Association analysis based on linkage disequilibrium (LD) is an efficient way to dissect complex traits and to identify gene functions in rice. Although association analysis is an effective way to construct fine maps for quantitative traits, there are a few issues which need to be addressed. In this review, we will first summarize type, structure, and LD level of populations used for association analysis of rice, and then discuss the genotyping methods and statistical approaches used for association analysis in rice. Moreover, we will review current shortcomings and benefits of association analysis as well as specific types of future research to overcome these shortcomings. Furthermore, we will analyze the reasons for the underutilization of the results within association analysis in rice breeding. Oryza sativa L.) is one of the most important components of the human diet in many regions of the world and feeds more than 50% of the world's population. Thus, increasing the yield of rice through genetic improvement is important to meet the food demands of a growing global population. After the completion of the rice genome, extensive genetic studies have been conducted to characterize the biological functions for hundreds of rice genes.Rice . Therefore, the accuracy of QTL detection largely depends on the selected lines  eliminate the influence of linkage, population structure, and familial relatedness to reduce the false positives in AA; (2) reduce the false negatives that can lead to overcompensating for population structure and relatedness in AA based on a mixed linear model (MLM) or other models, and limited power to detect LD among the populations with lower genetic diversity ; (3) improve the computational capacity of a model for AA; (4) improve the repeatability of significant trait-marker associations in AA; and (5) utilize AA in rice breeding.A review about rice AA will be very useful for AA applications in other plants because rice is considered as a monocot cereal model plant. In this review, we first describe the population type, population structure, LD level and the genotyping methods and statistical approaches used for rice AA. Then, we review the benefits of association analysis, shortcomings, and the possible types of future research to overcome these shortcomings. Furthermore, we also discuss the reasons for the underutilization of AA in rice breeding.GWAS in crops usually requires a permanent resource—a population of diverse (and preferably homozygous) landraces or cultivars that could be re-phenotyped for many traits  in the world  and re-sequencing. High-throughput loci or markers were developed for genotyping the individuals among AA populations based on the genomic variations. The AA methods in model species  will guide and push forward the development of the other plants AA.Information about the population structure and extent of LD within the population is of fundamental importance for association mapping  were identified within 20 rice varieties/landraces  were detected within the entire population by different statistical methods, and SG 1 was divided into four sub-subgroups, including intermediate seasonal indica, sub-tropical indica, late seasonal indica, and early seasonal indica  dropped to half of its maximum value. Significant LD surrounding the Xa5 locus of rice was observed between the sites up to 100 kb apart  than in the japonica subpanel  markers, restriction fragment length polymorphism (RFLP) markers, inter simple sequence repeat (ISSR), insertion-deletion (InDel), and diversity arrays technology (DArT) markers were not used so frequently Table . For CGAThe technique of GBS has recently been successfully utilized for AA studies in maize , which determined candidate loci associated with ozone tolerance.Furthermore, agronomic and quality traits as well as rice food safety under fluctuating environment of earth may be the hotspot for future rice AA. It was found that chronic ozone exposure significantly decreased seed weight, culm length, number of primary rachis branch, and number of spikelets per panicle in an Nucleotide diversity measure, discriminant analysis, elliptic fourier analysis, nested clade analysis, principle component analysis, generalized linear model (GLM), MLM, logistic regression (LR), and simple linear model (SLM) were used for rice AA Table . There wIt is important to point out more explicitly that GWAS is likely to identify associations of common alleles, but are not suitable for the analysis of rare alleles/haplotypes due to statistical significance issues unless the use of specifically designed balanced population. Almost all of the statistical methods used for rice AA could filter the variants or loci with minor allele frequency (< 0.05), and this leads to missing of some functional rare alleles. Therefore, a new statistical method, called as Anderson-Darling (A-D) test, which could control rare alleles in GWAS, was reported. Moreover, the A-D test is one of the useful complement for GWAS analysis of complex quantitative traits in rice AA. The A-D test balances the false positives and statistical power  cut-off for significance in rice AA ranged from 10−8 to 0.05  are often recommended to control the effects of population structure in association studies, and these three methods are well-summarized in review of Gupta et al. . HoweverMoreover, the population structure identified by principal component analysis (PCA), principal coordinate analysis (PCoA), and LAP is highly related to the known germplasm type information as well as the STRUCTURE subgroups  caused by overcompensating corrections of multiple testing for significant associations and problems with rare alleles.q-value  Bonferroni correction Moran, ; (2) Hol Storey, ; and (5) Storey, . Gupta e Storey,  has expl Storey, .Furthermore, GWAS has low power for rare alleles, which makes a substantial proportion of natural variations. The sites with weaker effects may play an important role in evaluation of traits like the sites with stronger effects. Some studies about the detection of rare alleles have been performed. For instance, several statistical models for rare alleles in AA have been summarized Gibson, . MoreoveAbout 44% of the SNPs are of low frequency  in rice. It has been concluded that the use of a large sample size or the construction of multiple bi-parental cross populations  may be helpful in rice GWAS for rare alleles  choose large sampling populations. Large sampling populations may contain more genetic recombinations and could be helpful in reducing false negatives  have led to the discovery of thousands of genetic signals across the rice genome associated with plant quantitative traits. However, as GWAS is a relatively new approach, there are few studies that have conducted follow-up tests of candidate genes. It is time to slow down the pace of GWAS and think about how we can conduct analyses post-GWAS. Our opinion about post-GWAS is as follow: we should concentrate on the identification of true significant trait-marker associations, especially those loci that have not been detected in previous linkage mapping, and dissecting the function of candidate genes or loci by using reverse genetics and bioinformatic tools, including meta-analysis as well as a combination of CGAS and GWAS. Si et al.  identifiThis review was conceived by PZ, KZ, and HT, the manuscript was drafted by PZ, KZ, MS, and HT. HT acted as a co-corresponding author. All authors read and approved of the final manuscript.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.


Inbreeding and relatedness in wild panda populations are important parameters for panda conservation. Habitat loss and fragmentation are expected to increase inbreeding but the actual inbreeding levels in natural panda habitats were unknown. Using 150,025 SNPs and 14,926 SNPs selected from published whole-genome sequences, we estimated genomic inbreeding coefficients and relatedness of 49 pandas including 34 wild pandas sampled from six habitats. Qinling and Liangshan pandas had the highest levels of inbreeding and relatedness measured by genomic inbreeding and coancestry coefficients, whereas the inbreeding levels in Qionglai and Minshan were 28–45% of those in Qinling and Liangshan. Genomic coancestry coefficients between pandas from different habitats showed that panda populations from the four largest habitats, Minshan, Qionglai, Qinling and Liangshan, were genetically unrelated. Pandas between these four habitats on average shared 66.0–69.1% common alleles and 45.6–48.6% common genotypes, whereas pandas within each habitat shared 71.8–77.0% common alleles and 51.7–60.4% common genotypes. Pandas in the smaller populations of Qinling and Liangshan were more similarly to each other than pandas in the larger populations of Qionglai and Minshan according to three genomic similarity measures. Panda genetic differentiation between these habitats was positively related to their geographical distances. Most pandas separated by 200 kilometers or more shared no common ancestral alleles. The results provided a genomic quantification of the actual levels of inbreeding and relatedness among pandas in their natural habitats, provided genomic confirmation of the relationship between genetic diversity and geographical distances, and provided genomic evidence to the urgency of habitat protection. Over recent years, knowledge of the panda genetic diversity based on the analysis of molecular variants has been growing at a fast pace. A whole-genome sequence study using structure analysis and principal component analysis (PCA) classified wild pandas sampled from all six panda habitats into three genetically different groups [Understanding genetic diversity including genetic relatedness and inbreeding levels in wild panda populations is important for preserving panda genetic diversity through t groups  but thist groups ,3, inbret groups , and vart groups . Currentt groups . HoweverAlthough studies using microsatellite markers contributed to the understanding of panda genetic diversity and relationships, the small number of microsatellite markers could only cover a small fraction of the panda genome, leaving unanswered question whether the limited genome coverage could have affected the results. In contrast, single nucleotide polymorphism (SNP) markers from the panda whole-genome sequence data would offer the most complete coverage of the panda genome , and shoHabitat size and genetic diversity are two related issues in panda conservation. Habitat loss was one of the major factors contributing to the declines of the wild panda population leading to 1988 when China’s Wildlife Protection Law was enacted . The recIn this study, we estimated genomic inbreeding and relatedness in wild panda populations within and across their natural habitats using the approach of genomic relationship and high quality SNPs covering the entire panda genome selected from the panda whole-genome sequence data . This daThe forty-nine pandas used in this study were from a published study , with thftp.ddbj.nig.ac.jp/ddbj_database/dra/fastq/SRA053/SRA053353. Trimmomatic [The resequencing reads for the forty-nine pandas deposited in the NCBI Sequence Read Archive (SRA) under accession SRA053353 were downloaded from DNA Data Bank of Japan at: mmomatic  was usedmmomatic  with BWAmmomatic  using thmmomatic  for sortAg) and genomic dominance relationship matrix (Dg) were calculated using three definitions of genomic relationships. The three methods used in this study were Definitions I, IV and IVb implemented by GCORRMX program in the GVCBLUP program [f) was calculated based on the diagonal element of the individual (Aii) in the Ag matrix, i.e.,The genomic inbreeding coefficient of an individual was calculated based on the individual’s own diagonal element in the genomic additive relationship matrix , and a c program ,22, wher program , and Def program ,23 was sf–I, f–IV and f–IVb respectively. The genomic mean coancestry coefficient within a habitat was defined as the average of all fjk values between n pairs of individuals in the habitat, i.e.,fjk) was calculated as:jk = genomic additive relationship between individuals j and k. Genomic dominance relationship or fraternity coefficient (djk) between