latter is less common due to financial and time costs.Numerous behavioural tests are applied to dogs. Some measure only a single trait: for example, the Ainsworth’s Strange Situation Test measures the attachment between dog and owner. Others measure different aspects of temperament or aptitude for a particular function. In their review of the behavioural testing methodology used in over 30 studies, Diederich and Giffroy found a The Dog Mentality Assessment, one of the more common standardised behavioural tests available, is used to test thousands of Swedish dogs each year. Comparing test results with owner questionnaire responses, it appears to reliably measure playfulness, sociability and curiosity/fearlessness and the boldness-shyness personality dimension. HoweverLivestock breeding programmes demonstrate that using objective trait testing procedures is critical in establishing successful breeding programmes for complex traits. The impStatistical analysis of performance recording data needs to correct phenotypic information for known environmental factors. In two studies of Finnish hunting dogs, weather conditions, such as the presence of wind and snow, and the month the trial was held significantly affected performance, 31. LiiOwner-based questionnaires have several advantages over battery testing. The assessor is intimately familiar with the subject and can assess behaviour over numerous events compared to assessment based on a single trial. The assessment is also carried out in the home environment of the dog, rather than the artificial environment of a testing area. Because questionnaires are relatively economical, they are commonly used in research.The Canine Behavioural Assessment and Research Questionnaire (C-BARQ) is a validated questionnaire that has been used in several studies–35. OwneThe main disadvantages of owner-based questionnaires are possible reductions in validity, reliability and objectivity. Each question must be validated to ensure it is measuring the behaviour in question. The large number of assessors will affect inter-assessor reliability. As each participant has a different assessor, there is the risk of each placing a slightly different interpretation on the question and on the dog’s behaviour. One questionnaire designed to reduce this subjectivity is being used to phenotype dogs for a genome-wide association analysis of noise phobias and anxieties. Owners Again, meta-analysis of canine behavioural research projects is difficult as so few studies use the same questionnaire for phenotyping. More progress could be made if behavioural studies could be directly compared and results pooled. Developing a manual of standardised canine phenotyping techniques, containing both testing procedures and questionnaires, would greatly assist progress and be a very useful resource for researchers.Inconsistency in terminology is recognised as a major handicap to advancing behavioural science and was the subject of a round-table discussion among 15 international veterinary behaviourists. While pIn its simplest form, an aggressive response tells us that the dog has been pushed to defend its resources, its pups or itself. NeverthFears, anxiety disorders and phobias are often grouped together and can show similar physiological signs typical of heightened arousal. Both fearful and anxious responses are essential for survival, allowing the dog to avoid the threat currently and in the future, 45. ThaAnother major difficulty for behavioural researchers is that the term ‘behaviour problems’ has been used to encompass behavioural disorders as well as normal dog behaviours that the owner sees as a problem. Dogs are considered to have a behavioural disorder when their behavioural responses interfere with the dog’s normal function, are persistent, out of proportion to the stimuli, or are triggered by harmless stimuli or a non-existent threat. Behavioural disorders can be due to both maladaptive and pathological/malfunctional causes.Regardless of cause, the bond between dog and owner will become strained if there is a significant divergence between the dog’s behaviour and the expectations of the owner. Behavioural problems are a common reason for relinquishment and it is estimated that they account for 10-15% of all euthanasias of dogs and cats in North America and 21% chd8, dyrk1a, grin2b, katnal2, pogz and scn2a. With access to data on up to 10,000 families, the consortium aims to use a combination of whole-genome sequencing and whole-exome sequencing to identify and validate further at-risk genes and clarify genotype-phenotype relationships[International sharing of information and pooling of data would greatly increase the power of association studies