Recently, joint analysis of multiple traits has become popular because it can increase statistical power to identify genetic variants associated with complex diseases. In addition, there is increasing evidence indicating that pleiotropy is a widespread phenomenon in complex diseases. Currently, most of existing methods test the association between multiple traits and a single genetic variant. However, these methods by analyzing one variant at a time may not be ideal for rare variant association studies because of the allelic heterogeneity as well as the extreme rarity of rare variants. In this article, we developed a statistical method by testing an optimally weighted combination of variants with multiple traits (TOWmuT) to test the association between multiple traits and a weighted combination of variants (rare and/or common) in a genomic region. TOWmuT is robust to the directions of effects of causal variants and is applicable to different types of traits. Using extensive simulation studies, we compared the performance of TOWmuT with the following five existing methods: gene association with multiple traits (GAMuT), multiple sequence kernel association test (MSKAT), adaptive weighting reverse regression (AWRR), single-TOW, and MANOVA. Our results showed that, in all of the simulation scenarios, TOWmuT has correct type I error rates and is consistently more powerful than the other five tests. We also illustrated the usefulness of TOWmuT by analyzing a whole-genome genotyping data from a lung function study. Many large cohort studies collected many correlated traits that can reflect underlying mechanism of complex diseases. For example, the UK10K cohort study collected 64 correlated phenotypic traits ; metabolSeveral statistical methods have been developed to test the association between multiple traits and a single common variant. These methods can be roughly divided into three groups: dimension reduction methods , 13–15, As we pointed out above, it is essential to develop statistical methods to test the association between multiple traits and multiple variants (common and/or rare variants). Very recently, a few statistical methods for this purpose are appeared , 46–50. In this article, we developed a new statistical method by testing an optimally weighted combination of variants with multiple traits (TOWmuT) to test the association between multiple traits and a weighted combination of variants (rare and/or common) in a genomic region. TOWmuT is based on the score test under a linear model, in which the weighted combination of variants is treated as the response variable and multiple traits including covariates are treated as independent variables. The statistic of TOWmuT is the maximum of the score test statistic over weights. The weights at which the score test statistic reaches its maximum are called the optimal weights. TOWmuT is applicable to different types of traits and can include covariates. Using extensive simulation studies, we compared the performance of TOWmuT with single-TOW , GAMuT , MSKAT , AWRR 11 and MANn unrelated individuals. Each individual has K potentially correlated quantitative or qualitative traits  and has been genotyped at M variants in a genomic region. Let kth trait value of the ith individual and ith individual at the mth variant, where ith individual carries at the mth variant. We first centralize Yi =T, Xi =T, Y =T, and X =T. For the ith individual, we consider a linear combination of the variants w =T are weights and their values will be decided later.We consider a sample with H0:β1 = ⋯ = βK = 0 is given byWe first describe our method without covariates. Consider the linear modelXTX/n with the diagonal of XTX/n and let A = diag(XTX/n). This simplification was also used in the past by Pan [σ2 becomes Tscore becomes W = A1/2w, then λmax(•) indicates the largest eigenvalue of a matrix. Let W0 denote the eigenvector of A−1/2XTY(YTY)−1YTXA−1/2 corresponding to the largest eigenvalue, then w0 = A−1/2W0 is the optimal weights. Actually, we do not need to calculate w0 in order to calculate TTOWmuT. If we let C = XA−1XT, thenTo simplify the computation of Eq , we replt by Pan  and Sha t by Pan . Then σ2TTOWmuT. In details, we randomly shuffle the traits in each permutation. Note that C and (YTY)−1 do not change in each permutation. Suppose that we perform B times of permutations. Let TTOWmuT based on the bth permuted data, where b = 0 represents the original data. Then, the p-value of TTOWmuT is given byWe use a permutation test to evaluate the p-value of p covariates and zi1,…zip denote the p covariates of the ith individual. Consider the linear modelH0:β1 = ⋯ = βK = 0 is given byyik and xim underyik and xim by their residuals Tscore, it becomes the score test statistic with covariates Assume that there are Therefore, we define TOWmuT statistic with covariates asyik and genotypic score xim for the covariates by applying linear regressions in (8) and apply TOWmuT without covariates to the residuals In summary, to apply TOWmuT with covariates, we adjust both trait value We compare the performance of our proposed method with the following methods: Multivariate Analysis of Variance (MANOVA) , MSKAT , GAMuT , AWRR 11 and sinMANOVA: Consider a multivariate multiple linear regression model: Y = Xβ+ε, where Y denotes the n×K matrix of phenotypes; X denotes the n×M matrix of genotypes; β is a M×K matrix of coefficients; ε is the n×K matrix of random errors with each row of ε to be i.i.d. MVN, where Σ is the covariance matrix of ε. To test H0:β = 0, the likelihood ratio test is equivalent to the Wilk’s Lambda test statistic of MANOVA, that is, H0 to the likelihood function under H1, l is the log-likelihood function, β, and |•| denotes the determinant of a matrix. The test statistic has an asymptotic MSKAT: MSKAT extends the commonly used SKAT [sed SKAT  for singGAMuT: GAMuT compares the similarity in multivariate phenotypes to the similarity in rare-variant genotypes in a genomic region by a machine-learning framework called kernel distance covariance.AWRR: by collapsing genotypes using adaptive weights, AWRR uses the score test to test association based on the reverse regression, in which collapsed genotypes are treated as the response variable and multiple traits are treated as independent variables.Single-TOW: Let kth trait and the genotypes at the variants in a genomic region. The test statistic of single-TOW is given by Tsingle–TOW = mink≤K1≤pk, where pk is the p-value of k = 1,…,K. The p-value of Tsingle–TOW is estimated using a permutation procedure.In our simulation studies, we use the empirical Mini-Exome genotype data provided by the genetic analysis workshop 17 (GAW17) to generate genotypes. This dataset contains genotypes of 697 unrelated individuals on 3205 genes. Same as the simulation studies in Sha et al.  and Fangnc rare variants as causal variants, where nc is determined by the percentage of causal variants among rare variants. We use nr and np to denote the number of risk rare variants and protective rare variants, respectively, where nr + np = nc. Let qth risk rare variant and the jth protective rare variant for the ith individual, respectively. We assume that genotypes impact on L traits. Let h and hl denote the heritability of all the nc rare causal variants for the L traits and the lth trait among the L traits, respectively. We generate L random numbers t1,…,tL from a uniform distribution between 0 and 1. Then, the heritability of lth trait among the L traits is lth trait hl, we generate nc random numbers mth causal variant for the lth trait is given by We assume that all causal variants are rare (MAF < 0.01). We randomly choose Z1 and Z2, where Z1 is a continuous covariate generated from a standard normal distribution, and Z2 is a binary covariate taking values 0 and 1 with a probability of 0.5. We generate K traits by considering the factor model [y = T; e = T, λ =  is the vector involved genotypes; f = T ~ MVN, Σ = (1−ρ)I + ρA, A is a matrix with elements of 1, I is the identity matrix, and ρ is the correlation between fi and fj; R is the number of factors; γ is a K by R matrix; c is a constant number; ε = T is a vector of residuals; and ε1,…,εK are independent, εk ~ N for k = 1,…,K.In our simulation studies, we consider two covariates or model , 13, 21c2 and the between-factor correlation is ρ1 = ρc2.As in Wang et al. , we consModel 1: There is only one factor and genotypes impact on 6 traits with the same effect size. This is equivalent to set R = 1 and γ = T. In details,Model 2: There are five factors and genotypes impact on 6 traits. We set R = 5 and γ = diag, where i = 1,…,5. In details,Model 3: There are two factors and genotypes impact on 6 traits. That is, R = 2 and γ = diag, where i = 1,2. In details,Model 4: There are five factors and genotypes impact on one trait. That is, R = 5 and γ = diag, where i = 1,…,5. In details,Model 5: There are only two factors and genotypes impact on one trait. That is, R = 2 and γ = diag, where i = 1,2. In details,Model 6: There is K factors and genotypes impact on 6 traits. That is, R = K, γ = I, and c = 1. In details,λk = 0 for k = 1,…,K in all of the 6 models. We consider different models, different sample sizes, different significance levels, and different types of traits. In our simulations we consider 10 traits (K = 10). In each simulation scenario, we estimate the p-values of TOWmuT using 1000 permutations and evaluate the type I error rates of TOWmuT using 10,000 replicated samples. For 10,000 replicated samples, the 95% confidence interval (CI) for the estimated type I error rates of nominal level 0.05 is  and the 95% CI at the nominal level of 0.01 is . Tables To evaluate the type I error rates of the proposed test TOWmuT, we set For power comparisons, we consider different models, different types of traits, different percentages of protective variants, different values of heritability, different values of between-factor correlation, and different values of within-factor correlation. In each of the simulation scenarios, we estimate the p-values of TOWmuT, AWRR and single-TOW using 1,000 permutations and we estimate the p-values of MANOVA, GAMuT, and MSKAT using their asymptotic distributions. We evaluate the powers of all of the six tests using 1,000 replicated samples at a significance level of 0.05.We also compare the powers of the six tests for the power as a function of the within-factor correlation for models 1–5 and between-factor correlation for model 6 for 10 quantitative traits  is a common disease in elderly patients that causes significant morbidity and mortality . The Gen−6. To evaluate the performance of our proposed method on a real data set, we applied six methods  to the COPDGene of NHW population to test the association between each of 50-SNP blocks and the seven quantitative COPD-related phenotypes. To identify significant 50-SNP blocks associated with the phenotypes, we used Bonferroni correction to decide the significance level. The total number of 50-SNP blocks is 12617, therefore, the Bonferroni corrected significance level is 0.05/12617 ≈ 4×10In this article, we developed TOWmuT to perform joint analysis of multiple traits in gene-based association studies. The motivations to develop this method are based on the following: (1) for complex diseases, multiple correlated traits are usually measured in genetic association studies; (2) there is increasing evidence demonstrating that pleiotropy is a widespread phenomenon in complex diseases ; and (3)Recently, it has become a major focus of investigation to identify a small number of rare causal variants that contribute to complex diseases . SeveralThe computation time required for running TOWmuT depends on the number of traits, the sample size, the number of permutations, and the number of variants in a genomic region. The running time of TOWmuT with 1000 permutations on a data set with 5000 individuals, seven traits, and 10 variants in a genomic region on a laptop with 4 Intel Cores @ 3.30GHz and 4 GB memory is about 0.14s. To perform real data analysis at a genome-wide level, we can first select genomic regions that show evidence of association based on a small number of permutations , and then use a large number of permutations to test the selected regions.Y = T, Zi = T, Z = T, and x = T. Under the linear modelα = T, β = T, and ε1,…,εn are independent and εi ~ N. Then,α and σ2 under null hypothesis H0:β = 0. Then, P = Z(ZTZ)−1ZT. Let θ = T. The score and information matrix are U = YT(I−P)x = YT(I−P)Xw. The score test statistic is given byV = YT(I−P)Y. Note that (I−P)2 = I−P. We have xim under the linear regression model (8); yik under the linear regression model (8). Therefore,We use the same notations in the method section. Let S1 File(PDF)Click here for additional data file.