individuals j and k was calculated as the corresponding off-diagonal element in Dg, i.e.,The genomic inbreeding coefficients corresponding to Definitions I, IV and IVb will be denoted by fficient ,24, genoTo interpret the degree of severity of genomic inbreeding and coancestry coefficient as well as dominance relationships, we compare the genomic estimates with the pedigree expectations of typical relationships including parent-offspring, full-sibs and half-sibs , and witAA and aa genotypes) to exclude parent-offspring relationship between two individuals. In addition, multidimensional scaling (MDS) of the IBS matrix was calculated and plotted. The IBD, IBS and MDS measures were calculated using PLINK [We estimated additional measures of genomic relatedness and similarity: probability of alleles identical by descent (IBD) to serve as a measure of genomic relatedness and a comparison with genomic conancestry coefficient, probability of alleles identical by state (IBS) as a measure of common alleles shared by two individuals, probability of SNP loci identical by genotype (IBG) as a measure of common genotypes shared by two individuals, and probability of non-shared genotypes between two genotypes (NSG) as a measure of opposing genotypes without common alleles , the overall exclusion probability is: Q = 1–1.39(10)−56. Therefore, the expected exclusion power of the 150,025 SNPs to exclude a false parent-offspring relationship in pandas is virtually 100%. Even if the 150,025 SNPs only had 10% of independent SNPs, the overall exclusion would be Q = 0.9999974, still virtually 100%. Yet, these are the most conservative estimates assuming the smallest observed NSG value for any panda and the smallest expected NSG value per SNP.The NSGAA and aa genotypes) to exclude parent-offspring relationship between two individuals.Genomic inbreeding, additive and dominance relationships were estimated using two sets of SNP markers (the 150K and the 15K SNP sets) for forty-nine pandas including thirty-four wild pandas sampled from all six panda habitats, Minshan, Qionglai, Qinling, Liangshan, Daxiangling and Xiaoxiangling [f) of each panda by the three methods of Definitions I, IV and IVb [f-I, f-IV and f-IVb respectively. Genomic inbreeding coefficients by these three methods mostly overlapped for individual pandas  and ). Although Liangshan had significantly higher genomic inbreeding coefficients than Minshan and Qionglai, the interpretation of the Liangshan results requires caution because Liangshan only had two pandas in the sample. The lowest estimate of genomic inbreeding coefficient for the Qinling pandas (0.090) was above the average inbreeding levels of Minshan and Qionglai, indicating that the Qinling population likely had widespread inbreeding. The results of average inbreeding coefficients were consistent with the population sizes because the Qinling and Liangshan populations with high levels of inbreeding were smaller than the Minshan and Qionglai populations with relatively low levels of inbreeding. According to the Third National Panda survey, the numbers of pandas in Minshan, Qionglai, Qinling and Liangshan were 708, 437, 275 and 115 respectively [f ≥ 0.10 by f-IV and Qionglai had four such pandas (27%), and Minshan and Qionglai each had one panda with f ≥ 0.125 that is equivalent to the inbreeding level of half-sib mating  (The average genomic inbreeding coefficients ( N = 15) , Fig 1.  N = 15) . Althougectively  Table 1f¯ calculectively –32. Althb mating . The Daxf-IV), consistent with the expectation that crossbred pandas between habitats without common ancestors should have ‘0’ inbreeding coefficients if different habitats are genetically independent as shown in the next section. Two Minshan × Liangshan crossbreds had genomic inbreeding coefficients f = 0.082–0.164 by f-IV using the 150K SNP set  calculated as the average of genomic coancestry coefficients between all pairs of individuals between two different habitats, ranging from fm = −0.070 between Qinling and Qionglai to fm = −0.010 between Liangshan and Qionglai  plots for all pairs of the first four MDS dimensions  for all The Daxiangling and Xiaoxiangling habitats  each had one panda in this study. Results of these two pandas showed that the Daxiaingling and Qionglai populations either were the same population or shared common ancestors, whereas the Xiaoxiangling panda either migrated from Qionglai or had a problem of DNA sample mixing with a Qionglai panda.fm = 0.022 with the fifteen Qionglai pandas, compared to fm = 0.025 within Qionglai, and was unrelated to pandas in the other habitats (-0.069 ≤ fm ≤ 0.007) (fjk) involving GP38 was 0.039 between GP38 and a Qionglai panda (GP27). Other than Qionglai pandas, the highest fjk involving GP38 was fjk = 0.004 between GP38 and a Minshan panda (GP14) (The Daxiangling panda (GP38) had genomic relationship estimates consistent with those of a Qionglai panda. This panda had ≤ 0.007) . The higa (GP14) . These rdjk = 0.430 and fjk = 0.388. The second highest values of any other panda pair were djk = 0.196 between GP23 and GP27 (two Qionglai pandas) and fjk = 0.305 between GP5 and GP10 (two Qinling pandas)  parent-offspring and half-sib relations were expected to have no dominance relationship (djk = 0) [The Xiaoxiangling panda (GP39) and a Qionglai panda (GP31) had the highest genomic dominance relationship and coancestry coefficient:  pandas) . The addSummarizing the analysis of wild pandas from all six habitats, the four largest panda populations in Minshan, Qionglai, Qinling and Liangshan were genetically unrelated with little genetic exchange between them. Qinling and Liangshan had highest internal levels of relatedness, and Minshan and Qionglai each had a panda with genomic relationships exceeding those expected from a half-sib mating system while on average had low levels of relatedness. The Daxiangling population either was part of the Qionglai population, or shared common ancestors with the Qionglai population, or had a panda migrated from Qionglai. The genetic status of Xiaoxiangling should be considered unknown.fm) between different habitats in fm) and the average similarity measures of IBS, IBG and NSG between different habitats in fjk≤ 0), and this prediction was consistent with most of the actual observations. Although all similarity measures including IBS, IBG and NSG were significantly correlated with the geographical distances and with each other  having f ≥ 0.125 and 23.8% of the pandas having f ≥ 0.25 [The high levels of inbreeding most likely were due to longtime accumulation of inbreeding rather than recent inbreeding between close relatives, as indicated by the low dominance relationships for most panda pairs within each habitat. Among full-sib, half-sib and parent-offspring relationships, only full-sibs are expected to have nonzero dominance relationships with the expected value of The inbreeding situation in the Qionglai and Minshan habitats was considerably more optimistic than in Qinling and Liangshan, because the inbreeding levels of b mating . HoweverThe result that the four largest habitats were genetically unrelated provides an opportunity to use habit-controlled breeding to avoid hidden inbreeding by using mates from different habitats because mates from different habitats are expected to share no IBD alleles. The habitat origin of a mating candidate can be determined from of the pedigree of the captive panda population . This tyGenome-guided breeding could reveal hidden inbreeding of a potential breeding pair by estimating the genomic coancestry coefficient of each potential mating pair. The threshold value of genomic coancestry coefficient to exclude a potential matting pairs from the breeding plan should be established by comparing observed genomic coancestry coefficients with those calculated from pandas with known relationships such as full-sibs, half-sibs, and parent-offspring. Genome-guided breeding should genotype SNPs for all available pandas particularly breeding pandas to provide complete understanding of panda relatedness. Genomic coancestry coefficient between each breeding pair can be used to predict the inbreeding level of the hypothetical offspring of this breeding pair because parental genomic coancestry coefficient was shown to have a high correlation with the offspring’s pedigree inbreeding coefficient . The resThe implementation of genome-guided breeding within the framework of ‘genome-guided conservation’ is most ideal to fully utilize all available SNP information in captive and wild panda populations. A DNA bank for all captive and wild pandas is the foundation of genome-guided conservation, and such DNA bank should benefit panda conservation and research for many years to come. Accordingly, a database of panda sequences and SNP genotype data for all pandas should be established. The SNP data will serve multiple purposes for the captive and wild populations, including calculation of genomic inbreeding and coancestry, parentage and sex determination, updating pedigree using genomic coancestry for the captive population, genome-guided breeding in the captive population, construction of genomic pedigree for the wild populations, estimation of genetic diversity in the wild populations, and assessing the origin of random pandas. The knowledge of inbreeding and relatedness in wild pandas is helpful for assessing the genetic impact of reintroducing a captive-born panda into the wild (candidate panda). The relatedness between the candidate panda and different habitats can be assessed by analyzing the genomic coancestry coefficients between the candidate panda and wild pandas in different habitats. This analysis will provide genomic evidence for either preserving the genetic diversity by releasing the candidate panda into a habitat with similar genomes, or for reducing inbreeding by releasing the panda into a genetically unrelated habitat known to have a high level of inbreeding such as Qinling. The SNP database could provide rapid identification of the origin of random pandas such as rescued pandas and deceased pandas in the wild. An example of such random pandas would be the lone female panda that was killed in late 2014 in Yunnan province where no panda had been known to exit in modern times. Analysis of the SNP data of this lone female panda against the SNP database could identify its origin, and possibly its relatives if the SNP database were sufficiently complete in covering the captive and wild panda populations. Results of genomic coancestry and similarity in this study indicate that adding the sequence data of this lone random female panda to the sequence data of the forty-nine pandas in this study could yield evidence whether this panda was from any of the four largest populations, Minshan, Qionglai, Qinling and Liangshan. Ultimately, genome-guided breeding and conservation will provide complete information about each panda’s genome for breeding and reintroduction and will allow precision breeding and conservation.The estimates of panda inbreeding coefficients and relatedness using nineteen microsatellite markers  were thef-IV using the 150K SNP set Click here for additional data file.S2 FigA: Probability of alleles identical by state (IBS) as a measure of common alleles shared by a pair of individuals. B: Probability of SNP loci identical by genotype (IBG) as a measure of common genotypes shared by a pair of individuals. C: Probability of non-shared genotypes (NSG) as a measure of two genotypes of a pair of individuals without at least one common allele. D: Dominance relationship or fraternity coefficient (djk) that is particularly useful for identifying full-sibs. These figures provided additional evidence that Qinling and Liangshan to have high degrees of genomic relatedness and similarity, and the four largest habitats  to be genetically unrelated. Crossbreds between two habitats generally had visible genomic relatedness with their ancestral habitats for all similarity measures except dominance relationships.(PDF)Click here for additional data file.S3 FigC1-C4 are the four MDS dimensions calculated by PLINK . IBS = p(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 Table(PDF)Click here for additional data file.S1 Text(PDF)Click here for additional data file.


