The Electronic Medical Record (EMR) is a potential source for high throughput phenotyping to conduct genome-wide association studies (GWAS), including those of medically relevant quantitative traits. We describe use of the Mayo Clinic EMR to conduct a GWAS of red blood cell (RBC) traits in a cohort of patients with peripheral arterial disease (PAD) and controls without PAD.P<5×10−8) with one or more of the RBC traits . Three of these loci  had been identified in recent GWAS and the allele frequencies, effect sizes, and the directions of effects of the replicated SNPs were similar to the prior studies.Results for hemoglobin level, hematocrit, RBC count, mean corpuscular volume, mean corpuscular hemoglobin, and mean corpuscular hemoglobin concentration were extracted from the EMR from January 1994 to September 2009. Out of 35,159 RBC trait values in 3,411 patients, we excluded 12,864 values in 1,165 patients that had been measured during hospitalization or in the setting of hematological disease, malignancy, or use of drugs that affect RBC traits, leaving a final genotyped sample of 3,012, 80% of whom had ≥2 measurements. The median of each RBC trait was used in the genetic analyses, which were conducted using an additive model that adjusted for age, sex, and PAD status. We identified four genomic loci that were associated (Our results demonstrate feasibility of using the EMR to conduct high throughput genomic studies of medically relevant quantitative traits. As costs of genotyping continue to drop, accurate phenotyping is emerging as the rate-limiting step for conducting genomic studies. Consequently, there is considerable interest in leveraging the electronic medical record (EMR) for high-throughput phenotyping of diseases and medically relevant traits. Repositories of DNA from patients seen in the clinical setting can be matched with the EMR and genotyping/sequencing conducted to identify genetic variants associated with human diseases as well as related quantitative traits. Such an approach may reduce the time, effort, and cost involved in conducting genomic studies to identify disease susceptibility loci.In 2007, National Human Genome Research Institute (NHGRI) funded the Electronic Medical Records and Genomics (eMERGE) consortium to develop and implement approaches for leveraging biorepositories with EMR systems for large-scale genomic research, including but not limited to genome-wide association studies (GWAS), sequencing, and structural variation Disorders involving RBCs, including anemia and polycythemia, have been associated with adverse cardiovascular outcomes as well as hypertension and heart failure A total of 3,487 patients (PAD cases and controls), were recruited through 09/30/2009 for the Mayo Clinic eMERGE study. We excluded 12,864 records and 200 individuals based on the algorithm shown in PLINKP<5×10−8) within four genomic regions that were associated with four RBC traits. Quantile-quantile plots for the QTL for six RBC traits are shown in P value for these SNPs. The variance of RBC traits explained by the associated SNPs ranged from 0.7%–2.2%.The distribution of the number of measurements for each RBC trait is shown in HBS1L) and v-myb myeloblastosis viral oncogene homolog (avian) (MYB)] were associated with RBC count, MCV, and MCH: five SNPs with RBC count , six SNPs with MCV  and MCH . These SNPs were located within two different linkage disequilibrium (LD) blocks based on HapMap CEU samples  ( samples . SNPs rsTMRPSS6) on chromosome 22q12.3 was associated with MCV , MCH , and MCHC . We also noted other SNPs within this region to be associated with MCH [rs5756504 (intronic) and rs4820268 (synonymous)] and MCHC (rs4820268). These three SNPs showed a high level of LD  within the transmembrane protease, serine 6 gene  on chromosome 6p22.1 was associated with MCH   that was associated with MCH, within solute carrier family 17 (sodium phosphate), member 1 (SLC17A1) gene on chromosome 6p22.2.A nonsynonymous SNP  within the hemochromatosis gene ( = 1.1%) . We alsoP values and patterns of LD along these genomic regions (We compared our results with recently reported GWAS of RBC traits in subjects of European ancestry  regions .HBS1L/MYB (chromosome 6q23.3) has been found to be associated with MCV r2 = 0.953)] identified by Soranzo et al. r2 = 0.602 with rs4895441) within this genomic region was associated with RBC count HBS1L. In addition, we found this locus to be associated with MCH (P = 3.1×10−14), a finding not observed in previous studies.The SNP rs4895441 within TMPRSS6  was found to be associated with hemoglobin P = 5.4×10−9), MCH (P = 2.8×10−9), and MCHC (P = 2.4×10−11) in the present study (r2 = 0.737 with rs855791) and rs5756506 (r2 = 0.347 with rs855791) were also noted to be associated with MCV The SNP