that are currently limited by small numbers of cases and controls. This is demonstrated by the impressive progress of the Autism Sequencing Consortium since its formation in 2010. Whole-exome sequencing of 1,000 families has identified six genes associated with Autism Spectrum Disorder: ionships. Data shionships, pigs[5ionships and poulionships.In 2012, the Swedish Kennel Club hosted a meeting of stakeholders to improve international efforts in the management of canine inherited disorders . Fearful behaviour was identified as the most globally detrimental behaviour across the breeds. Attendees developed plans for both national and international genetic evaluation programmes for dogs, 58. SucMany behaviours seen in domestic dog breeds do exist in their wolf ancestors, but artificial selection has refined and exaggerated some desirable companion qualities and specialist working skills required by owners. For example, pointing (raising a paw in attending to prey) is part of the wolf hunting ethogram that we have intensified in gundogs to alert handlers to the presence of game. As a result of selection, several dog breeds have been developed to show other elements of the lupine hunting ethogram. HerdingBreed predilections for behaviour were first described in a long-term project looking at the genetics of social behaviour of dogs. Five brThis overt variation in behaviour between breeds has been observed in many subsequent studies. When more than 13,000 dogs belonging to 31 breeds were subjected to the Swedish Dog Mentality Assessment, the aggression scores varied significantly between breeds, although there was also high variance within breeds. AggressMore recently, genetic researchers have favoured molecular methods to look for the genes underlying behavioural disorders. The aim of the molecular approach is to identify a potential genetic test that either helps breeders avoid the expression of the phenotype in their pups, or informs better treatment options. Success to date has been hampered by using genetic marker arrays designed for within-breed genetic mapping in an acpde6b, while in collies, it is a 22 base insertion in rd3 that leads to the same early-onset signs[Different genes may be fixed in each breed. Thus, association signals identified in one breed may not be associated in all breeds, unless there is similar intense selection pressure on those genes across breeds. This is evident in the canine ocular disease Progressive Retinal Atrophy. It has a similar presentation in different breeds but can be caused by a variety of mutations. In Irish setters, the condition is due to a single base mutation in et signs. It is ccomt and the glutamate receptor (slc1a2) – significantly related to a principal component described as ‘activity’. Dogs with the genotype slc1a2 TT were significantly more active than CT or CC. The same authors examined this slc1a2 polymorphism in shiba inu and found dogs with the genotype CC were significantly less aggressive to strangers than those with a genotype TC. Those with genotype TT were excluded from the analysis due to the small sample size[Conversely, mutations in the same gene may produce diverse phenotypes in different breeds. Takeuchi et al. examinedple size.Breed and familial predilections for compulsive disorders suggest a genetic basis. For example, bull terriers are prone to spinning or tail chasing, while fIt must be acknowledged that several breeds have changed considerably over time. As the selection emphasis for physical or behavioural traits changes, breed phenotypes may shift in response. Svartberg proposesDogs are unique in their morphological range. For example, across approximately 400 breeds, the variation in canine body size is immense. The Chihuahua reaches a maximum height of 20 cm and weight of 2 kg while the Newfoundland stands at a height of 70 cm and weighs 60 kg. Skull dimensions vary enormously too. Cephalic index (CI: skull width divided by skull length × 100) varies from 37.1 in the borzoi to 101.8 in the French bulldog. This diA need to improve efficiency and skill within service-dog programmes has motivated the desire to understand the genetic contribution to canine behaviour in working dogs. Working dogs belong to a diverse group of service areas including assistance (e.g. guide dogs), hunting, herding, livestock protection, defence and detection. The significant cost of training dogs for specialised occupations means that indicators of working success are highly desirable to prevent unnecessary expenditure on training dogs with below-average aptitude for the required tasks. There may also be welfare implications for dogs unsuited to a particular style of training or work.The emphasis of breeding