For a family-based sample, the phenotypic variance-covariance matrix can be parameterized to include the variance of a polygenic effect that has then been estimated using a variance component analysis. However, with the advent of large-scale genomic data, the genetic relationship matrix (GRM) can be estimated and can be utilized to parameterize the variance of a polygenic effect for population-based samples. Therefore narrow sense heritability, which is both population and trait specific, can be estimated with both population- and family-based samples. In this study we estimate heritability from both family-based and population-based samples, collected in Korea, and the heritability estimates from the pooled samples were, for height, 0.60; body mass index (BMI), 0.32; log-transformed triglycerides (log TG), 0.24; total cholesterol (TCHL), 0.30; high-density lipoprotein (HDL), 0.38; low-density lipoprotein (LDL), 0.29; systolic blood pressure (SBP), 0.23; and diastolic blood pressure (DBP), 0.24. Furthermore, we found differences in how heritability is estimated—in particular the amount of variance attributable to common environment in twins can be substantial—which indicates heritability estimates should be interpreted with caution. Under polygenic inheritance, the effects of segregation at single loci are assumed to be too small to estimate individually and the total genetic variance has been considered to identify the overall genetic effect underlying a trait. Genetic variance consists of additive, dominant, and epistatic components. However, the amount of dominant variance is usually assumed to be relatively small compared to the additive variance and is never identified without a family-based sample that includes bilineal relatives. Similarly, estimation of the epistatic variance (which may include additive components) requires special relationships in family data and is also assumed to be small. Therefore, the estimation of genetic variance has been confined to the additive genetic variance and, to estimate heritability, the proportion of the phenotypic variance attributable to only additive genetic variance has been used even though this can lead to biased estimation in the presence of dominant variance, epistatic variance, and gene × environmental interaction .In general, a parameter allowing for additive polygenic variance can be incorporated into the phenotypic covariances between pairs of individuals, and there are two main ways for incorporating this parameterization. In the absence of population substructure, dominance or any environmental effect shared by family members, the phenotypic covariances can be expressed as a function of the kinship coefficient between family members in family-based samples. Under this parameterization, the additive polygenic variance is obtained from the covariances between family members using variance component models –5. AlterIn this paper, motivated by wishing to calculate the heritability of cardiovascular disease related traits in the Korean population, we examine to what extent estimates of heritability depend on how they are estimated. We calculate the heritability of various traits related to cardiovascular disease in a Korean population using two family-based cohorts, the healthy Twin Study, Korea (HTK)  and AnsuThree cohorts, all part of the Korean Genome Epidemiology Study (KoGES) which is an ongoing prospective epidemiological study, have been utilized to estimate heritability: the KARE project  cohort aP values for departure from Hardy-Weinberg equilibrium (HWE) less than 10−5, with genotype call rates less than 95%, or minor allele frequencies (MAF) less than 0.01, leaving 350,364 SNPs for subsequent analysis. Individuals with low call rates , high heterozygosity , gender inconsistencies (n = 41), or serious concomitant illness (n = 101) were excluded from analysis, along with 601 individuals related or identical whose computed average pairwise identical in state value was higher than that estimated from first-degree relatives of Korean sib-pair samples (>0.8). In total 8,842 individuals were analyzed. In 20 randomly selected duplicate samples, we found that genotype concordance rates exceeded 99.7%, with no single SNP excessively discordant.The KARE project, with 10,038 participants who were living in Ansung  and Ansan (urban), was initiated in 2007 for large-scale genome-wide association studies (GWAS) based on the Korean population. Among the 10,038 participants, 10,004 individuals were genotyped for 500,568 SNPs with the Affymetrix Genome-Wide Human SNP array 5.0. We discarded SNPs with P values for departure from HWE less than 10−5 or MAF less than 0.01. In addition, SNPs were excluded if Mendelian errors or double recombinants were found in at least 3 families, and in total 520,484 SNPs were used for analysis. We calculated the proportion of genotypes identical in state between individuals in each family and excluded those with any inconsistency between the genetic and reported relationship (n = 58). Also, individuals who had coding errors for MZ/DZ status (n = 2) were excluded, and as a result genotypes for 1801 family members were available for analysis. Among the genotyped individuals, there are 4 pairs of MZ twins and 393 genotyped individuals whose MZ twin siblings were not genotyped. Also 84 pairs of DZ twins were genotyped, and there are 16 additional genotyped individuals whose DZ twin siblings' genotypes were unknown. There are 162 nuclear families and 3 families consisting of individuals in three generations that include MZ/DZ twins.The HTK cohort was initiated to identify genetic variation responsible for complex traits as well as the role of the environment in the etiology of complex diseases. Some healthy twins in this cohort were recruited through advertisements in a nationwide newspaper and through posters in about 300 hospitals. Other twin families were selected from the large Korean Genomic Cohort Study of adult individuals and the KoGAP. Then the family members of the selected twins were recruited into this cohort. It should be noted that health status was not considered for sampling. This type of family study can be useful for detecting quantitative trait loci and genetic variations underlying common diseases . Among thttp://dx.doi.org/10.1155/2015/671349) reveal that any ascertainment bias would not be substantial. In these samples, 456 individuals who were included in the KARE project were genotyped with the Affymetrix Genome-wide Human SNP array 5.0, and another 781 individuals were genotyped with the Affymetrix Genome-wide Human SNP array 6.0. Individuals were excluded if they reported relationships in the family inconsistent with the genotypic relationships estimated by the proportion of genotypes identical in state (n = 41) or had unavailable trait data (n = 412). Also, SNPs were excluded if Mendelian inconsistency was found in at least 3 families, the P values for HWE were less than 10−5, or the MAF was less than 0.01. As a result, 784 family members with 417,719 SNPs were used for our analysis.In the Ansung area, 5,018 unrelated and related participants were initially recruited for the KARE project; another cohort to study type 2 diabetes was initiated in this area in 2007. In this cohort, some individuals were selected from the KARE project, and their family members and other individuals from the Ansung area who were not in the KARE project were included, if they were diagnosed as having type 2 diabetes and agreed to participate in this study. This sampling scheme could lead to the presence of ascertainment bias, but the small correlations between type 2 diabetes status and the traits of interest   and the T method  which inyij denote the response for individual j in family i, where i = 1,…, n and j = 1,…, ni; n and ni indicate the number of families and the number of individuals in family i, respectively. Also, let xij indicate covariates that affect yij. Then, denoting πijj′ as the kinship coefficient between individual j and individual j′ in family i, we letσa2, σd2, and σ2. If we also denote the w × w identity matrix by Iw, the linear model used in ASSOC for random mating and only additive effects isФi will be called the familial relationship matrix (FRM) in the remainder of this paper. Furthermore, ASSOC can estimate the variances separately attributable to polygenic, common sibship, and marital effects as described by Elston et al. [Under the multivariate normality model, the covariance between family members can be expressed as a function of their kinship coefficients and this can be utilized to estimate heritability. We estimated the heritability from the family data, separately in the HTK and ASF cohorts, with the ASSOC program in S.A.G.E. (ver. 6.2) . ASSOC in et al. .S.A.G.E. ASSOC was used to estimate heritability in the family-based HTK and ASF cohorts and, for a fair