rs855791 within nt study . SNPs rsHFE  was previously identified to be associated with hemoglobin P = 5.8×10−7), MCH (P = 2.8×10−9), and MCHC (P = 1.5×10−7) in the present study. Chambers et al. The SNP rs1800562 within P<5×10−8) within four genomic loci associated with four RBC traits. Of these, three genomic loci  recently identified as being associated with RBC traits, were replicated, highlighting that phenotypes extracted from the EMR can be used for GWAS of quantitative traits. The fourth genomic locus − SLC17A1 − a gene involved in sodium-phosphate co-transport system in the kidney, is a novel locus that we found to be associated with MCH.The EMR contains diverse and rich phenotypic information and DNA repositories linked to the EMR allow rapid assembly of patient sets for genomic studies. However, the utility of EMR-based approaches for discovery or validation of genotype-phenotype associations remains unproven. In the present study, we demonstrate that a biorepository matched to the EMR can be leveraged to conduct a GWAS of RBC traits. We extracted RBC traits values over a span of 15 years from the EMR, and used a billing code and NLP-based algorithm to exclude values that may have been affected by comorbidity, medication use or major surgery. We identified 11 unique significant SNPs  within SLC17A1 was found to be associated with transferrin saturation (P = 5×10−8), by Benyamin et al The molecular functions of the four genomic regions that were associated with RBC traits are summarized in A limitation of the use of EMR in genomic studies is the potential for selection and referral bias. Considerable effort may be needed to develop and validate phenotyping algorithms. The present study required a combined approach of NLP to identify prescribed medications and billing codes to exclude RBC values that might have been affected by chronic disease or medication use, while capturing a sufficiently large sample size. How well the genetic architecture of quantitative traits can be delineated from EMR-based genomic studies may vary with the trait of interest and will be influenced by trait heritability, variance in trait values, and how comorbidities affect trait values. In the present study, our ability to replicate may have been made easier by the fact that measurement of RBC traits is relatively precise in the clinical setting, trait values are stable over times, values may be relatively less affected by acute phase response, and that the traits have relatively high heritability. Additional GWAS of several quantitative traits are currently in progress within the eMERGE consortium, and will provide further insights in this regard.The present study lays the groundwork for a GWAS of RBC traits across the five eMERGE sites . We anticipate detection of additional novel genetic loci influencing RBC traits in the consortium-wide analyses. Although the availability of multiple measurements of a trait within the EMR may provide a more precise estimate of the trait value as well as change in trait value over time, it is not clear how to deal with multiple measurements in GWAS analyses. We are investigating the statistical power of different regression methods in dealing with multiple measurements. Finally, consistent with the goals of the eMERGE network, we are developing phenotyping algorithms to enable EMR-based genomic studies of other medically relevant quantitative traits and assessing the extent to which the algorithms are portable across EMR systems.In conclusion, we demonstrate the use of the EMR to replicate genetic loci associated with inter-individual variation in RBC traits in prior cohort studies. As genotyping costs continue to decrease, phenotyping is emerging as the major bottleneck for identifying genetic loci influencing disease susceptibility or variation in medically relevant quantitative traits. Mining of the EMR is a high throughput, relatively inexpensive method to facilitate genetic studies of quantitative traits. Increasing use of the EMR affords an opportunity to expedite the investigation of genetic architecture of common and rare diseases as well as quantitative traits of medical importance.In October 2006, a biorepository of plasma and DNA samples was initiated by recruiting patients referred for lower extremity arterial evaluation to the Mayo Clinic's non-invasive vascular laboratory and individuals referred to the stress ECG laboratory to screen for coronary artery disease. Between October 2006 and May 2009, 3,527 patients were recruited. We used the following criteria to define presence of PAD: 1) an ankle brachial index (ABI) ≤0.9 at rest or 1 min after exercise; or 2) presence of poorly compressible arteries; or 3) normal ABI but prior history of revascularization for PAD The complete blood count is