programmes is on improving the success rates of dogs enrolled in their training programmes–79. A quMost canine breeding programmes are selecting dogs from a single breed to perform a particular function. One of the few exceptions to this is the Swedish Dog Training Centre which breeds and trains both German shepherds (used for guarding or police work) and Labrador retrievers (used as guide dogs). The dogs are raised in the same environment and undergo the same assessments for courage, sharpness, defence drive, prey drive, nerve stability, hardness, temperament, cooperation, affability and gun shyness, 84. TheHunting is another working context for which dogs have been intensively selected to show behaviours such as pointing, searching, pursuit and retrieval. The majority of desired hunting traits have positive genetic correlations. This ishcrtr2) gene[Breeding programmes have also assisted the search for causative genes in medical research. The identification of the causative allele for canine narcolepsy was made possible by the establishment of a colony of narcoleptic Dobermanns and Labradors. Twenty years after the colony was established at Stanford University, linkage analysis identified the causative allele on the hypocretin receptor 2 (r2) gene. HypocreA classic behavioural experiment spanning three decades studied the genetics of nervousness in English pointers, 88. TwoIt is worth remembering that heritability calculations are only accurate for that population, in that environment and at that time. Despite this, heritability estimates are still a very useful guide for breeding programmes: the higher the heritability estimate, the more gain will be made by selection. Even traits with modest heritability can demonstrate considerable genetic improvement through selection based on estimated breeding values. The chaMolecular approaches to the amelioration of behavioural disorders have concentrated on those genes involved in the regulation of common neurotransmitters. Serotonergic receptor genes have been considered candidate genes in many studies looking at panic disorders in humans, but results have been inconsistent. Anxious dogs had significantly higher plasma concentrations of dopamine and serotonin compared with controls. The invdrd1), serotonin receptors 1D and 2C (htr1d and htr2c) and neurotransmitter transporter slc6a1[Examining similar candidate genes for human-directed aggression in English cocker spaniels identified risk and protective haplotypes in the dopamine receptor D1  has been previously associated with novelty seeking behaviour in humans[drd4 with fearfulness and fearlessness (phenotyped by testing for avoidance of a stranger) in 264 Korean native dogs. Although the results suggested that fear could not be perfectly described by this gene, markers at the D4 receptor were found to significantly predict canine fearfulness. Differing variable number tandem repeats in drd4 have also been associated with activity and impulsivity in German shepherds[The D4 dopamine receptor gene , a widely expressed gene involved in pre- and post-synaptic adhesion. The risk genotypes (TT or CT) were more frequent in the severe phenotypes. However, polygenic inheritance is still suspected. This modest amount of success speaks to the underlying genetic complexity of such disorders in all species.To date, only one study has achieved genome-wide statistical significance identifying a gene relating to a behavioural disorder. In theiThe influence of genetics on both desirable and undesirable behavioural phenotypes is considerable and, consequently, many traits relating to behaviour should be amenable to selection. Significant improvement in the efficiency of selection for desirable behavioural traits is possible when objective standardised phenotyping is used. Additional efficiency can be gained by employing modern animal-breeding technologies, such as best-linear unbiased predictor-based estimated breeding values. In this review we demonstrate that programmes that have undertaken rigorous standardised phenotyping of working dogs and that have also employed proven quantitative genetic approaches have already demonstrated impressive genetic progress.Medical genetic research in all species is progressing rapidly. While interest and endeavour in researching behavioural genetics is certainly present, and some exciting advances have been made, progress has been slow. By using standardised phenotyping, standardised terminology and encouraging collaboration among research groups, many of the current limitations to behavioural genetics research will be overcome, allowing us to improve the lives of our closest companions and better understand human psychiatric disorders.