comparison with GCTA, only genotyped individuals were analyzed this way. In the HTK cohort, 1801 genotyped individuals were considered, and there are 4 pairs of MZ twins among those genotyped. S.A.G.E. cannot easily handle MZ twins, and a single individual for each MZ twin was randomly selected for analysis with both ASSOC and GCTA. There is other software available that can handle MZ twins –17 in peσa2. The minor allele frequencies for GRM were estimated by using all individuals even when some individuals were correlated. Because the genetic relationship is estimated with genotypes, GCTA can be applied to both family-based and population-based samples. In addition, the GCTA program can estimate the variance components by both the restricted maximum likelihood (REML) and ML methods. The REML method provides more unbiased estimates of the variance components than the ML method. Therefore we estimated heritability by the REML method when applying GCTA to the KARE project, the HTK cohort, and the ASF cohort, though for these large samples the difference in the estimates is expected to be trivially small. Yang et al. [When large-scale genotypes are available, the GRM can be estimated with the software GCTA  and, insg et al.  suggeste2, and sex as covariates. Residuals from this linear model were used to estimate the empirical correlations between family members and their 95% confidence intervals with FCOR in S.A.G.E.FCOR in S.A.G.E.  can estiIf we assume an additive model with no interaction, the phenotypic variance consists of the genetic variance and a common environmental variance component. However, the variance for environmental effects shared by family members is in general unidentifiable. If we further assume that the amount of covariance between MZ twins attributable to a common environmental effect is similar to that between DZ twins  and thatσc2, the polygenic model provides the following variance-covariance structure between twins:σY2 = var(yij), rDZ = (σc2 + 0.5σa2 + 0.25σd2)/σY2, and rMZ = (σc2 + σa2 + σd2)/σY2. We define two matrices A and B as follows:rMZ and rDZ should be between −1 and 1. We used the REML method to estimate variance parameters, and each parameter was estimated by the average information method [http://healthstat.snu.ac.kr/data/heritability_Rcode.zip. It is simple to show that, ignoring any epistatic effects, 2σDZ − σMZ is σc2 − 0.5σd2 and, if we assume that σd2 = 0, 2σDZ − σMZ becomes σc2 and the proportion of variance attributable to common environment, ρc, can be calculated by 2rDZ − rMZ. If we let P = V−1 − V−1X(XtV−1X)−1XtV−1, the Fisher information matrix for σ2, rMZ, and rDZ can be obtained byn is a sample size and p is the number of covariates. Thus the variance of ρc can be obtained by Ψ−1t. Provided the environmental correlation is the same for both MZ and DZ twins, this estimate can be utilized as a lower bound for the variance attributable to the environmental effects shared by siblings.We separated out all the MZ and DZ twins, whether genotyped or not, from the HTK cohort, so that the members in each family are always either MZ or DZ twins in this analysis. In total, 958 individuals (479 pairs) comprising MZ twins and 224 individuals (112 pairs) comprising DZ twins were analyzed. If we denote the common environmental variance by n method , 20. R cr, between individuals in each pair were generated to be 1/2,1/4,…, 1/128, or 0. A pair of individuals with r = 1/2 indicates siblings or a parent-offspring pair. To generate pairs of individuals with correlation of genotypes r, randomly selected alleles from two individuals were generated to be identical by descent with probability r/2. The minor allele frequencies were generated from U and genotypes were generated with the binomial distribution under Hardy-Weinberg equilibrium (HWE). Monomorphic variants were excluded from the analyses, and all markers were assumed to be in linkage equilibrium. If there are too many redundant SNPs in linkage disequilibrium with the causal variants, the empirical standard deviation of heritability estimates can be inflated and the analysis with GCTA should be modified as indicated by Speed et al. [With extensive simulation studies, we investigated the accuracy of heritability estimates for various scenarios. We generated 5000 pairs of individuals with 100,000 SNPs, and heritability was estimated by GCTA without activating the GRM-cutoff. The individuals in different pairs were generated to be independent and the correlations of genotypes, d et al. .N. To create a polygenic effect we simulated 100 independent causal SNPs and we assumed that all or 50 randomly selected ones of these causal SNPs were genotyped. The additive disease mode of inheritance was assumed and a single SNP genetic effect is denoted by βl. Letting pl be the allele frequency for causal SNP l   and heritability be h2, the genetic effect, βl, was calculated aspl were generated from U or U, respectively, and the genetic effects 2βl2pl(1 − pl), for the 100 causal SNPs, were taken to be equal. σ2 was assumed to be 1 and h2 was taken to be 0.1, 0.3, 0.5, 0.7, or 0.9.The traits were generated by summing a polygenic effect and a random effect. The random effect was generated from From However, even though ASSOC can detect the presence of some environmental effects shared by family members, the heritability estimates it produces for family-based samples are still much larger than those produced by GCTA from population-based samples. Examination of the familial correlations (Table S11) provides evidence that heritability estimated with family-based samples may be inflated if, unlike the analysis we performed with ASSOC, the sibling and marital correlations are ignored. First, the mother-father correlations for height, BMI, and DBP are significantly larger than 0 at the 0.05 significance level, whereas the usual polygenic model assumes that their correlations are 0. At the same time, in large pedigrees this positive mother-father correlation could lead to inflated parent-offspring correlations, but this effect cannot be completely handled in the existing software. Even though ASSOC can allow for a mother-father correlation, the parent-offspring correlation could be larger than expected as a result of the positive mother-father correlation; to allow completely for this, the polygenic variance should be allowed to decrease from one generation to the next. The larger correlations between siblings than those between parents and offspring could thus conceivably be partially attributable to this. Second, correlations between siblings are much larger than those between parents and offspring. In particular for log TG, TCHL, and LDL, this occurs even though the mother-father correlations are around 0. If we assume that dominant polygenic effects are small, the environmental effect shared by siblings seems to be larger than that shared by parents and offspring. The program ASSOC in S.A.G.E. appropriately allows for both a marital correlation and a common sibling component of variance over and above that due to an additive polygenic variance, though that variance is assumed to be constant across generations.ρc shows that the proportion of variance explained by shared environment for height may be 69.4%, and we can conclude that the correlations generated by the environmental effects shared by family members are usually much more substantial than we expect.U or U, respectively. Each case was summarized with 200 replicates, and in Figures h2 was set at 0.5. The results show that heritability estimates are always around the proportion of variances explained by all causal variants, 0.5, when all the causal SNPs are used to estimate the GRM. However, when half the causal SNPs are used to estimate the GRM and r is larger than 0.125, heritability estimates are overestimated. There is a tendency for the overestimation to be proportional to r. Figures r. In Supplementary Figures  3–6  h2 was assumed to be 0.1, 0.3, 0.7, or 0.9, respectively, and we found that our results are the same as in Figures Figures U0,0. or U, TCHL, HDL, LDL, SBP and DBP. Heritability in three Korean populations was estimated with S.A.G.E. and GCTA, and variance-covariance matrices for their linear mixed models were parameterized with FRM and GRM respectively. Supplementary Table S10: presents missing rates for height, BMI, log(TG), TCHL, HDL, LDL, SBP and DBP in each cohort. Supplementary Table S11: contain correlations between family members. The mother-father, parent-offspring and sibling correlations, and their 95% confidence intervals were estimated. Supplementary Figures S1-S2: present Q-Q plots for height, BMI, log(TG), TCHL, HDL, LDL, SBP and DBP in each cohort. Supplementary Figures S3-S6: present heritability estimates for various levels of genetic correlation with 10,000 individuals when heritability was assumed to be 0.1, 0.3, 0.7, or 0.9.