While it is well established that genetics can be a major contributor to population variation of complex traits, the relative contributions of rare and common variants to phenotypic variation remains a matter of considerable debate. Here, we simulate genetic and phenotypic data across different case/control panel sampling strategies, sequencing methods, and genetic architecture models based on evolutionary forces to determine the statistical performance of rare variant association tests (RVATs) widely in use. We find that the highest statistical power of RVATs is achieved by sampling case/control individuals from the extremes of an underlying quantitative trait distribution. We also demonstrate that the use of genotyping arrays, in conjunction with imputation from a whole‐genome sequenced (WGS) reference panel, recovers the vast majority (90%) of the power that could be achieved by sequencing the case/control panel using current tools. Finally, we show that for dichotomous traits, the statistical performance of RVATs decreases as rare variants become more important in the trait architecture. Our results extend previous work to show that RVATs are insufficiently powered to make generalizable conclusions about the role of rare variants in dichotomous complex traits. One proposed source of this so‐called “missing heritability” are rare variants, which are hotly debated but have been implicated as a nonnegligible source of genetic variance in prostate cancer  can dramatically affect genome‐wide patterns of genetic variation in a population  to ~0.004–0.006% , the $1000 per genome cost still means performing WGS on any sizeable group of individuals remains prohibitively expensive for all but the largest consortia. Genotyping arrays make acquiring genetic data for a large number of individuals significantly less expensive, but lack coverage of rare variation. With larger WGS reference panels like the Haplotype Reference Consortium  and the functional relationship between fitness effects and phenotypic effect sizes (through τ and δ). In particular, a causal variant with fitness effect s will have effect size zs as follows:The second step is to project the allele frequencies of our list of functional variants down to the desired sample size , and transform fitness effects to phenotypic effect sizes using the Uricchio et al.  model. Tρ, the effect size zs of a site is a direct function of the site's fitness effect (s), otherwise, the effect size zs is a function of a randomly sampled fitness effect (sr) drawn from the entire list of functional variants generated by the first step above. In this model, δ is +1 or −1 with equal probability to enable trait‐increasing and trait‐decreasing effects.Under this model, with probability Yi, for the ith individual) is then generated under an additive model by summing the effect sizes of all causal alleles that they carryzj is the effect size of causal variant j, Xij is the number of causal alleles carried by individual i at site j, and ϵ is a Normal random variable with mean 0 and variance σenvironment2 (which ensures the desired level of heritability of the trait). See Table ⍴, τ, and heritability that are evaluated in this study. In contrast to previous work with this phenotypic model , and the remaining individuals to be our population of controls. We then sample cases and controls from their respective populations. For the random sampling strategy, we sample cases in proportion to the prevalence of the trait, while for the 50/50 sampling strategy we sample equal numbers of cases and controls. The random sampling strategy is used as a worst‐case scenario to establish the worst possible power under that sampling strategy.2.5In some analyses, we evaluate the effectiveness of genotype imputation. Such analyses require two data sets: the phenotype sample , and an imputation reference panel. The dichotomized phenotype individuals are generated as above, with their genetic data down‐sampled to mimic a genotype array platform. We then sample an additional set of individuals from the total population to form the imputation panel. The down‐sampled genotype data is then prephased using SHAPEIT2  using the rvtests software  is the site frequency spectra (SFS), that is the proportion of sampled alleles at frequency y, and E(z2|y) is the mean‐squared effect size of variants at frequency y. We pool 20 simulations of 300kbp in 50k African individuals using msprime to obtain an accurate measure of the SFS and the expected effect size of variants at frequency x. To normalize across genetic architectures, we divide by V1, which is the total additive genetic variance. The V0.01/V1 values (denoted as just V0.01 below) are used to denote the degree to which rare variants (variants with MAF ≤ 1%) matter under a particular pair of parameters under the Uricchio genetic architectures.We follow  combinations of the Uricchio model being studied here (see Methods and Table 0.01), which varies dramatically between 99% when ⍴ = 1, τ = 1, to less than 1% when ⍴ = 0, τ = 0.5. We note that when τ = 1 and ⍴ ≠ 0, rare variants constitute a substantial fraction of the genetic variance (V0.01 > 40%), and the majority of the rare variant contribution is explained by singletons in this simulated sample of 50,000 individuals. In contrast, when τ = 0.5 and ⍴ ≠ 0, V0.01 ranges from ~20%–60% but singletons are expected to make a more subtle contribution to the genetic architecture of the trait.To determine whether there is genetic variance explained by rare variants, we calculated the expected genetic variance analytically under different . As expected, power is higher when the causal signal is more concentrated . Given the correspondence among tests, we will focus on SKAT‐O in further analyses.Figure 3.3V0.01 increases , the power of SKAT‐O decreases. This pattern holds across all sampling strategies and for different levels of polygenicity . These results show patterns that will repeat in future sections: the extremes study design demonstrates the best overall power, followed by 50/50 and then random. Further, a more concentrated signal  improves power. We found that as the functional form relating effect size to selection coefficient changes from τ = 0.5 to τ = 1, power increases slightly again, suggesting that V0.01 may be an overly simplistic characterization of the genetic architecture. Finally, applying SKAT‐O to imputed data (bottom facet) reproduces all of the patterns we see when RVATs are applied to sequencing data (top facet), albeit with slightly worse power.We then ask how SKAT‐O power changes as a function of genetic architecture. In Figure 3.4The number of individuals sequenced as part of a study is a key design parameter of that study. To understand how increasing the number of individuals improves the statistical power of SKAT‐O, we simulate across genetic architectures and study designs to find the increase in power per individual using SKAT‐O from 2,500 to 20,000 individuals Figure . In the 3.5Most genetic association studies have started with genotyping arrays to collect genomic data, followed by imputation against WGS reference panels to maximize discovery potential with single variant analyses. As WGS cost falls, more studies will conduct large‐scale WGS, but here we ask if there is a potential opportunity to discover rare variant associations with imputed data. In Figure 3.6The general process of discovering genetic associations typically begins with genotyping and imputing a sample of individuals, followed by GWAS. The  genetic architecture of the trait determines the likelihood that a common variant will be detected with GWAS, and whether a rare variant association signal should be expected. Rastering over parameters of our phenotype model, a genome‐wide significant single marker association (GWAS) was identified at 44.4% of causal loci. Figure V0.01 increases).We then mimic the process of first doing locus discovery on a sample of imputed individuals followed by sequencing for different sampling strategies. In Figure 3.7In Figure 4GWAS so far have produced thousands of SNP associations for hundreds of traits Witte, . However10(MAF) as proposed by Wu et al., ρ and the relationship between selection and effect size through τ, which enables a thorough exploration of different genetic architectures a trait could have  parameterizations under the Uricchio model . We show that SKAT‐O power decreases as V0.01 increases, meaning SKAT‐O performance is worst when rare alleles make the largest contributions to trait variance. Although counterintuitive, as one would expect RVATs are best tuned for the scenarios where rare variants matter most in the genetic architecture, our result mirrors the findings of Uricchio et al. .The next step in characterizing RVAT power is to consider the genetic architecture of the trait of interest. Though complex trait architectures are not thoroughly understood, we used the Uricchio model to simulate different architectures and label these architectures using the amount of cumulative genetic variance explained by all variants under 1% minor allele frequency  of causal regions are identified by SKAT‐O and not by GWAS. We see little downside in testing for causal regions using SKAT‐O following GWAS, with the ability to pick up additional causal regions on the same data. We caution that this effect declines significantly as rare variants explain more of the genetic variance.Finally, the number of loci contributing to a trait (or its polygenicity) may be another important component of the trait's architecture. It is not surprising that we found that for a fixed heritability of a trait, RVAT discovery power is higher when there are fewer true causal loci (as effect sizes are concentrated into fewer variants). However, it is possible that the polygenicity of a trait could be constraining the possible range of genetic architectures.This study has a few limitations. It is based on simulated data that matches inferred human evolutionary history (including selection and demographic history) but these models and simulations are incomplete representations of nature. We do not explore the effects of gene size, mutation rate, haplotype length, or degree of linkage disequilibrium between causal regions. We do not consider the differences between coding and noncoding regions, which have different selection coefficient distributions and potentially different contributions to the genetic architectures for a trait. Future work should consider a phenotype model where the function of a region is taken into account, as ENCODE (The ENCODE Project Consortium, The authors declare that there is no conflict of interest.Supplementary informationClick here for additional data file.