Testing rare variants directly is possible with next-generation sequencing technology. In this article, we propose a sliding-window-based optimal-weighted approach to test for the effects of both rare and common variants across the whole genome. We measured the genetic association between a disease and a combination of variants of a single-nucleotide polymorphism window using the newly developed tests TOW and VW-TOW and performed a sliding-window technique to detect disease-susceptible windows. By applying the new approach to unrelated individuals of Genetic Analysis Workshop 18 on replicate 1 chromosome 3, we detected 3 highly susceptible windows across chromosome 3 for diastolic blood pressure and identified 10 of 48,176 windows as the most promising for both diastolic and systolic blood pressure. Seven of 9 top variants influencing diastolic blood pressure and 8 of 9 top variants influencing systolic blood pressure were found in or close to our top 10 windows. More thysiology . Althougysiology -8, the iysiology . One potSeveral statistical methods have been proposed to detect associations of rare variants, including the combined multivariate and collapsing (CMC) method  and the In this article, we report a novel whole genome sliding window approach to detect genetic association between a trait and single-nucleotide polymorphism (SNP) regions across the entire genome. This approach integrates TOW and VW-TOW with the concept of sliding window . Appliedn individuals. Each individual has been genotyped at M variants in a genomic region. Denote ith individual, where ith individual has at the mth variant.Consider a sample of p covariates. Let ith individual. We adjust both trait value Suppose we have Let Using the generalized linear model (GLM) to model the relationship between trait values and genotypes is equivalent to modeling the relationship between the residuals of trait values and the residuals of genotypes through GLM (1), where S asymptotically follows a chi-square distribution with k. In rare variants association studies, to test for the effect of the weighted combination of variants, Under the GLM, the score test statistic to test the null hypothesis Because rare variants are essentially independent, we haveLet Then, the score test statistic is approximately equal to As a function of p value of K subintervals of equal-length. Let Define the test statistic of VW-TOW as p values of both p value of the test p value of the test is the proportion of the number of permutations with B times of permutations to evaluate the p value of p value of We use permutation tests to evaluate We use TOW and VW-TOW to analyze the data set of unrelated individuals of GAW18 replication 1 on chromosome 3. To apply TOW and VW-TOW to the entire chromosome 3, we propose a sliding-window approach . To use p values of TOW for DBP and SBP data, and 100,000 permutations to evaluate the empirical p values of VW-TOW for DBP and SBP data. Becausethe sample of unrelated individuals in GAW18 is relatively small, it is not so reasonable to claim the significance either by the false-discovery rate or by the Bonferroni-corrected threshold. Therefore, we recommend the top 10 most promising windows with the smallest p values for follow-up studies.To analyze the data set of GAW18 replication 1, chromosome 3 for unrelated individuals, we set the window size as 20. First we performed quality control tests for the genotype data with the PLINK toolset. We used 10,000,000 permutations to evaluate the empirical We applied TOW and VW-TOW incorporating the sliding window approaches to analyze the hypertension unrelated individuals'data set of GAW18. To facilitate comparisons among GAW18 contributions, we analyzed only replicate 1 on chromosome 3. To evaluate type I error rates of TOW and VW-TOW, we used all 200 replicates of simulated phenotype data. There are 157 unrelated individuals in the GAW18 pedigree-based sample. Among the 157 individuals, 142 have observations for SBP, DBP, and other demographic/clinical variables at exam 1. Our analysis was based on the 142 individuals and their genotypes, quantitative trait SBP, DBP, and other characteristicsat exam 1.The total genotyping rate in the 142 individuals is 0.9997. We did not find any duplicated samples or sample contamination. No individual was filtered out from the multidimensional scaling (MDS) analysis. Of the 1,215,399 SNPs on chromosome 3, we removed 251,892 completely missing SNPs and retained 963,507 SNPs for final analysis. Because SBP and DBP varied by sex and increased with age, age and sex were considered as covariates in this study.MAP4, which is the most susceptible gene on chromosome 3 for hypertension. Seven of 9 top variants influencing DBP and 8 of 9 top variants influencing SBP on chromosome 3 were found in or close to our top windows. Tables p values of TOW in the top 3 windows of Table We listed the top 10 most promising windows out of 48,176 windows across the entire chromosome 3. The top 8 windows all reside in gene p value for each replicate and each block. Figure To evaluate the type I error rates of the proposed sliding window approach, we chose 100 blocks (20 variants in each block) from chromosome 3 that are far from causal variants. In each block, we applied TOW and VW-TOW to each of the 200 replicates to