The results show that the HC approach is preferred for detecting weak genetic effects.Because of low statistical power of single-variant tests for whole genome sequencing (WGS) data, the association test for variant groups is a key approach for genetic mapping. To address the features of sparse and weak genetic effects to be detected, the higher criticism (HC) approach has been proposed and theoretically has proven optimal for detecting sparse and weak genetic effects. Here we develop a strategy to apply the HC approach to WGS data that contains rare variants as the majority. By using Genetic Analysis Workshop 18 "dose" genetic data with simulated phenotypes, we assess the performance of HC under a variety of strategies for grouping variants and collapsing rare variants. The HC approach is compared with the minimal  Whole genome sequencing (WGS) is able to reveal complete genetic variations across the entire genome. It is deemed as the hope of decoding the mystery of genetic pathology to complex traits . CompariTo design appropriate association tests, it is critical to understand the properties of the data and the putative genetic variants. After the "lower fruits" have been picked up, the remaining variants to be identified usually have weak statistical associations with the response, because of either low allelic effects or rare variations . At the p-value from the association test of each genetic variant follows a uniform distribution. Let p-values from n individual variants. Under the null, i/n. As a maximum of the normalized empirical process, the HC statistic measures how much the p-values depart from the uniform distribution:The HC procedure was designed for multiple hypotheses testing  and can p-values as input, it is readily applicable for detecting genetic associations for either quantitative or binary traits in either population-based or family studies as long as the corresponding p-values are appropriately obtained. Here we used the two-tailed p-values to accommodate two directions of genetic effects. In analyzing the GAW18 data, the original genotype of common variants and the collapsed genotypes of rare variants (see later discussion) were applied to get p-values and thus the HC statistic.Because the HC statistic uses a set of The sequence kernel association test (SKAT) is a supervised test for the association between genetic variant groups and a continuous or dichotomous trait while accounting for covariates . SKAT prp-value method (minP), each individual variant within a group is tested, and the smallest p-value is used to measure the significance of the group.In the minimum We considered four strategies to group variants according to fixed genome windows with lengths 10, 100, or 500 kbps and functional genes from the UCSC Known Gene [A variant is defined as rare if its MAF is less than a threshold. Here the MAFs were estimated by the proportion of the minor alleles among the total observed alleles. We considered either 0.01 or 0.05 as the threshold. Within each window group, the rare variants allocated between any adjacent common variants were collapsed by two strategies: equal-weight sum or Madsen-Browning (MB) weight sum  of the op-value for a group window is the proportion of the permutation statistics that are equal or more extreme than the corresponding statistic calculated from data.For HC and minP, a permutation test is needed to accommodate the different variant numbers and correlation structures within different genome segment windows. Specifically, for each genome segment window, 1000 permutations of the genotype data were made, and test statistics were calculated. The empirical Considering population-based studies, we included 142 independent individuals who have no missing genotype to the data analysis. We used the WGS dose files of chromosomes 1, 3, and 5 as the genotype data and the systolic blood pressure (SBP) as the phenotype. We considered two concepts of statistical power. First, the power indicates the ability of detecting overall true associations. It was estimated by the true positive rate of true association windows. Second, the power measures the ability of detecting a specific variant group with a specific genetic effect pattern. It was estimated by the true positive rate of the 200 simulation replicates. The knowledge of the simulated true variants was only used for evaluating the power of the association test, not for the design of the tests and data analysis.p-values of false windows on chromosome 3 based on 10-kbps fixed windows for grouping variants. Certainly, the type I error is well controlled because the observed p-values are close to the expectation and the values of genomic inflation factor λ[We assessed the type I error control for HC under various grouping and collapsing strategies. Figure  factor λ is near p-value cutoffs, bigger windows have higher power. However, the 10-kbps window is preferred when the p-value cutoff is less than 0.1, where it is of more practical interest for controlling type I errors appropriately. The middle panel in Figure p-value cutoff is less than 0.05. It seems the MB weight does not help much.We compared the power of HC test for detecting true association windows on chromosome 3 under different grouping and collapsing strategies. The left panel in Figure p-values. However, minP is not good for weak effects because its power curve drops quickly for larger p-value cut-offs. Our power cure is essentially a receiver operating characteristic curve if a full range of cutoffs in  is used. Regarding to the area under curve (AUC), HC has the largest value (0.6555) followed by SKAT (0.6496) and minP (0.6327).We compared the power of the above association tests for detecting all true 10-kbps windows on chromosome 3, with equal-weight collapsing and MAF threshold 0.05 for rare variants. From the right panel of Figure Figure To study the capabilities of the association tests in detecting specific signal patterns, we studied their power  in detecting specific windows over 200 simulation replicates. As illustrated in Figure We compared the HC and SKAT at a "plain" setup with equal weighting scheme and fixed windows, with no bias in choosing variants engaged into the test procedure. This helps us to understand the statistical foundation of these two methods for fair comparison. HC is likely preferred for weak and sparse signals and did show stronger performance in this scenario according to the WGS data and the GAW18 simulations. On the other hand, both methods have great potential to improve the power through, for example, including environmental factors as covariates into the testing.p-values for genome-wide type I error control. Third, more sophisticated collapsing strategies should be studied based on prior information of genetic architectures. For example, we can consider weighting based variants' apparent effect sizes [p-value combination approach, it can be flexibly applied to broader context, such as for family data analysis based on mixed effect models or for meta-analysis, which combines different data resources or research results.Several future works could be considered based on the limitations of the current study. First, it would be nice to further confirm the patterns of comparisons among these association methods by simulated and real data with much larger sample size. Second, asymptotic distribution or larger permutations are needed for HC to obtain more accurate ct sizes  or data-ct sizes . We can ct sizes  or accorct sizes . Last, bWe proposed a framework to apply the HC approach to WGS data. Our analysis of GAW18 simulation data shows that the accurate type I error control by HC is not affected by various grouping and collapsing strategies for rare variants. Our results show that smaller grouping windows  are preferred over larger windows or gene-based grouping. For collapsing rare variants at a type I error rate less than 0.05, the MAF threshold of 0.01 is superior to 0.05, and a MB-weighted sum does not provide improvement over an equal-weighted sum. HC likely performs better than SKAT and the minP method in detecting weak and sparse genetic effects.The authors declare that they have no competing interests.ZW designed the overall study. JX, LY and ZW conducted statistical analyses and drafted, read, and approved the final manuscript.


Identifying subpopulations within a study and inferring intercontinental ancestry of the samples are important steps in genome wide association studies. Two software packages are widely used in analysis of substructure: Structure and Eigenstrat. Structure assigns each individual to a population by using a Bayesian method with multiple tuning parameters. It requires considerable computational time when dealing with thousands of samples and lacks the ability to create scores that could be used as covariates. Eigenstrat uses a principal component analysis method to model all sources of sampling variation. However, it does not readily provide information directly relevant to ancestral origin; the eigenvectors generated by Eigenstrat are sample specific and thus cannot be generalized to other individuals.We developed FastPop, an efficient R package that fills the gap between Structure and Eigenstrat. It can: 1, generate PCA scores that identify ancestral origins and can be used for multiple studies; 2, infer ancestry information for data arising from two or more intercontinental origins. We demonstrate the use of FastPop using 2318 SNP markers selected from the genome based on high variability among European, Asian and West African (African) populations. We conducted an analysis of 505 Hapmap samples with European, African or Asian ancestry along with 19661 additional samples of unknown ancestry. The results from FastPop are highly consistent with those obtained by Structure across the 19661 samples we studied. The correlations of the results between FastPop and Structure are 0.99, 0.97 and 0.99 for European, African and Asian ancestry scores, respectively. Compared with Structure, FastPop is more efficient as it finished ancestry inference for 19661 samples in 16 min compared with 21–24 h required by Structure. FastPop also provided scores based on SNP weights so the scores of reference population can be applied to other studies provided the same set of markers are used. We also present application of the method for studying four continental populations .We developed an algorithm that can infer ancestries on data involving two or more intercontinental origins. It is efficient for analyzing large datasets. Additionally the PCA derived scores can be applied to multiple data sets to ensure the same ancestry analysis is applied to all studies.The online version of this article (doi:10.1186/s12859-016-0965-1) contains supplementary material, which is available to authorized users. Genome wide association (GWA) studies usually evaluate data from thousands of individuals. Identifying the subpopulations within the data set and inferring biogeographic origins of the samples are important steps in the conduct of any study. Not allowing for population substructure in the analysis will introduce false positives . FurtherWe selected 2318 SNPs across the whole genome based on having a large fixation index (FST) value among European, African and Asian populations for PCA analysis. We conducted PCA analysis of 505 Hapmap samples with European, African or Asian ancestry along with a collection of 19661 additional samples of unknown ancestry. To perform PCA, we use the eigendecomposition method, which parses the covariance relationships among markers.Define For the mean-centered data matrix, we need to compute the mean on each SNP,Then, we generate the mean-centered data matrix asN > P). We construct the covariance matrix asAssume that there are larger number of samples than number of SNPs  and the matrix λi.In PCA, the ZN × k = YN × P × PP × k (1). Where k = 2 or 3 is adequate for capturing ethnic similarities when considering 3 or 4 continental origins respectively. The eigenvectors areFor our purposes we find that selection of SNPs to maximize interancestral variability ensures that the first few eigenvectors capture interpopulation variation. We therefore obtain a low dimensional projection, score matrix Once we select the