Autism spectrum disorder (ASD) is a highly heterogeneous neurodevelopmental disorder characterized by impaired social communication coupled with stereotyped behaviors and restricted interests. Despite the high concordance rate for diagnosis, there is little information on the magnitude of genetic contributions to specific ASD behaviors. Using behavioral/trait severity scores from the Autism Diagnostic Interview-Revised (ADI-R) diagnostic instrument, we compared the phenotypic profiles of mono- and dizygotic twins where both co-twins were diagnosed with ASD or only one twin had a diagnosis. The trait distribution profiles across the respective twin populations were first used for quantitative trait association analyses using publicly available genome-wide genotyping data. Trait-associated single nucleotide polymorphisms (SNPs) were then used for case-control association analyses, in which cases were defined as individuals in the lowest (Q1) and highest (Q4) quartiles of the severity distribution curves for each trait. While all of the ASD-diagnosed twins exhibited similar trait severity profiles, the non-autistic dizygotic twins exhibited significantly lower ADI-R item scores than the non-autistic monozygotic twins. Case-control association analyses of twins stratified by trait severity revealed statistically significant SNPs with odds ratios that clearly distinguished individuals in Q4 from those in Q1. While the level of shared genomic variation is a strong determinant of the severity of autistic traits in the discordant non-autistic twins, the similarity of trait profiles in the concordantly autistic dizygotic twins also suggests a role for environmental influences. Stratification of cases by trait severity resulted in the identification of statistically significant SNPs located near genes over-represented within autism gene datasets. Autism spectrum disorder (ASD) is a highly heritable and heterogeneous neurodevelopmental disorder which is characterized by deficits in social communication and reciprocal interactions as well as by stereotyped behavior and restricted interests, often accompanied by language difficulties, especially in the area of pragmatics . ASD is Ever since the twin study of Bailey et al.  reportedWhile twin studies make it apparent that genetics plays a significant role in ASD and associated phenotypes, no one genetic profile emerges due to the heterogeneity of ASD. In order to overcome this issue, some groups have attempted to reduce the heterogeneity by clustering individuals according to clinical, behavioral, or molecular subphenotypes. Previously, we used cluster analyses of severity scores on a broad spectrum of traits and behaviors probed by the Autism Diagnostic Interview-Revised (ADI-R) instrument  to identThe goals of this study were to: (1) investigate how genetics influences specific autism-associated behaviors and traits among monozygotic versus dizygotic twins, either concordant or discordant for autism diagnosis; (2) utilize ASD trait distribution profiles based on individual ADI-R scores in quantitative trait association analyses to identify single nucleotide polymorphisms (SNPs or quantitative trait nucleotides [QTNs]) that associate with specific traits; (3) determine whether the QTNs can differentiate cases from controls using individuals with ASD at the extremes of each trait distribution profile to reduce the phenotypic heterogeneity of cases for case-control association analyses; and (4) identify genes, pathways, and biological functions associated with specific traits. The results of these deep phenotyping analyses suggest that while shared genotype is a strong determinant of the severity of autistic traits in discordant monozygotic twins, the similarity of trait profiles of genetically distinct dizygotic twins concordant for diagnosis of ASD also suggests a role for shared environment. Moreover, genetic analyses which utilize both quantitative trait and case-control association analyses in which clinical or phenotypic heterogeneity is reduced by limiting the cases to those at the extremes of trait severities reveal highly significant SNPs associated with genes enriched in autism datasets and over-represented in neurological functions relevant to ASD.A total of 284 pairs of twins represented in the Autism Genetic Resource Exchange (AGRE) were included in this study. The twins were sorted into subgroups based on validated zygosity (monozygotic versus dizygotic) as well as by diagnostic concordance (concordant or discordant) for ASD. Each individual’s ADI-R scores for 88 items covering five ASD traits  were downloaded from AGRE and were used to establish trait severity distribution profiles for each subgroup of twins  between the non-autistic MZ and DZ twins for a majority of the items  software with a focus on identifying genes that impact nervous system development and function. n = 36) as controls for the diagnosed dA.DZ co-twins (n = 38). Interestingly, over 140 genes were associated with a total of 390 SNPs that exhibited a nominal p-value ≤ 0.05 and odds ratio ≥ 3 (q = 1.84 × 10−7) and from an exome-sequencing study [q = 4.64 × 10−8). Pathway analysis of this gene set using IPA revealed that netrin signaling  and axon guidance signaling  were among the top 10 canonical pathways represented with Fisher’s Exact p-values of 2.56 × 10−3 and 6.18 × 10−3, respectively. Several of the above-mentioned genes  are also significantly over-represented in additional pathways potentially relevant to ASD, including melatonin signaling (p = 1.18 × 10−2) and synaptic long-term potentiation (p = 4.45 × 10−2). Functional analysis showed significant over-representation of many neurological processes commonly impacted by autism, notably neuritogenesis, axonogenesis, neuronal migration, and axon guidance  examine the influence of genetics on specific behaviors and traits of ASD; (2) identify SNPs  that associate with a particular ASD trait; (3) determine if trait QTNs can discriminate between cases and controls, where the cases are individuals at the extremes of phenotypic severity across five autistic traits; and (4) to identify pathways and functions implicated by the genes associated with the QTNs. To accomplish these goals, we developed a novel approach which utilized MZ and DZ twins who are either concordant or discordant for diagnosis of autism to reveal differences in phenotypic severity among and within the subgroups of twins defined by diagnostic status and by zygosity. Then, we used the phenotypic (trait) profiles of each subgroup of twins to perform quantitative trait association analyses to identify SNPs that may be functionally associated with the respective ASD trait . Case-control association analyses were then performed with the QTNs for five autistic behavioral traits using the six different subgroups of twins at the extreme ends  of the respective quantitative trait distribution curves as cases and a large group of unrelated controls. We show here that this novel combination of experimental strategies allowed us to identify significant SNPs that could distinguish individuals with autism from controls. Genes harboring these SNPs are significantly enriched for autism risk genes annotated by SFARI Gene.Numerous studies using both monozygotic and dizygotic twins have sought to determine the role of genetics versus environment with varying results, as described earlier. The quantitative trait distribution profiles generated in this study demonstrate significant differences in severity between clinically discordant non-autistic MZ and DZ co-twins, with the profiles of the MZ twins being significantly more severe than DZ twins across all traits, while the profiles of all diagnosed twins are virtually indistinguishable from each other, regardless of zygosity . These dQTL association analyses allowed us to discover SNPs that may be functionally relevant to autism traits. The genes associated with trait QTNs  are overCase-control association analyses using individuals at the extremes of phenotypic  severity (Q1 and Q4) as cases enabled the identification of significant trait QTNs that were demonstrated to discriminate between cases and controls. This approach allowed reduction in the phenotypic heterogeneity of the individuals within each subgroup of twins for genetic analyses. In fact, genetic differences between the first and fourth quartiles of trait severity for all twin subgroups are quite clear. Notably, for SNPs associated with both Q1 and Q4 subgroups, the odds ratios for the two extreme groups are distinctly different and often in opposite directions  relative to unrelated controls , therebyp-values ≤ 0.05 remained significant after correction for multiple testing, there were 390 SNPs with nominal p-values ≤ 0.05 and odds ratios ≥ 3 (ranging from 3 to 11)  . HypergeWhile the use of discordant non-autistic DZ twins as a control group for their autistic co-twins in case-control association analyses may seem unconventional, there is precedence for family-based genetic studies in which concordant MZ twin pairs were compared against their parents by whole genome and exome sequencing, with each study revealing novel and rare variants in the probands ,29. The An advantage of quantitative trait association analysis is that it allows the identification of SNPs that may potentially be more functionally related to the condition, thus reducing the number of SNPs to be considered for further case-control association analyses. A possible disadvantage is that this procedure may exclude some ASD-relevant but not trait-associated SNPs from case-control analyses. Another limitation is that we did not separately analyze male and female twins due to the relatively small and variable number of females in the different subgroups of twins, and thus cannot eliminate sex as a confounding factor. However, a prior analysis of affected males and females from the AGRE repository using cluster analyses of ADI-R scores as described previously  showed nBecause of the extreme heterogeneity of ASD, there has been increasing attempts to stratify or subgroup individuals with ASD by specific phenotypes to obtain more homogeneous sample groups for large-scale genetics analyses. While some autism studies have been conducted using individuals at the top 5% of an autistic trait ,25,27,32Case-control association analyses using clinically discordant DZ twins as both cases and controls, while underpowered, identified a large number of nominally significant SNPs associated with genes that are significantly enriched in autism risk genes. While this study shows that reduction of genetic heterogeneity by stratification of cases according to trait severity or by use of discordant DZ twins as cases and controls increases the ability to identify common genetic variants associated with ASD, future studies with greater numbers of individuals in each subgroup are required to replicate these findings.We present here a novel experimental design using MZ and DZ twins, either concordant or discordant for ASD, which evaluates the role of genetics in contributing to the severity of autistic traits and identifies significant SNPs that can distinguish cases from unaffected controls by capitalizing on the extreme phenotypic differences exhibited especially by discordant MZ and DZ twins. Although prior studies have consistently indicated that genetics is a major contributor to the overall diagnosis of ASD, deep phenotypic profiling shows that almost all ASD traits are significantly more severe in non-autistic MZ twins than in non-autistic DZ twins, suggesting a dominant influence of genotype on ASD phenotypes probed by the majority of items on the ADI-R diagnostic instrument . At the Quantitative trait association analyses using ASD trait profiles reveal SNPs (QTNs) associated with genes that provide meaningful insight into neurological functions and pathways commonly associated with ASD, thus linking genotype to phenotype  as well as to underlying molecular pathology. Moreover, reducing phenotypic heterogeneity by using individuals at the extremes of trait severity for case-control association analyses with the