test association between genotypes and the trait DBP. We obtained 1 In this article, we proposed a sliding-window-based optimal weighted approach to test for the effects of both rare and common variants across the whole genome. In each window, our recently developed TOW and VW-TOW were applied to test genetic association between a disease and a combination of variants. Then, we applied the method to unrelated individuals of GAW18 on replicate 1, chromosome 3. We detected 3 susceptible windows across chromosome 3 for DBP and identified 10 out of 48,176 windows as the most promising windows for DBP and SBP. Becausethis is a simulated dataset, it is possible that the other genes identified were not listed in the top 10 windows but are actually related to SBP or DBP.In this study, we use each window of size 20 across the entire chromosome 3. How to choose an appropriate window size is a critical question. We evaluated the effect of window size by running window sizes at 30, 40, and 50, respectively. However, the power of TOW was not increased when using a larger window size. Although the power of VW-TOW was slightly increased when using a larger window size, no window can pass the entire chromosome 3 Bonferroni-corrected threshold.K principalcomponents (PCs) of genotypes at genomic markers as covariates when calculating the residuals of trait and of genotype matrix. In this GAW18 data analysis, we did not adjust for PCsbecausewe believed that population stratification was not severe in this data based on our MDS analysis.TOW and VW-TOW can be robust to population stratification by adjusting the first MAP4 and DBP. The MAP4 was split into 44 windows (blocks) with 20 variants in each window. In each window, we calculated the power of each method based on 200 replicates. The power comparisons based on phenotype measurement DBP are given in Figure To further assess our new approach, we compared the power of TOW, VW-TOW, CMC, and WSS to detect association between gene The authors declare that they have no competing interests.XW designed the overall study. XZ and XW conducted statistical analysis. XZ, QS, and SZ drafted the manuscript. All authors read and approved the final manuscript.


In many medical studies the likelihood ratio test (LRT) has been widely applied to examine whether the random effects variance component is zero within the mixed effects models framework; whereas little work about likelihood-ratio based variance component test has been done in the generalized linear mixed models (GLMM), where the response is discrete and the log-likelihood cannot be computed exactly. Before applying the LRT for variance component in GLMM, several difficulties need to be overcome, including the computation of the log-likelihood, the parameter estimation and the derivation of the null distribution for the LRT statistic.To overcome these problems, in this paper we make use of the penalized quasi-likelihood algorithm and calculate the LRT statistic based on the resulting working response and the quasi-likelihood. The permutation procedure is used to obtain the null distribution of the LRT statistic. We evaluate the permutation-based LRT via simulations and compare it with the score-based variance component test and the tests based on the mixture of chi-square distributions. Finally we apply the permutation-based LRT to multilocus association analysis in the case–control study, where the problem can be investigated under the framework of logistic mixed effects model.The simulations show that the permutation-based LRT can effectively control the type I error rate, while the score test is sometimes slightly conservative and the tests based on mixtures cannot maintain the type I error rate. Our studies also show that the permutation-based LRT has higher power than these existing tests and still maintains a reasonably high power even when the random effects do not follow a normal distribution. The application to GAW17 data also demonstrates that the proposed LRT has a higher probability to identify the association signals than the score test and the tests based on mixtures.In the present paper the permutation-based LRT was developed for variance component in GLMM. The LRT outperforms existing tests and has a reasonably higher power under various scenarios; additionally, it is conceptually simple and easy to implement. In many medical researches the main interest often lies on the problem of testing whether a random effects variance component is equal to zero within the mixed effects models framework. The variance component test has long been a statistical challenge and received much attention in the literature; see for example, Self and Liang , Stram aThe variance component test is nonstandard in the sense that under the null the variance component is on the boundary of the parameter space. In this situation it is not easy to obtain the null distribution of the likelihood ratio statistic. Under some regularity conditions Self and Liang , Stram a Ruppert  argued t Ruppert  developeInstead of using the equal-weight mixture as done in Self and Liang  and LianThe work aforementioned shows clearly that it is difficult to obtain an analytical expression for the null distribution of the likelihood ratio statistic. On the other hand, when encountering complex hypothesis testing