first k eigenvectors, named as SNP weights, which we would like to keep among the principal components computed from the discovery data, we can predict new scores in the new data using pre-computed SNP weights.Let PP × k from the original analysis, compute the new score matrix, Z*N × k = WN × P × PP × k (2). For prediction of new score matrix, we recommend that the SNP weights should be generated from large samples (N> > P) to avoid variance shrinkage if the eigenvectors will be applied to a subsequent data set [Using the SNP weights data set .We started with three well characterized continental populations, studied by the HapMap consortium of European, Asian, and African descent, since characterizing ancestry for these populations is often a major goal in genome-wide association studies. The centroid of each known Hapmap population was characterized by the multivariate mean of the first and second score Fig. . A trianhttp://hapmap.ncbi.nlm.nih.gov/downloads/genotypes/hapmap3_r3/plink_format/.The approach can also be generalized to include additional populations. When we plotted the first three PC scores for individuals coming from four distinct populations , we observed a three-dimensional tetrahedron instead of a two dimensional triangle for three populations, which suggested we could extend the triangle algorithm to a tetrahedron-based algorithm to incorporate four populations. When applied to four populations, a similar approach to that taken for 3 populations is employed. We first define regions for which the closest point to an ancestry tetrahedron is a vertex, and for those individuals, a single continental ancestry is assigned. For points outside the tetrahedron but closest to a side, we project to the nearest face of the tetrahedron (as described in the Supplementary methods) and then use equation 4 to estimate the proportions of ancestry for each of three origins for that face. For points inside the tetrahedron, an extension of equation 4 to encompass a mixture of 4 populations is applied. In this case, the projections are to each of the four faces of the tetrahedron. For interior points, once the sample was mapped to the two-dimensional face  is modeled by a characteristic set of allele frequencies and the main modeling assumptions are Hardy-Weinberg equilibrium within populations and complete linkage equilibrium between loci within populations . StructuPCA has become a standard procedure in population genetics study for substructure analysis. The eigenvectors from PCA are easy to use for population adjustment in GWA studies. However it lacks the ability to provide clear information for ancestral origin. To fill this gap, we developed an efficient tool for inference of ancestry with PCA scores as the input. The PCA scores generated by FastPop can be used to identify ancestries of individuals or could be used to adjust for population structure in association analysis. The scores are based on SNP weights so the scores of reference population such as Hapmap samples can be applied to other studies provided the same set of markers are used. This characteristic is attractive especially in large consortia studies when multiple independent studies may be analyzed by individual laboratories. The PCA scores generated in one site can be adopted by other sites thus to reduce the repetitive work and ensure consistency among analyses. In current GWA studies, sample sizes keep increasing and now involve tens of thousands individuals. FastPop can be more efficiently implement than Structure in analyzing data with a large sample size.FastPop provides the estimated centroids from a training set considering the users may have a small data set and may require a golden standard for the centroid positions for the populations. Theoretically, the triangle model in FastPop will work without training samples. When the sample size of a data comprising of three populations is big enough, we can calculate the centroids position for each population based on the principal component values from the study samples instead of deriving centroid positions from Hapmap samples. We also tested this idea by inferring ancestry for 19661 study samples without using Hapmap samples, and the correlations of the results between FastPop and Structure were still > 95 %. For this approach, one needs to define a set of centroids for defining ancestral origins.As a further comparative analysis, we also evaluated linear discriminative analysis (LDA) method applied to PCA scores as input to predict ancestry. Compared to LDA, FastPop had better performance in terms of the estimated proportions, consistent performance across different cut off values for decisions and a lower excess positive rate for Europeans. We are using the term ‘excess positives’ here to denote the classification of individuals who may have multiple ancestries into a single ancestry group by LDA  – the Institutional Review Board (IRB) at Dartmouth College. All human subjects involved in this study consented to research involving genetic analysis. All individuals signed Institutional Review Board approved consent documents related to genetic analysis of germline samples. Samples were deidentified prior to analysis. All the analysis was performed at Dartmouth College.Additional file 1:Supplementary Materials. (DOCX 35 kb)


Approaches based on linear mixed models (LMMs) have recently gained popularity for modelling population substructure and relatedness in genome-wide association studies. In the last few years, a bewildering variety of different LMM methods/software packages have been developed, but it is not always clear how (or indeed whether) any newly-proposed method differs from previously-proposed implementations. Here we compare the performance of several LMM approaches  via their application to a genome-wide association study of visceral leishmaniasis in 348 Brazilian families comprising 3626 individuals (1972 genotyped). The implementations differ in precise details of methodology implemented and through various user-chosen options such as the method and number of SNPs used to estimate the kinship (relatedness) matrix. We investigate sensitivity to these choices and the success (or otherwise) of the approaches in controlling the overall genome-wide error-rate for both real and simulated phenotypes. We compare the LMM results to those obtained using traditional family-based association tests  and to alternative approaches implemented in the software packages MQLS, ROADTRIPS and MASTOR. We find strong concordance between the results from different LMM approaches, and all are successful in controlling the genome-wide error rate . We also find high correlation between LMMs and alternative approaches . We conclude that LMM approaches perform well in comparison to competing approaches. Given their strong concordance, in most applications, the choice of precise LMM implementation cannot be based on power/type I error considerations but must instead be based on considerations such as speed and ease-of-use. Recently, statistical approaches known as linear mixed models (LMMs) have become popular for analysing data from genome-wide association studies. In the last few years, a bewildering variety of different LMM methods/software packages have been developed, but it has not always been clear how (or indeed whether) any newly-proposed method differs from previously-proposed implementations. Here we compare the performance of several different LMM approaches (and software implementations) via their application to a genome-wide association study of visceral leishmaniasis in 348 Brazilian families comprising 3626 individuals. We also compare the LMM results to those obtained using alternative analysis methods. Overall, we find strong concordance between the results from the different LMM approaches and high correlation between the results from LMMs and most alternative approaches. We conclude that LMM approaches perform well in comparison to competing approaches and, in most applications, the precise LMM implementation will not be too important, and can be chosen on the basis of speed or convenience. Recently, linear mixed models based approaches have been proposed as appealing alternatives to principal component based approaches when adjusting for population substructure in genome-wide association studies of apparently unrelated individuals Fitting a full linear mixed model for each SNP in turn across the genome is computationally challenging. These computational considerations have led to the development of several faster approximations for constructing tests of the fixed SNP effects of interest in the linear mixed model A limited comparison of several LMM implementations, via application to real and simulated data from Genetic Analysis Workshop 18 (GAW18) Here we expand the investigation of Eu-ahsunthornwattana et al. The approaches are compared via application to real and simulated data derived from a genome-wide association study of visceral leishmaniasis (VL) in 348 Brazilian families comprising 3636 individuals (1970 with both genotype and phenotype data). This Brazilian family data set was used (together with a larger Indian case/control data set) by Fakiola et al. --indep 50 5 2 command in PLINK http://www.staff.ncl.ac.uk/richard.howey/mapthin/). In addition to exploring the kinship estimates provided by various LMM software packages, we also investigated those provided by the software packages PLINK Before embarking on a detailed comparison of different methods, we explored the use of different SNP sets (containing different numbers of SNPs) for estimating pairwise kinship measures, in order to identify a robust set of SNPs that could be used for subsequent comparisons. We considered using either the full genome-wide set of SNPs , a ‘pruned’ set of 50,129 SNPs selected to have minor allele frequencies A comparison of the kinship estimates output by different software packages based on the pruned set of SNPs is shown in Within any given method, we found the kinship measures  and p-values obtained  based on the full SNP set to be very similar to those based on the pruned set, whereas those calculated based on the thinned set were less similar see . The perListgarten et al. oint see . We founk-fold cross-validation The automated version of FaST-LMM-Select available as an option within the current version of the FaST-LMM package uses a slightly different strategy involving We compared the performance of the different LMM and alternative approaches listed in The success of the various approaches in controlling the overall genome-wide type 1 error rate  analysis of the pruned SNPs in PLINK . The resulting genomic control inflation factor was 1.08, considerably smaller than the unadjusted inflation factor of 1.23, but still not perfectly controlled. Inclusion of MDS coordinates as covariates, similar to including principal components scores, might be expected to account for more subtle levels of population substructure than are accounted for by the use of the ADMIXTURE program , which perhaps explains the greater success of this procedure. However the fact that LMM approaches based on estimated kinships still do better  data sets can be obtained from Although the LMM  approaches show similar overall levels of power, an interesting separate question is the degree of concordance between the different methods with respect to the association signals detected. In the real data set we found the p-values obtained at each SNP from the different LMM methods to be highly concordant , while tThe high concordance between the different LMM methods  is also seen for the simulated (weak disease) trait ; similarMost LMM packages  allow a separation between the ‘estimation of kinships’ step and the ‘association testing’ step. This is convenient as it allows the user to read in theoretical or estimated kinships as desired, and to consider using an alternative package for estimating kinships to the one used for the actual association testing. We investigated performing an analysis in FaST-LMM , but with the kinships estimated from various different software packages see . Use of Given that many of the software implementations we investigated  showed similar levels of power and type 1 error, and gave rather similar inference in