trait-associated QTNs resulted in the identification of SNPs that significantly discriminate both affected and non-autistic co-twins from a large group of unrelated controls. These results suggest an underlying genetic liability towards autistic traits, even in the undiagnosed individuals . Genes implicated by the QTNs that survive correction for multiple testing in case-control association analyses are statistically enriched in ASD-associated genes revealed by significant overlap with those in the SFARI Gene database. Finally, case-control association analysis using dA.DZ twins as cases and their discordant non-autistic co-twins (dNA.DZ) as ‘controls’ also reveals a large number of neurologically relevant genes that are significantly over-represented in both SFARI Gene and exome sequencing datasets.t-test in the StatPac statistical software package (https://statpac.com/index.htm) was used to determine significance of differences in severity scores of overall ASD traits and specific ADI-R items based on p-values ≤ 0.05.Detailed demographic information of the 284 pairs of twins included in this study is shown in p-values testing significant deviation from Hardy–Weinberg equilibrium that were ≥ 0.001. Only subjects of European ancestry were genotyped and thus, only Caucasian twins could be included in the genetic association analyses, eliminating concerns about population stratification as a confounding factor. This publicly available dataset contained the genotypes for 74.3% of MZ twins (85 pairs) and ~85.4% of DZ twins (146 pairs) in this study. Controls were comprised of 2438 unrelated non-autistic individuals of European ancestry for whom genome-wide genotyping data was also available from the same GWAS study [Genome-wide genotype data for the twins and 2438 unaffected (non-autistic) controls were derived from a previously published genome-wide association study (GWAS) by Wang et al. , with daAS study . The worp-value ≤ 1.0 × 10−5 were identified as QTNs which were subsequently used in case-control association analyses as described below. The overlap of trait-associated genes implicated by the SNPs was determined using Venny 2.1.0, an online software package for creating Venn diagrams [PLINK 1.07 software  was useddiagrams .To reduce ASD heterogeneity for genetic analyses, only cases at the extremes of a defined ASD trait were used in separate case-control association analyses. These individuals exhibited cumulative trait severity scores within the first or fourth quartiles. The first quartile (Q1) was comprised of twins who exhibited the least severe phenotype for that trait and the fourth quartile (Q4) was comprised of twins who exhibited the highest severity for that trait. Cumulative trait scores at Q1 and Q4 for each subgroup of twins were determined using Tyers Box Plot software  see Sch. Individp-value ≤ 0.05).Significant SNPs were annotated using SNPper  and/or Shttp://keisan.casio.com/exec/system/1180573201), with significance determined by an upper cumulative q-value ≤ 0.05.SNP-associated genes were then compared to a list of known autism risk genes in the SFARI Gene database  and/or aDeep phenotyping analysis of monozygotic and dizygotic twins concordant or discordant for diagnosis of ASD indicates that the identical genotype of non-autistic MZ twins with their respective affected co-twins strongly influences the severity of autistic traits in comparison to the trait severity expressed by non-autistic DZ twins. Quantitative trait association analyses using trait distribution profiles and genotype data for the respective twin groups identify SNPs linked to traits. Case-control association analyses using these QTNs and individuals at the extremes of trait distribution profiles reveal significant SNPs associated with genes that are functionally significant to the known pathobiology of ASD. Finally, we suggest that more effective treatment strategies may be derived by associating specific phenotypes with genotype-implicated genes and related functional deficits manifested by a given subgroup of individuals.


Inflorescence capacity plays a crucial role in reproductive fitness in plants, and in production of hybrid crops. Maize is a monoecious species bearing separate male and female flowers . The switch from open-pollinated populations of maize to hybrid-based breeding schemes in the early 20th century was accompanied by a dramatic reduction in tassel size, and the trend has continued with modern breeding over the recent decades. The goal of this study was to identify selection signatures in genes that may underlie this dramatic transformation. Using a population of 942 diverse inbred maize accessions and a nested association mapping population comprising three 200-line biparental populations, we measured 15 tassel morphological characteristics by manual and image-based methods. Genome-wide association studies identified 242 single nucleotide polymorphisms significantly associated with measured traits. We compared 41 unselected lines from the Iowa Stiff Stalk Synthetic (BSSS) population to 21 highly selected lines developed by modern commercial breeding programs, and found that tassel size and weight were reduced significantly. We assayed genetic differences between the two groups using three selection statistics: cross population extended haplotype homozogysity, cross-population composite likelihood ratio, and fixation index. All three statistics show evidence of selection at genomic regions associated with tassel morphology relative to genome-wide null distributions. These results support the tremendous effect, both phenotypic and genotypic, that selection has had on maize male inflorescence morphology. Zea mays L.) is a branched structure that displays remarkable morphological diversity. Tassels vary in length, number of branches, compactness, and curvature, all of which are capable of affecting the quantity and dispersal of pollen. Inflorescence architecture is crucial to reproduction in wind pollinated plants  and teosinte glume architecture1 (tga1), which were targets of domestication that changed plant and inflorescence architecture between teosinte and modern maize (barren infloresence2 (bif2) locus (Previous studies have identified quantitative trait loci (QTL) and quantitative trait nucleotides associated with different aspects of tassel morphology and development that colocalize with 2) locus . The sam2) locus .Until 1935, most of the maize grown in the North American Corn Belt consisted of open-pollinated populations, in which plants are allowed to reproduce freely with each other. Within 4 years, however, >90% of maize grown in Iowa had transitioned to higher-yielding hybrids created by controlled crosses, and the rest of the Corn Belt soon followed .The shift in breeding methods to single-cross hybrids placed an emphasis on developing inbred lines with characteristics that enhance their potential to serve as parents. These parents are subsequently crossed to each other to produce vigorous hybrid offspring. In open-pollinated populations, a competitive advantage was conferred by greater pollen production and dispersal . Inbred a priori selection candidates, and compared selection statistics at those SNPs to their genome-wide distribution. If selection by breeders between the BSSS and modern ex-PVPs acted to reduce tassel size, we expect that loci associated with tassel morphology phenotypes would show enrichment for selection signatures relative to the rest of the genome. Indeed, we observe an enrichment of selection statistic scores in regions containing SNPs associated with tassel morphological traits, a finding that is consistent across three different selection statistics.Among the germplasm used in this study are inbred lines derived from the original BSSS population, as well as a number of commercially developed inbred lines for which the Plant Variety Protection certificates have recently expired (ex-PVPs). These ex-PVP lines represent the most modern germplasm from private seed companies that is available to the public, and they can be traced back to founder lines from the BSSS population. These two sets of materials afford us an opportunity to evaluate changes in maize tassel architecture caused by the accelerated evolutionary process of modern breeding. We used single nucleotide polymorphisms (SNPs) identified as significant in association mapping as 2 of the original parents.This study used two populations of maize inbred lines: a diversity panel and a nested association mapping (NAM) population. The diversity panel (WiDiv-942) consists of 942 diverse lines that typically reach grain physiological maturity in the Midwest regions of the United States, and represents an expansion of the 503 line Wisconsin Diversity panel , tassel length (TL), and spike length (SL) on three representative plants per plot during or after flowering. BN was quantified as the number of primary tassel branches, TL was measured as the distance in cm from the lowest tassel branch to the tip of the spike, and SL was measured as the distance in centimeter from the uppermost tassel branch to the tip of the spike. All traits were measured in all environments with the exception of SL, which was not measured in the PHW65 NAM at West Madison in 2014. Three derived tassel traits can be calculated from these measurements: branch zone length (BZ) as TL minus SL, branch density (BD) as BN divided by BZ, and spike proportion (SP) as SL divided by TL.In addition to manual measurements, tassels measured in 2015 were also imaged and measured automatically using TIPS  for all manually measured traits, except TW, were calculated as the random genotypic effect predictions from the linear model Heritability was calculated on an entry-mean basis for all manually measured traits except for TW as Genotypic and phenotypic correlations between all traits were calculated for each population. Because of differing numbers of phenotyped lines and differing numbers of environments in which the traits were evaluated, the correlations were only calculated using data from the West Madison 2015 location, and only with lines that were phenotyped for all 15 traits in that environment .The WiDiv-942 lines were genotyped by RNA sequencing as described in Inbred lines in the PHW65 NAM population were genotyped using genotyping-by-sequencing (GBS) as described in The four parents of the PHW65 NAM population were resequenced and genotyped at 23.3 million SNPs  with theWe identified lines that represent early Stiff Stalk germplasm, recent ex-PVP Stiff Stalk germplasm, and publicly developed Stiff Stalk germplasm that represents a temporally intermediate group between the two.The WiDiv-942 contains 47 inbreds derived through self-pollination from the original BSSS population (referred to hereafter as BSSSC0), which represent maize Stiff Stalk germplasm from the early 20th century.R2 value >0.1 within the window were discarded, leaving 109,605 SNPs. The pruned marker set was used in ADMIXTURE without seeding founding individuals. Ten-fold cross-validation of the errors was minimized at K groups equal to eight as an appropriate model for this marker set. These eight groups represent the resulting subpopulations; B14, B37, B73, Oh43, Lancaster, Iodent, Iodent-Lancaster, and Flint. To identify lines that both display evidence of descent from the BSSS as well as exclude lines with evidence of introgression from other germplasm pools, individuals were required to have a sum of >95% identity to the B14, B37, and B73 groups, as well as <2% identity to each of the other groups. Of the lines that met this requirement, 21 had been phenotyped and were kept for subsequent analysis. Those BSSS-descended ex-PVP lines are referred to hereafter simply as ex-PVPs. Hierarchical clustering of the ex-PVPs and BSSSC0 lines revealed six of the BSSSC0 lines did not cluster with the others. Those six were removed from further analysis, leaving 41 BSSSC0 lines.From all ex-PVP lines in the WiDiv-942, inbreds were chosen that showed genotypic evidence of being directly descended from the BSSS population (File S1). Although pedigree information was available for some