scenarios in practical data analyses, resorting to resampling-based methods is a very natural and effective strategy. Faraway  and SamuAt present most of the work concerning the likelihood-ratio based variance component test has been mainly investigated under the context of linear mixed models (LMM), in which the response variable is continuous and the closed-form log-likelihood function is easily obtained and calculated ,19. Howei) unlike in LMM for the continuous data, the closed-form log-likelihood function of GLMM can be no longer yielded except in some extremely limited situations, thus the computation of the likelihood ratio statistic is not easy; (ii) the exact parameter estimation in GLMM is often impossible because of the need of high-dimensional numerical integration; (iii) the null distribution of the likelihood ratio statistic in GLMM is complicated, and similar to the case in LMM it cannot be obtained analytically.The difficulty of performing the likelihood ratio variance component test in GLMM arises in several aspects:  that are significantly related to diseases. Two commonly used methods in genome-wide association studies are respectively single marker analysis and multiple markers analysis . CompareK SNPs within a functional gene are grouped into an SNP set. The objective is to test whether these K SNPs are jointly associated with the disease of interest, say y. Here we assume y is a binary variable. If the number of SNPs  is small, we can perform traditional fixed effects model and test to achieve this aim; however, if the number of SNPs is large, the traditional test such as the Wald test or the score test is typically underpowered for the null due to the large number of degrees of freedom, and the fixed effects model may be subject to some numerical issues, e.g., the problem of multicollinearity since the SNPs within a gene may be highly correlated due to the linkage disequilibrium.More specifically, suppose that in multilocus association analyses As an effective alternative, if the effects of SNPs are assumed to be random with a common variance component , then thIt should be emphasized that our main objective is focused on the hypothesis testing of variance component in GLMM instead of the parameter estimation. In this paper we attempt to explore the application of LRT in logistic mixed effects model based on the well-developed theories for GLMM.The organization of this paper is given as follows. The likelihood ratio statistic is constructed by taking full of the working response generated in the estimation process of GLMM. To circumvent the derivation of the analytical expression for the null distribution of the likelihood ratio statistic, we use the permutation procedure. We implement simulation studies to evaluate the performance of the proposed permutation-based LRT in the context of genetic association studies. Finally we apply the proposed LRT to multilocus association analysis for the binary genetic data.X =  and Z =  be n × (p + 1) and n × K matrices for covariates, respectively, where X0 = 1 corresponds to the intercept term, n is the total sample size; and let y = ’ be a n-dimensional vector for a binary response variable coded as 0 and 1, such as y = 0 for the control and y = 1 for the case in case–control studies. Assume the relationship between y, X and Z is characterized via the following logistic modelLet α =  are considered as fixed effects, while β =  are considered as random effects following a normal distribution with mean zero and variance component τ2. Under these settings model (1) becomes the logistic mixed effects model which has been widely studied in the literature . Following Breslow and Clayton , say Tobs;step 2: Generate a new dataset D* by resampling;step 3: Calculate the new value of T according to (4) using D*, say T*;step 4: Repeat the steps 2–3 above B times, get T*b, b = 1, 2, …, B;step 5: The resampling-based null distribution of T can be approximated by Tb*, and the Monte Carlo p value of T is estimated by the proportion of Tb* equal to or greater than Tobs.To obtain the null distribution of the likelihood ratio statistic rocedure -38. The y and X as a whole while keeping Z fixed, then we are performing the permutation test , we first generated G =  via the standard normal distribution with pairwise correlation between Gk and Gk’ to be 0.5k - k’||, and then set Zk = 0, 1 and 2 according to whether Gk < −c, −c ≤ Gk ≤ c or Gk > c, where c is the third quartile of the standard normal distribution. We set K = 20, 30 and 40, and β = 0 in model (5) for the type I error simulation and sampled β from a normal distribution with mean zero and variance τ2 = 0.15 and 0.20 for the power evaluation. The results are given in Tables We first evaluated the type I error and power of the proposed LRT in the context of multilocus association analyses with different number of SNPs and various random effects variance component. To obtain Z =  at random. The results are given in Table This simulation is mainly designed to see the influence of non-normally distributed random effects in multilocus association studies. Here the variable Z in model (5) was generated via the software COSI  based onaffection status  and five covariates including age , smoking status , and three continuous variables Q1, Q2 and Q4. The number