terms of localisation of signals and With respect to computational speed, as a rule of thumb we found Mendel , FaST-LMM (approximate) and GenABEL (GRAMMAR-Gamma) to be the fastest LMM implementations, taking between 3 minutes and a quarter of an hour on our system to analyse 545,433 SNPs in 1972 genotyped individuals. These were closely followed by EMMAX and MMM (approximate) which took around half an hour, GenABEL (FASTA), GEMMA, FaST-LMM (exact) and MMM (exact) which typically took 1–2 hours, Mendel (estimated kinships) which took around 2.5 hours, and GTAM which took around 4 hours. Of the non-LMM methods, FBAT, MQLS and MASTOR were the fastest, taking a few hours to perform the analysis, while ROADTRIPS was the slowest, taking several days. Inputting estimated  kinships into MQLS increased the time taken to around 4 days . Although less satisfactory than a proper longitudinal analysis that takes into account correlations due to both relatedness between individuals and repeated measures within individuals We also investigated a ‘proper’ longitudinal analysis implemented within the R software package longGWAS Another program that can, in theory, implement a ‘proper’ longitudinal analysis is the lmekin function within the R package coxme. We found this function to be computationally infeasible for analysis of genome-wide data, but application to a selected set of 2423 SNPs (of different effect sizes) in the sim-L20 data suggested that the results were very similar to those obtained from GenABEL (FASTA), EMMAX, FaST-LMM, GEMMA and MMM. However, we were unable to get lmekin to give meaningful results (most results were “NA”) when applied to the sim-P20 data. We also speculated that a ‘proper’ longitudinal analysis should, in theory, be implementable in the package Mendel Here we have demonstrated, through simulations and application to real data, that linear mixed model approaches such as those implemented in the packages GenABEL, EMMAX, FAST-LMM, GEMMA and MMM offer a convenient and robust approach for family-based GWAS of quantitative or binary traits, are successful in controlling the overall genomic inflation factor to an appropriate level, and offer higher power than traditional family-based association analysis approaches such as those implemented in FBAT. Similar inference is also provided by related and alternative approaches implemented in the software packages Mendel, ROADTRIPS, MQLS and MASTOR, although our results from analysis of the real data suggest that, for Mendel, MQLS and MASTOR, care may need to be taken to use estimated kinships based on SNP data rather than known pedigree relationships, if one is to avoid any inflation in the test statistics.Our current study focused mostly on family data in which genuine close relationships between many individuals exist. Nevertheless we found similar results with respect to the LMM methods investigated (adequate control of type 1 error and extremely similar performance in terms of power and concordance between top findings) when applied to a subset of 462 founder individuals from our pedigrees, selected to be approximately unrelated to one another see . TherefoTraditional methods for family-based association analysis make use of pedigree relationships either (e.g. FBAT) through direct use of known pedigree structure or else  through use of a covariance matrix that involves the known kinship between each pair of individuals . The assumption that all founders in a pedigree share no alleles identical by descent is clearly a fiction, given human population history, while the assumption that all pedigrees are correctly specified and unrelated to one another is also likely to be violated in most real studies. The use of estimated kinships based on SNP data rather than theoretical kinships based on known pedigree relationships removes the reliance on these untenable assumptions, and allows essentially the same analysis approaches to be applied to apparently unrelated individuals (who may nevertheless display distant levels of shared ancestry). The question then arises as to what exactly these estimated kinships (or related measures) are actually measuring? We consider a detailed discussion of this issue to be beyond the scope of the current manuscript, but we refer the reader to the more detailed expositions given in The recent popularity of LMM approaches for the analysis of apparently unrelated individuals An interesting finding of our current study was the fact that longitudinal traits (repeated measures) could be successfully analysed in an LMM framework simply by treating each measurement as if it came from a separate person and expanding out the genetic data set accordingly . From a practical point of view this is useful as analysis of an expanded data set in standard LMM software is computationally convenient; we found a ‘proper’ analysis using software such as longGWAS A caveat to all the results presented here is that they relate to genotypes derived from a single data set, our Brazilian family study of visceral leishmaniasis On this note, we point out that each package has its own particular advantages (and disadvantages). These include the fact that EMMAX, GEMMA and MMM allow the input of dosages derived from imputed  genotypes; MMM has the advantage of allowing the output of regression coefficients and standard errors for the SNP effects on the (log) odds ratio scale, making it convenient to compare or combine the results with results from traditional case/control studies analysed via logistic regression; GenABEL (GRAMMAR-Gamma) has the advantage of scaling linearly with sample size, which makes it attractive for the analysis of very large data sets; FaST-LMM has the advantage, along with EMMAX and Mendel, of internally imputing missing data at any (genetic or non-genetic) covariates, which can make it convenient for implementing stepwise conditional analyses; and, unlike most LMM implementations, ROADTRIPS, MQLS and MASTOR have the advantage of using all phenotype information, including that for individuals that have not been genotyped, which can in theory generate a small increase in power.One of the main differences between the different software implementations we investigated was the time taken to perform the analysis (not including the time required to re-format data into an appropriate format for a given package). We were unable to do a strict head-to-head comparison as the precise timings depend on a number of factors including the computer architecture available , however our rough comparison , assuminIn conclusion, we recommend linear mixed model approaches as a convenient and powerful approach for family-based GWAS of quantitative or binary traits. We find these approaches to be successful in controlling the overall genome-wide error rate and to perform well in comparison to competing approaches.Ethical approval for the Belem Family Study was obtained originally from the local ethics committee at the Instituto Evandro Chagas, Belém, Para, Brazil. Approval for continued use of the Belem Family Study samples, and for collection and use of the samples from Natal, has been granted from the local Institutional Review Board at the Universidade Federal do Rio Grande do Norte (CEP-UFRN 94–2004), nationally from the Comissão Nacional de Ética em Pesquisa (CONEP: 11019), and from the Ministerios Cencia e Tecnologia for approval to ship samples out of Brazil . Informed written consent for sample collection was obtained from adults, and from parents of children –Z-genome command in PLINK Sample collection and genotyping of the Brazilian subjects used here is described in detail in For the majority of analyses considered here, we used either the 1972 genotyped individuals or else the entire set of 3626 individuals (with or without genotype data) that are required to define the ‘known’  pedigree relationships. For power comparisons between LMM methods, we also investigated use of a subset of 462 ‘founder’ individuals, chosen on the basis of theoretical relationships and estimated kinships to be approximately unrelated to one another.jx was a variable coded  according to the number of copies of the risk allele possessed at causal SNP j (with j = 1 corresponding to rs9271252 and j = 2 corresponding to rs233722), the baseline penetrance We generated simulated phenotypes for the 1972 individuals that had genome-wide SNP data available. We used two different models for generating binary (disease) traits, one corresponding to ‘strong’ genetic effects (sim-D1) and one corresponding to ‘weak’ genetic effects (sim-D2), with the trait in both cases governed by two SNPs (rs9271252 and rs233722) located on chromosomes 6 and 12 respectively. In addition to modelling genetic effects at rs9271252 and rs233722, we allowed for 22 weaker ‘polygenic’ effects caused by genotype at the 100th SNP on each autosomal chromosome. Each effect contributed multiplicatively to the probability of developing disease. Thus, the mathematical model for generating the simulated phenotype was ijx was a genotype variable for person i at SNP j coded as above, i were set to 1, and We also simulated a model (sim-Q) for quantitative traits, again governed by rs9271252 and rs233722 on chromosomes 6 and 12. The traits were generated as a linear combination of the effect from each of the strong and polygenic effect SNPs, with a normally distributed error component, thus: k = 20 repeated measures for each individual) in a rather similar manner, with individuals' non-genetic variation accounted for by another error term We simulated a model (sim-L20) for longitudinal quantitative traits  in which the strong effects We generated 1000 replicates of each simulated data set, apart from the longitudinal and polygenic longitudinal data sets for which we only simulated a single replicate. For visualisation of results from a whole genome scan, we analysed only a single replicate (replicate 1). For investigation of power, type 1 error and concordance, to reduce computation time we analysed all 1000 replicates but only generated test statistics at 40 SNPs that lay within 40 kb of the simulated disease loci  and 20 SNPs that lay well outside the region of any simulated disease loci . By default, the programs Mendel and ROADTRIPS require all SNPs that are being used to estimate genome-wide relatedness to also be read in and tested for association; to perform the analysis of all 1000 replicates in reasonable time we therefore included the 50,129 ‘pruned’ SNPs rather than the full genome-wide set of SNPs that would normally be used by these programs.n subjects, Q and I is the All the LMM implementations evaluated here attempt to fit either an exact or an approximate version of the standard linear mixed model: mmscore and polygenic functions of the GenABEL package --fast-Assoc option of the MERLIN The n-dimensional vector of fitted values of the response from the reduced model, n-dimensional vector of unconditional expectations of genotype scores at the test SNP , and n-dimensional vector Rather than fitting the full linear mixed model grammar function of the GenABEL package The i from the reduced model. These residuals are then used as the independent trait in a simple linear regression model: ie is assumed to be independently normally distributed. Estimation of In GRAMMAR In the original GRAMMAR publication TGRG = Tnew/γ that can be shown to be approximately equivalent to the FASTA statistic O(sn), where n is the sample size and s the number of SNPs to be tested).The GRAMMAR-Gamma method Kang et al. In the approach of Kang et al. In the approach of Kang et al. Although not entirely clear from the description in Kang et al. r the number of iterations i.e. the number of evaluations of the likelihood required) together with a computational complexity of The method of Kang et al. C) are estimated under the null hypothesis that mmscore and polygenic functions in GenABEL) that address the problem without making such an approximation are not computationally prohibitively time consuming. Therefore it is unclear why use of this approximation should be preferred. For this reason, given the extreme similarity between the methods implemented in EMMAX and TASSEL when no clustering is performed, we have not included TASSEL in our comparisons.A similar