ex-PVPs, the number of individuals that could be traced by pedigree back to BSSS-derived inbreds was low. Additionally, using genotypic information to identify BSSS-derived ex-PVP lines allows exclusion of individuals showing evidence of contamination from other breeding material. Population substructure within all the ex-PVP lines was estimated using ADMIXTURE  for all lines in the WiDiv-942 were calculated by the same models used to calculate BLUPs, but with genotype fit as a fixed rather than random effect. BLUEs for the BSSSC0, Public, and ex-PVP lines were compared for each of the 15 tassel morphological traits, and significant differences were evaluated by Tukey’s honest significant difference. .farmCPU  for the WiDiv-942 were performed in R  using th−5 to 1.5 × 10−4) and allowed terms to exit the model based on a limit set at twice the entry threshold. Residuals from the final stepwise model were calculated separately for each chromosome, with any SNPs on that chromosome excluded from the model. The residuals for each chromosome were used as the dependent variable in a resampling-based mapping method similar to that described in −4. This process was repeated 100 times for each combination of trait and chromosome, and each SNP fitted by the resampling GWAS method was assigned a resampling model inclusion probability (RMIP) between 0 and 1, reflecting the proportion of models in which that SNP was included. A permutation-based threshold for RMIP was calculated in a manner similar to that described in The PHW65 NAM was mapped using stepwise model selection with the GBS SNPs followed by resampling GWAS with the 10.6 million projected parental SNPs, as described in We used the 41 BSSSC0 and 21 ex-PVP lines to perform genome-wide scans for selection. The BSSSC0 lines represent maize Stiff Stalk germplasm from the early 20th century, while the ex-PVP lines represent the product of ∼60 years of commercial maize breeding. We calculated cross population extended haplotype homozogysity  on the same set of SNPs as XP-EHH, with a grid size of 100 bp, a genetic window size of 0.1 cM, a maximum of 50 SNPs per window, and correlation level of 0.7. The genetic positions of the WiDiv SNPs were estimated by linear interpolation of the NAM genetic map  between the two groups was calculated on the same set of SNPs as XP-EHH and XP-CLR, using http://beissingerlab.github.io/docs/vectorFst.R , we used 10,000 iterations of a circular permutation method , recombination rate (±20%), frequency of alleles in the BSSSC0 lines (±15%), and frequency of alleles in the ex-PVP lines (±15%) were randomly sampled without replacement. For tassel-associated windows with <50 matching windows genome-wide, the allele frequency criteria were omitted.P-value  and genotypic data for the WiDiv-942 can be found at https://doi.org/10.5061/dryad.6tg35t6 . Code is available on GitHub at github.com/joegage/tassel_selection. Supplemental material available at Figshare: https://doi.org/10.25386/genetics.7097813.Tassel images of both populations and genotypic data for the PHW65 NAM are available on the CyVerse Data Store  and an NAM population (PHW65 NAM) with PHW65 as the common parent and PHN11, MoG, and Mo44 as founder parents. These materials were grown in three environments between 2013 and 2015 in south central Wisconsin. The WiDiv-942 association panel used in this study is comprised of 942 diverse inbred lines, while the PHW65 NAM consists of three nested biparental populations of 200 individuals each. The WiDiv-942 was chosen to capture broad phenotypic and genetic diversity, whereas the PHW65 NAM leverages controlled biparental crosses between individuals with contrasting tassel morphologies. All tassels manually measured in 2015 were also photographed and measured using the image-based tassel phenotyping system TIPS  and those that contribute to tassel size by contributing to branchiness . Although TW and TWp are measures of mass rather than branching, both traits are affected more by changes in branchiness than changes in TL and therefore are included in the former group.For most traits, the PHW65 NAM population has a higher or equivalent mean to the WiDiv-942 population, with the exception of TWp (0.79 g lighter), BN (1.83 fewer branches), BNp (1.07 fewer branches), and BD (0.24 fewer branches/cm). As expected, given the allelic representation contained in each of the populations, phenotypic variability within the PHW65 NAM is lower than in the WiDiv-942, with the exception of TW (SD 0.3 g greater) and BNp (SD 0.07 branches greater).Heritabilities for manually measured traits ranged from 0.93  to 0.97 (BN) in the WiDiv-942 population and from 0.72 (BZ and SP) to 0.94 (BN and TW) in the PHW65 NAM population. Because images and TW were taken only at one location, repeatability was calculated for image-based traits and TW in place of heritability. Repeatabilities ranged from 0.72 (PR) to 0.86 (TWp) in the WiDiv-942 population and 0.63 (SLp and TLp) to 0.72 (SK) in the PHW65 NAM population . The higGenotypic and phenotypic correlations were calculated within the single environment in which all traits were measured . With the exception of CP, branchiness traits were generally positively correlated with each other in both populations. Similarly, length-related traits were all positively correlated with each other in both populations. Phenotypic and genotypic correlations were similar to each other in both populations, partly due to relatively high heritability of all traits and partly due to having been calculated within a single location.The WiDiv-942 association panel contains 41 inbred lines developed by selfing without selection from cycle 0 of the BSSS population (BSSSC0), 16 public inbred lines with pedigrees that trace entirely back to lines derived from the BSSS, and 21 ex-PVPs with genotypic evidence for descent from the BSSS (File S1). These three groups of lines allow comparison of tassel morphology over the course of modern maize breeding. The BSSSC0 lines represent the earliest material, the ex-PVPs represent the most recent and heavily selected material, while the public lines form an intermediate group.Comparison of BLUEs for each group revealed that the mean values of public inbred BLUEs for each trait showed between a 2% (FD) and a 16% (TWp and BNp) change relative to the BSSSC0 line, while ex-PVP lines displayed between a 4% (TLp) and a 45% (TWp) change in mean relative to the BSSSC0 lines . For allAll 15 traits were mapped in the WiDiv-942 association panel using the multiple locus linear mixed model implemented in FarmCPU . Generally, there is more concordance between SNPs associated with manual and image-based measurements for traits with higher heritabilities/repeatabilities (BN and TW) than lower heritabilities/repeatabilities (SL and TL). This is to be expected, as genetic signal is stronger when heritability is high, but the pattern seen in this study may be due only to chance as BN and TW are only marginally more heritable than SL and TL.a priori candidates for regions having undergone selection between the BSSSC0 lines and the ex-PVP lines. Scans for selection were conducted using LD-focused methods XP-EHH , as well as genome-wide null distributions generated by randomly sampling windows with similar characteristics , suggesting enrichment for selection signals in regions associated with tassel morphology.To test for genomic signatures of selection on tassel morphology, SNPs associated with tassel characteristics in the WiDiv-942 and PHW65 NAM lines were used as -EHH (ST . Genome-P = 2.9 × 10−3). Branchiness traits have more influence on tassel size and biomass than tassel and spike length. With the exception of BZ, all the length traits increased from the BSSSC0 to the ex-PVPs, whereas all the branchiness traits decreased. As such, most of the SNPs showing evidence of selection in the ex-PVPs are associated with traits that control overall tassel size and biomass and have decreased significantly since the 1930s.XP-EHH scores for tassel-associated windows  were enrSimilar to XP-EHH, XP-CLR is a haplotype-based method for identifying selective sweeps. Rather than identify alleles that have recently arisen to substantial frequency, as XP-EHH does, XP-CLR identifies alleles that have changed in frequency more quickly than expected under neutrality  show enrST, a measure of population differentiation based on allele frequencies, differs from the previous two selection statistics in that it is not haplotype based. FST values for tassel-associated windows . The lack of any difference could be due to the low number of SNPs we were able to directly test, or perhaps due to noise introduced by identifying SNPs that are not causative themselves but in LD with variants that directly affect tassel morphology.None of these three selection statistics show strong, systematic relationships with each other on a genome-wide basis  or among the tassel-associated windows . For the 101 significant associations that were genotyped in the WiDiv-942 , we hypothesized that alleles with higher frequency in the ex-PVPs would generally have allelic effects conferring more ex-PVP-like phenotypes, that is, positive values for TL, SL, TLp, SLp, and SP, and negative values for all other traits. However, we found no difference between the effect sizes of alleles with higher frequency in the ex-PVPs and alleles with higher frequency in the BSSSC0s  by breeders aiming to reduce overall tassel size. The enrichment for positive XP-EHH scores, although not as extreme as for negative scores, indicates a number of tassel-associated loci with slower LD decay in the BSSSC0 lines than in the ex-PVP set. One possible explanation for this observation is that prior to the creation of the BSSS, during a period characterized by open-pollinated populations, heavier tassels with more branches had a reproductive advantage due to higher pollen production. During the last century of maize breeding the selective pressure on high pollen production has been removed by a hybrid breeding scheme in which inbred combining ability and hybrid grain yield are prioritized. It is possible that the BSSSC0 lines show extended haplotypes due to selection favoring alleles that confer large tassel size, whereas modern breeding schemes have removed that selective pressure and allowed or encouraged recombination in previously selected regions.unbranched2 and unbranched3 have been shown to simultaneously decrease branch number and increase kernel row number, a trait that directly affects grain yield (zea floricaula/leafy 2 decrease both branch number and kernel row number (The results presented here provide evidence for selection by 20th century maize breeders on regions associated with maize tassel morphology. Whether these changes are the result of direct or indirect selection on tassel size and shape is unclear. Modern, commercially developed maize inbreds display a suite of characteristics that have systematically changed since the open-pollinated varieties of the 1930s, and it is difficult to disentangle selection for changes in tassel morphology from selection for traits that are regulated by loci pleiotropically involved in tassel morphology. Because the tassel and the ear follow a shared developmental path early in development, genes affecting morphology of one may very well have effects on the other. QTL have been discovered that exhibit pleiotropic behavior, conferring a positive relationship between tassel and ear length (w number . There iw number . AlthougChange in tassel size and shape between the early 20th century and modern day is a well-characterized phenomenon but the causes of that phenomenon and its potential causal effects on other agronomic traits and productivity are not fully known. Our results present evidence for enriched signals of selection in genomic regions associated with tassel morphological traits. Further, this selection took place in ∼60 years between the creation of the BSSS in the 1930s and the release of ex-PVP lines in the 1980s and 1990s, a tremendous example of the efficiency of modern crop breeding in imposing drastic genetic and phenotypic changes.