of individuals is 697. The details of this data were described in Almasy, et al. [ELAVL4, PRKCB1, PTK2B and SOS2 across all the 200 replicates of the GAW17 data.We applied the permutation-based LRT to the well-known Genetic Analysis Workshop 17 (GAW17) mini-exome sequencing data , which w, et al. . We implThe logistic mixed effects model for the GAW17 data is written asZ is the genotype of the selected gene, and α0- α5 are set to be fixed effects while β are set to be random effects. Our interest is to test H0: τ2 = 0 in model (6) to determine whether a given gene is associated with affection status. Since in this data we know which SNPs are causal, the proportion of p-values less than the given significance level provides a measurement of the empirical power for these methods. The results are given in Table here To reduce computation time of the permutation-based LRT, the simulations and data analyses were conducted with the high performance computing at the School of Public Health of Nanjing Medical University. More specifically, we use the function %dopar% in the R package doMC (version 1.3.3)  with theFrom Table τ2 has a greater influence on the statistical power for these tests than the number of random effects . For example, in Table K becomes from 20 to 40 and τ2 = 0.15, the increasing power for LRT is 0.137; when K = 20 and τ2 increases from 0.15 to 0.20, the corresponding change of power of LRT is 0.210.Table In Table In general, as expected the powers of these tests improve as the proportion of causal markers increases. In Table From Table As a reviewer pointed out that, in fact, the GAW17 data are not purely real data but rather 200 replicates, which were simulated independently based on the true genotype-phenotype association model with the same genotypes but different phenotypes. Therefore, it may be limited for evaluating the performance of these tests. Nevertheless, according to the results presented in Table In this paper we have applied the LRT to GLMM by taking full use of the PQL algorithm and the resulting working response variable. The main difficulties of using LRT in GLMM are the computation of the log-likelihood function for the alternative model  and the derivation of the null distribution of the likelihood ratio statistic. To avoid the direct computation we use the quasi log-likelihood of the working response, which can be deemed to be linear. By doing this the LRT in GLMM becomes computationally feasible. To obtain the null distribution of LRT we use the permutation procedure which has been extensively employed in practice and has proved to be valid ,17,38.In the present paper we only consider the permutation test for the likelihood inference, but extending to other resampling-based methods is straightforward; for example, the parametric bootstrap method. Still the permutation test has an advantage that it requires few model assumptions compared to other resampling-based methods ,17,38. VOur studies have shown that the permutation-based LRT has higher power than the score test and the tests based on mixtures under a wide range of scenarios and it still maintains a reasonably high power even when the random effects do not follow a normal distribution. The LRT has the advantage that it is conceptually simple and easy to implement, but the permutation-based LRT is computationally intensive. However, as Lee and Braun  pointed B in the permutation algorithm. Although having been performed the parallel computation, we still find that the permutation-based LRT is much slower than other methods, especially than the score test. For example, in Simulation 1 when the sample size is 400 and B = 1000 in the permutation-based LRT, running one simulation requires respectively 975 s, 702 s and 1217 s if K = 20, 30 and 40; whereas the score test only needs about 16 s, 23 s and 30 s if running ten simulations. All the times are obtained via the use of the function %dopar% as mentioned before.The computation time for the permutation-based LRT depends on the sample size, the number of random effects and the number of replicates Besides the increasing computational burden of the permutation-based LRT, another disadvantage is that the LRT may be numerically unstable to fit the alternative model when the sample size is limited and the number of the random effects is large. The third shortcoming of the LRT is that its validity and efficiency rely largely on the PQL algorithm, which had been already proved to be seriously biased downward ,22,47,48i) the effects of the markers are very weak; (ii) the non-causal SNPs included in the gene lead to the reduction of power; that is, not all the random effects have nonzero coefficients; (iii) the sample size is relatively small for identifying the association signal; (iv) in the GAW17 data most of the SNPs are rare variants, i.e., their minor allele frequencies are very low and typically less than 0.01 [Finally, we note in Table han 0.01 , which ahan 0.01 ,49. Theshan 0.01 ,50-52.In the present paper the permutation-based LRT was developed for variance component in GLMM. Via simulations and real application it has been demonstrated that the developed LRT method outperforms the existing tests and has a reasonably high power under various scenarios; additionally it is conceptually simple and easy to implement.