approach to Lippert et al. FaST-LMM uses either maximum likelihood (ML) or restricted maximum likelihood (REML). In early versions of FaST-LMM the default was ML but in later versions the default became REML. After some experimentation, we deemed ML to be the most reliable and have used that for all results presented here.r) required to reach convergence in GEMMA is expected to be slightly smaller than in FaST-LMM, owing to the use of a more efficient optimization method. GEMMA also has an attractive practical advantage of allowing the input of imputed Zhou and Stephens Pirinen et al. An approximate (score test) LMM implementation, suitable for analysis of GWAS data, has also been implemented in the software package Mendel Traditional approaches for family-based association analysis focus on the transmission of high-risk alleles through pedigrees, in an approach that is closely related to traditional linkage analysis. Indeed, the well-known transmission disequilibrium test (TDT) ijX is some genotype variable and ijT some trait variable for offspring i in nuclear family j. The exact form of FBAT thus depends on the genotype and trait coding used. Genotype is generally coded in allelic fashion with a variable coded  according to the number of copies of the high-risk allele possessed. The trait variable is constructed as ij is coded 0/1 (for binary traits such as disease status) and ij would generally correspond to the measured trait for offspring i in nuclear family j, with The TDT was originally designed for the analysis of case/parent trios (i.e. units consisting of an affected child together with their parents) but has been extended to allow analysis of nuclear families and larger pedigrees estimate of the probability of transmission of high-risk alleles to unaffected individuals , rather than comparing the transmission probability to affecteds with an assumed fixed value of 0.5. For complex diseases, where the effects of risk alleles are likely to be modest , this means that greater power would be expected from the default offset that considers transmissions to affected offspring only, without paying a penalty for (imperfect) estimation of the expected 0.5 transmission probability  from the data at hand.Although, for binary traits, contrasting transmissions to affecteds with transmissions to unaffecteds seems an attractive idea, in practice this results in comparing the probability of transmission of high-risk alleles to affected individuals  with an By default, FBAT divides larger pedigrees into nuclear families and constructs a test that corresponds to testing ‘linkage in the presence of association’ RObust Association- Detection Test for Related Individuals with Population Substructure’ in a package called ROADTRIPS. ROADTRIPS can be thought of as an extension of their previously-proposed Maximum Quasi-Likelihood Statistic (MQLS) Thornton and McPeek The ROADTRIPS test statistic takes the form: n individuals , V is a vector of length n coding for phenotype information (disease status) and known  relationships (see Y (so that Y) in an outbred population and Thornton and McPeek note that many commonly-used case/control statistics can be coerced into this form. Here Recently, Jakobsdottir and McPeek - -indep 50 5 2 command in PLINK The LMM approaches considered here, as well as methods such as MQLS, ROADTRIPS, MASTOR and GTAM, all involve modelling the relatedness between individuals through one or more kinship matrices, constructed either on the basis of known (hypothesized) pedigree relationships between individuals, or through estimating kinships on the basis of genome-wide SNP data (or from a subset of available genome-wide SNPs). The precise algorithms used to estimate kinships on the basis of genome-wide SNP data vary http://www.staff.ncl.ac.uk/richard.howey/mapthin/). In addition we explored the use of the FaST-LMM-Select procedure We also explored the use of a smaller set of 1900 ‘thinned’ SNPs to estimate kinships. This number was chosen to capitalise on the speed-up that can be achieved in FaST-LMM by restricting the number of SNPs used to construct the kinship matrix Several alternative packages exist for estimating genetic relationships from genome-wide SNP data, either for subsequent use in LMM type analyses Figure S1Comparison of estimated kinship measures and −log10 obtained based on full, pruned and thinned SNPs. (A) Estimated kinship measures (B) (TIF)Click here for additional data file.Figure S2QQ plots of real VL phenotype GWAS results, using different LMM software packages and different SNP sets for kinship estimation. The black diagonal lines represent the line of equality. The “theoretical” set used pedigree structure to derive theoretical kinship coefficients. EM_BN = EMMAX , EM_IBS = EMMAX (IBS method), FLMM_C = FaST-LMM using covariance matrix, FLMM_R = FaST-LMM using realised relationship matrix, GA_FA = GenABEL (FASTA), GA_GRG = GenABEL (GRAMMAR-Gamma), GMA_C = GEMMA using centred genotypes, GMA_S = GEMMA using standardised genotypes, MMM_E = MMM using full mixed model (exact) calculation, MMM_G = MMM using GLS approximation, Unadj  =  unadjusted analysis. For methods with two ways to estimate the kinships, the same “theoretical” results were plotted twice. Unadjusted analysis results were plotted once in each column only for comparison, and did not use the kinship estimates for adjustment.(TIF)Click here for additional data file.Figure S3Performance of FaST-LMM-Select. Genomic control factor ((TIF)Click here for additional data file.Figure S4Manhattan plots for real and simulated data sets using FaST-LMM. The points marked in red denote either the confirmed significant region from Fakiola et al. (2013) , or the regions close to the simulated strong/weak effect SNPs (simulated phenotypes). real  =  real VL phenotype, sim-D1 =  simulated strong binary (disease) trait, sim-D2 =  simulated weak binary (disease) trait, sim-Q =  simulated quantitative trait, sim-L20 =  simulated longitudinal quantitative trait with 20 observations, sim-P20 =  simulated polygenic longitudinal quantitative trait with 20 observations.(TIF)Click here for additional data file.Figure S5Manhattan plots for the simulated weak binary (disease) phenotype using FaST-LMM exact and alternative software packages. The points marked in red denote the regions close to the simulated weak effect SNPs. FLMM_E = FaST-LMM using exact calculation, RT = ROADTRIPS, FBATaff = FBAT using transmissions to affecteds only, FBATboth = FBAT using transmissions to both affecteds and unaffecteds. Results from all other LMM methods were indistinguishable from FLMM_E and so are not shown. MQLS and RT gave identical results with either 1972 or 3626 individuals, as phenotypes could only be simulated for the 1972 genotyped individuals.(TIF)Click here for additional data file.Figure S6Manhattan plots for the simulated strong binary (disease) phenotype using FaST-LMM exact and alternative software packages. The points marked in red denote the regions close to the simulated weak effect SNPs. FLMM_E = FaST-LMM using exact calculation, RT = ROADTRIPS, FBATaff = FBAT using transmissions to affecteds only, FBATboth = FBAT using transmissions to both affecteds and unaffecteds. Results from all other LMM methods were indistinguishable from FLMM_E and so are not shown. MQLS and RT gave identical results with either 1972 or 3626 individuals, as phenotypes could only be simulated for the 1972 genotyped individuals.(TIF)Click here for additional data file.Figure S7Comparison of −log10 using different LMM software packages, real disease phenotypes. Plots above the diagonal show a comparison of −log10, with correlations between the -log10 indicated below the diagonal. The grey solid lines represents the line of equality; the black dashed lines the linear regression line of the variable on the y axis on the variable on the x axis. EM_BN = EMMAX , EM_IBS = EMMAX (IBS method), FLMM_A = FaST-LMM using approximate calculation, FLMM_E = FaST-LMM using exact calculation, GA_FA = GenABEL (FASTA), GA_GRG = GenABEL (GRAMMAR-Gamma), GMA_C = GEMMA using centred genotypes, GMA_S = GEMMA using standardised genotypes, MMM_E = MMM using full mixed model (exact) calculation, MMM_G = MMM using GLS approximation, Unadj  =  unadjusted analysis.(TIF)Click here for additional data file.Figure S8Comparison of −log using LMM and alternative software packages, real disease phenotypes. Plots above the diagonal show a comparison of −log10, with correlations between the −log10 indicated below the diagonal. The grey solid lines represent the line of equality; the black dashed lines the linear regression line of the variable on the y axis on the variable on the x axis. FLMM_E = FaST-LMM using exact calculation, MQLS1972 = MQLS using 1972 genotyped individuals, MQLS3626 = MQLS using all 3626 individuals with or without genotype data, RT1972 = ROADTRIPS using 1972 genotyped individuals, RT3626 = ROADTRIPS using all 3626 individuals with or without genotype data, FBATaff = FBAT using transmissions to affecteds only, FBATboth = FBAT using transmissions to both affecteds and unaffecteds, MQLS_E = MQLS using estimated  kinships.(TIF)Click here for additional data file.Figure S9Comparison of −log using LMM and alternative software packages, simulated weak binary (disease) phenotype. Plots above the diagonal show a comparison of –log10, with correlations between the –log10 indicated below the diagonal. The grey solid lines represent the line of equality; the black dashed lines the linear regression line of the variable on the y axis on the variable on the x axis. The colours denote: red  =  the two weak effect SNPs, magenta = SNPs within 500 kb of the weak effect SNPs, blue  = 22 polygenic SNPs, green  = SNPs within 500 kb of the polygenic SNPs, black  =  all other SNPs. Because the black/green/blue SNPs were plotted before the magenta/red SNPs, they may be obscured by the latter. FLMM_E = FaST-LMM using exact calculation, MQLS = MQLS using 1972 or 3626 individuals, RT = ROADTRIPS using 1972 or 3626 individuals, FBATaff = FBAT using transmissions to affecteds only, FBATboth = FBAT using transmissions to both affecteds and unaffecteds. MQLS and RT gave identical results with either 1972 or 3626 individuals, as phenotypes could only be simulated for the 1972 genotyped individuals.(TIF)Click here for additional data file.Figure S10Comparison of −log10 obtained from FaST-LMM using alternative kinship estimates, real disease phenotypes. Plots above the diagonal show a comparison of –log10, with correlations between the –log10 indicated below the diagonal. The grey solid lines represents the line of equality; the black dashed lines the linear regression line of the variable on the y axis on the variable on the x axis. KING_H = KING homogeneous method, KING_R = KING robust method, Ped  =  theoretical kinship estimates based on pedigree information, FLMM_R = FaST-LMM's own realised relationship matrix, Unadj  =  unadjusted, Wrong  =  misspecified kinships, chosen to be inversely related to the true kinship value.(TIF)Click here for additional data file.Figure S11p-value threshold. Type 1 errors (right hand plots) are defined as the proportion of null SNPs  that reach the specified p-value threshold. Horizontal dashed lines indicate the target p-value thresholds (i.e. the expected type 1 error rates).Power and type 1 error of different LMM methods applied to 462 Brazilian founders. Powers (left hand plots) are defined as the proportion of replicates (out of 1000) in which both simulated disease loci are detected, with ‘detection’ corresponding to any SNP within 40 kb of the simulated disease locus reaching the specified (TIF)Click here for additional data file.Table S1Genomic control factors achieved in analysis of the real data, or a single replicate of the simulated data, when feeding externally estimated kinships into FaST-LMM.(PDF)Click here for additional data file.Table S2Computational speed and ease of use of various packages.(PDF)Click here for additional data file.Table S3Concordance between top SNPs identified by different LMM methods when using 462 founder individuals.(PDF)Click here for additional data file.Text S1Membership of Wellcome Trust Case Control Consortium 2.(DOC)Click here for additional data file.