The Disease Activity Score (DAS) is integral in tailoring the clinical management of rheumatoid arthritis (RA) patients and is an important measure in clinical research. Different versions have been developed over the years to improve reliability and ease of use. Combining the original DAS and the newer DAS28 data in both contemporary and historical studies is important for both primary and secondary data analyses. As such, a methodologically robust means of converting the old DAS to the new DAS28 measure would be invaluable. Using data from The Early RA Study (ERAS), a sub-sample of patients with both DAS and DAS28 data were used to develop new regression imputation formulas using the total DAS score (univariate), and using the separate components of the DAS score (multivariate). DAS were transformed to DAS28 using an existing formula quoted in the literature, and the newly developed formulas. Bland and Altman plots were used to compare the transformed DAS with the recorded DAS28 to ascertain levels of agreement. The current transformation formula tended to overestimate the true DAS28 score, particularly at the higher end of the scale. A formula which uses all separate components of the DAS was found to estimate the scores with a higher level of precision. A new formula is proposed that can be used by other early RA cohorts to convert the original DAS to DAS28.The online version of this article (10.1007/s00296-018-4184-0) contains supplementary material, which is available to authorized users. The Disease Activity Score (DAS) is a composite score developed as a means of quantifying the severity of rheumatoid arthritis (RA) . It is cSeveral versions of the DAS exist. The original DAS established that four measures could be combined to give an effective overview of the overall disease status of a patient: a 44 joint Swollen Joint Count (SJC), the Ritchie Articular Index (RAI) of 53 tender joints, the Erythrocyte Sedimentation Rate (ESR) and a Patient Global Assessment (PGA) of disease activity on a 100 mm visual analogue scale (VAS) , and areIt is agreed that the DAS and DAS28 scores cannot be used inter-changeably due to their differences in minimum and maximum values, and weighting used for each component of the score . HoweverMethods for transforming the original DAS to the DAS28 metric have been proposed, and used in a number of previous studies to try and facilitate direct comparisons –14. A coUsing a sub-group of patients from the ERAS cohort attending one centre where both DAS and DAS28 data are available, this paper explores the use of imputation methods, including the formula given by van Gestel et al., to calculate missing DAS28 scores where DAS are recorded. The analyses will compare levels of agreement of (1) the van Gestel formula, (2) univariable regression imputation using DAS to predict DAS28, and (3) multivariable regression imputation model using the separate components of DAS to predict DAS28. Finally, the paper will examine differences in trends over time using the different methods to calculate DAS28 to determine potential differences in interpretation. The aim is to provide a potentially more statistically reliable transformation formula for converting DAS to DAS28.The Early RA Study (ERAS) recruited a total of 1465 patients with early RA from nine centres in England between 1986 and 2001. All patients had a confirmed diagnosis of RA and were recruited within 2 years of symptom onset (median 6-months), prior to conventional DMARD initiation. All patients were treated based on standard clinical practice of the time. Standard clinical, laboratory and radiographic data were collected during outpatient appointments at baseline, 6 months, 12 months, and then yearly thereafter. Each centre closed to follow up at different times between 2001 and 2013 with a maximum follow-up of 30 years (median 10 years) for annual outpatient follow-up. ERAS received retrospective ethical approval from the East Hertfordshire Local Research Ethics Committee in 1994 and subsequently from the Caldicott Guardian.n = 298), where the component variables for both the DAS and DAS28 were recorded for the same patients by the same examiner. Restricting the analyses to the first 5 years, the 298 patients contributed a total of 1470 observations (mean 4.9 observations per patient).The analysis uses a subset of the main ERAS dataset with data from one centre ..1).1\docFor the subset of patients where the DAS28 component variables were collected, DAS28 was calculated using the four-variable formula  (Eq. 2)2r = .900 in the current data). Sub-analysis (not shown) found that there was higher agreement between the DAS28 and DAS28 using pain VAS compared to just the three-variable DAS28 score, therefore the four-variable DAS28 with either the PGA or pain VAS was used.While a PGA VAS was not routinely collected, patient assessment of global pain using a 0–100 VAS was. PGA was used where available but where missing (94% observations) the pain VAS was used in place. The large proportion of missing PGA data was due to the fact that PGA data was typically collected beyond the 5-year follow-up for patients recruited from this centre. Khan et al. indicates that different measures of global health can be used inter-changeably without significant impact on the DAS . This isThe conversion formula given by van Gestel et al.  for impuThe analysis examines three methods of imputing DAS28. Whilst other imputation methods have proven more effective in imputing missing data, such as multiple imputation , this isUnivariable mixed-effects linear regression models regressed the DAS28 on to the DAS for the DAS-only regression imputation. Mixed models were used to account for the longitudinal nature of the data. The fixed effects from the model, the coefficient for DAS and the constant, were then used to calculate imputed DAS28 scores. A similar procedure was applied for the multivariable mixed-effects linear regression imputation using the individual DAS components: the square-root of the 44-count SJC and the RAI, the natural logarithm of ESR and PGA/pain VAS scores will be used. Additionally, sex  and age in years were also included as predictors, since these are known to independently impact on ESR . The coeMean scores of the DAS28 over the first 5 years will be compared to the three imputation methods outlined, and the mean difference, along with levels of agreement, will be assessed using Bland and Altman plots . Bland an = 1465), 298 (20.3%) attending one centre had the component variables for both DAS and DAS28 collected. The 298 patients contributed 1470 observations over 5 years (mean 4.9 observations per patient). Demographic and baseline clinical measures for the whole cohort, and those with and without DAS28 measures over the first 5 years are shown in Table Of the patients from ERAS n = 465, 298 The fixed-effect estimates from the mixed-effects linear regressions for the univariable and multivariable regression imputations are shown in Table R2 for the univariable regression and multivariable regression model was 0.73 and 0.91, respectively, indicating high predictive accuracy. This was further supported by the results of the cross-fold validations  which indicate similar pseudo R2 across the models for the univariable and multivariable regression: 0.72 and 0.91, respectively.The effect estimates from the multivariable regression of DAS28 on the square-root 44-SJC and RAI, the log ESR, pain VAS, age and sex are as follows:Bland and Altman plots Fig. a–c were The Pearson correlation between the DAS28 and van Gestel formula was 0.85, for the univariable regression was 0.85 and for the multivariable regression was 0.95. The ICC for the transformation formula was the lowest at 0.72 , followed by the regression imputation using only the DAS at 0.84 (95% CI 0.83–0.86), and finally the highest ICC was observed for the multiple regression imputation with the component scores at 0.95 (95% CI 0.95–0.96).When categorised into remission, LDA, MDA and HDA, the recorded DAS28 scores indicated 22% of scores in remission, 12% of scores in LDA, 38% of scores in MDA and 28% of scores in HDA. The van Gestel formula saw an increased proportion of scores recorded as HDA at 45%, with lower proportions in the other groups. Conversely, both the univariable imputation and the multivariable imputation indicated slight underestimation in the remission and HDA categories, and slight overestimation in the LDA and MDA categories.The weighted Kappa agreement analysis of the DAS28 categories indicated the highest level of agreement between the multivariable imputation at 97.6% and a Kappa statistic of 0.91. Univariable imputation using only the DAS score indicated an agreement of 95.2%, with a Kappa statistic of 0.81, whilst the transformation formula method indicated the lowest agreement at 93.6% and a Kappa statistic of 0.77.The overall mean of the DAS28 over the first 5 years was 4.10 (SD 1.7). This compared to an overall mean of 5.09 (SD 2.19) using the van Gestel formula, 4.10 (SD 1.51) using univariable regression imputation of DAS and 4.11 SD 1.63) using the multivariable regression imputation with the separate DAS components. While the mean scores were similar for the univariable and multivariable regression scores, the variability in the DAS28 was better approximated by the multivariable imputation model. The mean and standard deviations for each method over 5 years follow-up is given in Table  using thUsing a sub-sample of early RA patients from a longitudinal cohort, this study found that multivariable regression imputation of the DAS28 using the separate components of the original DAS measure resulted in the highest level of agreement when compared with recorded DAS28 scores. Furthermore, using the formula provided by van Gestel et al. , resulteThe relatively large improvement in the mean difference between the univariable regression imputation using the total DAS in this analysis, compared to the formula by van Gestel et al.  suggestsThe analyses demonstrated that performing multivariable regression imputation using the separate components of DAS within the same dataset is the best approach for transforming DAS to DAS28. This is useful in situations where the DAS has been recorded but the DAS28 is preferred. Such instances include longitudinal studies considering secular trends over time , 14 and Other forms of imputation, such as multiple imputation using chained equations (MICE) are also available, that have been shown to be less biased and more robust in imputing missing data . SensitiExamination of demographic and baseline clinical variables for the sub-sample of patients with both DAS and DAS28 data indicated that, on average, these patients had higher disease activity at presentation. This could therefore indicate that the imputations were based on a sub-group of patients with more severe forms of RA. Interestingly, incidence of seropositivity and levels of ESR were lower than the rest of the cohort, suggesting that higher DAS may have been influenced more by TJC and pain VAS, the so-called subjective markers, rather than the more objective markers of inflammation , 24. NevIn summary, the analysis presented demonstrates the advantage of using multivariable regression imputation in situations where older data using DAS are to be converted to DAS28, to facilitate aggregation of data. While the best method is to use estimates from a regression model derived from the data itself, the paper provides a formula to transform data based on the separate components of the DAS, rather than just the overall DAS itself, in instances where data-specific parameters are not available. This formula provides an improved and statistically more reliable method for converting DAS to DAS28 for long-term analysis where research necessitates the combination of historical and contemporary data in RA.Below is the link to the electronic supplementary material.Supplementary material 1 (DOCX 57 KB)


The aim of this study was to estimate (co) variance components and genetic parameters for categorical carcass traits using Bayesian inference via mixed linear and threshold animal models in Anglonubian goats.Data were obtained from Anglonubian goats reared in the Brazilian Mid-North region. The traits in study were body condition score, marbling in the rib eye, ribeye area, fat thickness of the sternum, hip height, leg perimeter, and body weight. The numerator relationship matrix contained information from 793 animals. The single- and two-trait analyses were performed to estimate (co) variance components and genetic parameters via linear and threshold animal models. For estimation of genetic parameters, chains with 2 and 4 million cycles were tested. An 1,000,000-cycle initial burn-in was considered with values taken every 250 cycles, in a total of 4,000 samples. Convergence was monitored by Geweke criteria and Monte Carlo error chain.Threshold model best fits categorical data since it is more efficient to detect genetic variability. In two-trait analysis the contribution of the increase in information and the correlations between traits contributed to increase the estimated values for (co) variance components and heritability, in comparison to single-trait analysis. Heritability estimates for the study traits were from low to moderate magnitude.Direct selection of the continuous distribution of traits such as thickness sternal fat and hip height allows obtaining the indirect selection for marbling of ribeye. In animal breeding programs several traits are evaluated to identify genotypes with higher average according to the proposed objectives. The analyzed data for this purpose may be continuous, as an example of measurement performed in the loin eye area, which is assumed to have normal distribution, or discontinuous such as the case of categorical traits as carcass marbling. However, to obtain estimates of (co) variance components and genetic parameters for categorical data, some approaches that consider the discrete data distribution should be used to ensure greater accuracy of the estimates.in vivo evaluation, whose advantage is to obtain information of the nutritional status of animals. In goats, this technique is widely applied, however the use of ultrasound to evaluate carcass in live animals has spread because it enables the identification of carcass marbling based on intramuscular fat. It is a type of data with discrete distribution in which the longissimus dorsi is the main muscle for evaluation in the living animal.Within the categorical traits in meat goat production, the score assigned in the evaluation of body condition of animals is a criterion that has been used for carcass The estimation method with establishment of a model that correctly describes the nature of categorical data is an important factor to obtain genetic parameters . The metWith the use of threshold model it is considered there is an unobservable variable that takes the normal distribution underlying the discrete variable. The variable connection observed with the underlying continuous scale is made by a set of fixed thresholds. Thus, the underlying variable, defined as the sum of genetic and environmental effects which affect the susceptibility of a trait , is descBy comparison, the genetic gain estimated from genetic analysis of categorical data obtained by threshold models are higher due to the achievement of higher heritability in the underlying scale , thus reWith the advent of increasingly powerful processors, the Bayesian methodology reemerged as statistical tool to estimate components of (co) variance and genetic parameters in animal breeding. Bayesian inference allows the use of prior information of the studied trait being included in the analysis through information of a prior distribution of the parameters to be analyzed along with its uncertainty before the observation data. It also considers the different distributions of the studied data, increasing the accuracy of estimates and predictions.The aim of this study was to estimate (co) variance components and genetic parameters for categorical carcass traits using Bayesian inference via mixed linear and threshold animal models in Anglonubian goats reared in the Mid-North region of Brazil.The experimental procedure was approved by the Institutional Animal Care and Use Committee at Federal University of Piauí, Brazil (009/14).The database used in this research consisted of genealogical and production information measured in registered Anglonubian goats with genealogical records reared in the states of Piauí and Maranhão (Mid-North region of Brazil). The field data collection was carried out from the years 2012 to 2014.The traits evaluated in this study were: body condition score (BCS), marbling in the rib eye (MRE), ribeye area (REA), fat thickness of the sternum (FTS), hip height (HH), leg perimeter (LP), and body weight. These traits were measured at the same time in each animal. Goats of both sexes, aged from seven months and healthy were eligible to participate.For standardization during the farms data collection the following steps were adopted: after weighing on a scale with a capacity of 200 kg and precision of 0.10 kg, BCS of each animal was measured based on palpation and visualization of the lower back region, mimicking up motion grippers applying constant pressure around and between the transverse and spinal apophyses, also in the sternal region, assessing the amount of skin, muscle and fat density in two anatomical regions, according to methodology cited by . The scoThereafter, the following morphometric measurements were taken using hipometer and measure tape while the animal was restrained in a comfortable standing position: HH, distance between the sacral tuberosity of the ilium and the soil; and LP, measured on the median part of the leg above the femoral-tibial-rotulian articulation (in centimeters).In vivo evaluation of carcass was performed by means of ultrasound images captured using the apparatus Chison 600M equipped with linear transducer (13 cm) using a set of frequency 5.0 MHz.2) was measured through ultrasonographic cross-sectional images of the longissimus dorsi muscle in the intercostal space between the 12th and 13th ribs. With the same image the MRE was evaluated with by assigning grades from 0 (absence of intramuscular fat) to 6 points (abundance of intramuscular fat). This visual grading scale was an adaptation of that used by [The REA : rainy season, from January to May; and dry season, from June to December. The birth month of animal was also distributed in two birth seasons, namely rainy and dry seasons, similar to the format of CS. The age of the animal at the time of collection was grouped into age classes (AC), as follows: AC = 1, animals >six months and <two years; AC = 2, animals >two years but <four years; AC = 3, animals >four years. Finally, the evaluated goats were grouped into animal category (CAT) as follows: pregnant, kidding, and dry breeding does. In the formation of the contemporary group (CG), animals born on the same farm, in the same year, and same sex were taken into consideration.The data were edited and formatted with the statistical program SAS . After the consistency analyses a file containing animal information, parent, CG, year of collection (YC), age group (AC), animal category (CAT), and observations relating to the analyzed traits, totaling 385 animals with observations was edited. At the end, the numerator relationship matrix of Wright contained information from 793 different animals.The components of (co) variance and genetic parameters were estimated via linear and threshold animal model by Bayesian inference in single and two-trait analyses. Two-trait analyses were performed by combining the two categorical traits (two by two) with the continuous ones, totaling 11 analyses. Thus, two-trait analyses were performed in animal model, assuming two different distributions in the same analysis.Estimates of genetic parameters via Bayesian Inference were calculated with the aid of GIBBS1F90 and THRGIBBS1F90 applications, used for linear and threshold models, respectively , by testa posteriori distribution with 4,000 samples in which inferences were performed. Values for burn-in and sampling interval were defined based on preliminary analyses in which the convergence and distribution of samples were evaluated through the POSTGIBBS1F90 program [After burn-in of the first 1,000,000 samples samples were taken apart at every 250 cycles , resulting in  program , which u program  based ony = Xβ+Zα+ɛ, in which: y = vector of observations of the studied traits ; X = matrix n×f of incidence , which relates the findings to the systemic effects; β = vector of systemic effects of CG , YC, AC, and CAT; Z = the matrix n×N of incidence, which lists the observations to genetic additive direct effects, where n is the total number of observations and N number of individuals; α = vector of random effects representing the direct genetic additive values for each animal ; and e = vector of residual random errors associated to the observations.The animal model in matrix notation was: In Bayesian analysis the systemic and random effects included in the model are considered as random variables.y) and data  is the location vector of order parameters s with b  and order s with a (random genetic additive direct effect); W is a matrix incidence of order r by s; I is an identity matrix of order r by r; and In the threshold model the underlying scale assumes normal distribution represented as: yi that falls into the category j  with the given vectors β, α and t  and represented as:The conditional probability that i animals are defined by Ui, in the underlying scale, and BCS:The categories (scores) of the BCS and MRE traits for each n is the number of observations for each trait.Where As the residual variance is not estimable in threshold models, the parameter was assigned a value of 1 in order to obtain identifiability in the likelihood function . This asa priori distribution) for all initial variance, in other words, did not reflect the knowledge about the parameters to be estimated.Flat was defined (uninformative As the best model selection criteria for the traits in study it was used: deviance information criterion (DIC), which is obtained based on the posterior distribution of the deviation statistic ; and baya posteriori distributions of the deviance of each model, being defined by: DIC = D̄ (θ) + pD; in which: D̄ (θ) is the global adjustment measure that is the posteriori average of the deviance; pD is the penalty for complexity of the model (effective number of parameters) given by the difference between the average posteriori of the deviance and the deviance of the averages a posteriori of the model parameters of interest. Thus, the smaller the value of DIC the better the fit of the evaluated model [f(y|M) = ∫ L(θ|y) π (θ) dθDIC is a model comparison criterion following the proposition of , who suged model . As for Mi and Mj), the BF was defined as the reason for the marginal likelihoods of these two models: In analysis with two models  is the most plausible if FBi,j<1, the denominator model (Mj), is preferred, and if FBi,j = 1, the quality of the two models is the same (Mi = Mj). The threshold model was the FB denominator.The interpretation of this ratio was given according to , where: y|β, a, G0, R0~N ; a|G0, A~N; e|R0 ~N, thus: A, additive genetic relationship matrix among animals; G0, additive genetic (co) variance matrix among traits; I, identity matrix; and R0, residual (co) variance matrix among traits.In two-trait analyses it was assumed normal distribution traits for REA, FTS, HH, LP, and body weight, whereas for MRE and BCS these traits were considered as categorical discrete distribution. The same animal model of single trait was used in the analyses with the following presupposition: Convergence was monitored by Geweke criteria  and erroa posteriori distribution parameters, according to [In the examination of chain convergence, the Geweke criterion was significant (p<0.05) , indicatrding to .Comparing the linear model with the threshold applied to categorical data, using the DIC criteria, and the BF, it was observed that the threshold DIC model showed values equal to 421.00 and 706.74 , whereasBF, according to the used criterion, showed values lower than 1, since the denominator model was the threshold, then confirming that it is the most recommended for the inference of parameters, as interpretation proposed by .Estimates of heritability for BCS and MRE traits  obtained by the threshold model were lower than the values estimated by linear model. BCS equals to 0.29 and MRE equals to 0.12. The confidence intervals of heritability estimates showed variation of low magnitude when estimated by the threshold model. This amplitude permits inference with a greater reliability of the quality of the estimates.In two-trait analyses, where the marbling and BCS were paired with other traits with continuous distribution, it was used the threshold model for the categories that were the best adjustment for the ones used in single-trait analysis, while for continuous distribution the model was linear .The estimated heritability for continuous traits ranged from moderate (0.24) to high magnitude (0.54) . Table 4The good availability of food for the evaluated animals in study is well portrayed by the amount of body condition presented, in which the average was 3.27, higher than the median and mode. Therefore, animals with good tissue composition in terms of muscle mass in the lower back were samped. It is noteworthy, however, that animals which participated in exhibitions at agricultural fairs were also sampled, and this partly explains the relatively high value of the observed variation coefficient.In addition, since BCS and MRE are evaluated subjectively, these traits are greatly influenced by the experience of the appraiser and environmental factors such as food, physiological status, and health, which in this study are embedded in the value of CV 45.71 and 34.11 for BCS and MRE, respectively, enhancing the role of phenotypic variability that should be considered carefully if included in animal breeding programs.For the carcass fat thickness based on the value of MRE, the average of 2.55 points, that median and mode corrected to 3.0, is greater than what was found by  in crossThe superiority when comparing to the goats values to other genotypes, focusing on meat production, is explained by the case that the animals were intended for breeding were kept under more appropriate management. However, such superiority was also influenced by age, since animals aged 7 months were evaluated. After this age there is the possibility of increased deposition of fat in the carcass .The good body condition and potential of carcass marbling of the animals in study are emphasized when compared to results obtained in sheep. For MRE, the average value was 2.55 points, close to that observed in crossbred undefined sheep breed (SRD)×Santa Inês (2.98), which did not differ statistically from crossbred lambs SRD×Texel . Thus, dposteriori heritability coefficient, it does not change the value of this estimate, considering the second decimal place, as shown in Based on the Monte Carlo error (MCE), low values for both the analyses with linear and threshold models confirm the convergence, because according to , this oca posteriori were heritability valid estimates of categorical traits.Therefore, the convergence monitored by Geweke criterion and MCE indicated that the chain size used in this study was appropriate and the amount a posteriori interval probability [There is tendency of BF to be more sensitive to the choice of the prior distribution than the bability . Thus, tbability , relatedEven considering that in the literature there are few studies that compare linear and threshold models for analysis of categorical carcass traits in goats, our results agree with the consulted studies, mostly with cattle and sheep, indicating that the use of threshold model provides more accurate estimates than the linear model ,23. HoweThe lower variability of the genetic components of categorical traits, when estimated by linear model, could be an evidence of the inadequacy of its use for traits with this distribution, which may result in estimates that cause wrong inferences . ReflectIt was found that the use of the threshold model resulted in lower estimates for obtaining the studied heritability of categorical traits, because the residual variance estimates differed markedly between threshold and linear models. In addition, as the credibility regions do not overlap, this leads to rejection of statistical hypothesis of equality between the estimates generated by the two models .a posteriori distribution estimates of the parameters in two-trait analyses.As seen in the single-trait analysis, it was found that the Geweke convergence criterion presented significance level lower than 0.05, and MCE was low for all analyses , implyinIt was found in two-trait analyses increased contribution of the considered information number and also influence of the correlations between the characteristics to increase the estimated values for the components of (co) variance and heritability values of the traits in study , since tlongissimus dorsi. Thus, it is considered that this fact is an explanation for the low heritability estimates for MRE, and then much of the phenotypic variability of the trait is explained by environmental component, so it is important to pay attention to the environmental factors that influence the phenotypic expression of marbling.Adipose tissue is the component of the carcass which has the highest variability and influence of the environment , which mThe consulted literature was incipient to the heritability estimates of BCS and carcass marbling in goats. However, the heritability values of the traits MRE and BCS equal to 0.13 and 0.09, respectively. These values higher than the univariate analysis with threshold model, are of low magnitude, then show little potential response to selection based on these characteristics in the evaluated breed.So, there is low possibility for response to direct selection or by including these traits in selection indexes. Therefore, considering the producer interest in higher meat production and carcass yield, the index should prioritize animal selection with higher genetic value in REA, if the interest is the finishing precocity the FTS gains importance.These categorical traits should not be considered solely in meat goat breeding programs, because besides the amount of meat, the carcass needs adipose protection for cooling, which is guaranteed by the presence of subcutaneous fat, additionally it can be considered an early indicator of development . TherefoIt is observed in Identical situation was observed in the genetic correlation between FTS and MRE (0.58). So, considering the ease of measuring the thickness of subcutaneous fat in the sternal region, it is indication useful means of indirect selection for marbling. The heritability of FTS being 0.24 suggests the inclusion of this trait in the selection indexes for carcass production with good grades of marbling.Thus, BCS and FTS would be more suitable to be included in the composition of selection indexes, since they have higher heritability, but with equal values to 0.13 and 0.24, respectively, which are considered low values for direct selection purposes . Howeverlongissimus dorsi.However, BCS and FTS did not appear to be genetically correlated with each other, which was unexpected and fails to explain the presence of genetic correlation of moderate amplitude of both to the marbling. In other words due to existence of genes in common. However, it is relevant to consider that these traits are measured almost directly in the Considering that the estimated genetic correlation between MRE and HH was equal to 0.88  and the The genetic association of MRE with REA was small (0.03), implying low potential response correlated by selection based on the other one. As REA showed heritability equals to 0.28, considered moderate magnitude and response potential to direct selection, which was also found in cattle. It is recommended to compose selection indexes in the breed and it will not interfere in carcass marbling. The deposition profile of these tissues in the carcass may be related to this result, because as the muscle is earlier developed than the adipose tissue, which implies in low correlation between these characteristics [It is also observed that the genetic correlation between body weight and loin marbling had low magnitude, showing that heavy animals and, consequently, with better body condition, do not necessarily present greater amount of fat in the carcass. This result can be seen as an indication that goats present the “lean meat animal” profile, which has the disadvantage of limiting cryopreservation. On the other hand, it would meet market demands of low-fat products.Heritability estimates for categorical traits of BCS and carcass marbling using ultrasound were from low to moderate magnitude, so genetic progress is possible with animal selection based on these characteristics. The two-trait analysis provided higher estimates of heritability for the traits in study. The threshold model showed best adjustment for categorical characteristics, BCS, and carcass marbling using ultrasound, with overestimation trend of heritability when the data were submitted to analysis under the linear model. Direct selection of the continuous distribution of characteristics, such as thickness sternal fat and HH, allows obtaining the indirect selection for ribeye marbling.