a commonly performed laboratory test To extract data for RBC traits, we used separate relational databases as well as semi-structured data sources in the Mayo EMR. A schematic depicting extraction of RBC traits from the EMR is shown in Since RBC traits are affected by a wide array of medical conditions, we developed an EMR-based algorithm that includes billing codes and NLP of unstructured clinical notes to exclude values affected by comorbidities, medications or blood loss . We compEIGENSTRAT software n = 42). After QC steps, 3,012 samples with phenotype and genotype data were available for association analyses  pipeline developed by the eMERGE Genomics Working Group. This process includes evaluation of sample and marker call rate, gender mismatch and anomalies, duplicate and HapMap concordance, batch effects, Hardy-Weinberg equilibrium, sample relatedness, and population stratification. A total of 489,421 SNPs were used for analysis based on the following QC criteria: SNP call rate >98%, sample call rate >98%, minor allele frequency >0.05, Hardy-Weinberg equilibrium >0.001, 99.99% concordance rate in duplicates, and unrelated samples only. We excluded 11 samples with labeling errors. The data from all the patients, in addition to the HapMap III populations, were evaluated for population structure/substructure using analyses .PLINK using linear regression analysis that assumed an additive genetic model and incorporated age, sex, and PAD case-control status as covariates GC) for six RBC traits, and found these values to be below 1.020 without systematic inflation: 1.014 (hemoglobin), 1.017 (hematocrit), 1.007 (RBC count), 1.007 (MCV), 1.004 (MCH), and 1.016 (MCHC). After correcting for population structure using λGC, the significant loci identified in the present study remained at P<5×10−8. The power of our study was ∼85% to detect a QTL that explains 1.5% variance in an RBC trait, given a sample size of 3,000, a minor allele frequency of 0.05, and the significance level of 5×10−8. The data for the consortium-wide analyses of RBC indices will be uploaded to dbGAP (www.ncbi.nlm.nih.gov/gap).Single-locus tests of association were performed in Figure S1A. Schematic diagram of extracting data of RBC parameters from the EMR. B. The structure of extraction data from the EMR. Test description is the six RBC traits. C. Summary of the RBC traits in the extraction data. MCV, mean corpuscular volume; MCH, mean corpuscular hemoglobin; MCHC, mean corpuscular hemoglobin concentration.(2.56 MB TIF)Click here for additional data file.Figure S2Bar chart of the number of laboratory tests for RBC traits. MCV, mean corpuscular volume; MCH, mean corpuscular hemoglobin; MCHC, mean corpuscular hemoglobin concentration.(0.24 MB TIF)Click here for additional data file.Figure S3A flow chart of quality control of phenotypic and genotypic data for RBC traits in GWA studies.(2.30 MB TIF)Click here for additional data file.Methods S1Assessment of comorbidities and medications that can affect RBC traits.(0.04 MB DOC)Click here for additional data file.Table S1ICD-9-CM codes indicating the most commonly disorders that may affect RBC traits.(0.09 MB DOC)Click here for additional data file.Table S2ICD-9 and CPT-4 procedural codes indicating bone marrow and/or solid organ transplantation.(0.05 MB DOC)Click here for additional data file.Table S3CPT-4 codes indicating medications.(0.04 MB DOC)Click here for additional data file.Table S4Generic and brand names of commonly used oral chemotherapeutic and immunosuppressive medications.(0.05 MB DOC)Click here for additional data file.Table S5CPT-4 codes indicating anesthesia codes for surgeries that are likely to be associated with major blood loss and post-operative anemia.(0.09 MB DOC)Click here for additional data file.


Borderline personality disorder is a severe personality disorder for which genetic research has been limited to family studies and classical twin studies. These studies indicate that genetic effects explain 35 to 45% of the variance in borderline personality disorder and borderline personality features. However, effects of non-additive (dominance) genetic factors, non-random mating and cultural transmission have generally not been explored. In the present study an extended twin-family design was applied to self-report data of twins  and their siblings , parents  and spouses (N = 939) from 4,015 families, to estimate the effects of additive and non-additive genetic and environmental factors, cultural transmission and non-random mating on individual differences in borderline personality features. Results showed that resemblance among biological relatives could completely be attributed to genetic effects. Variation in borderline personality features was explained by additive genetic  and dominant genetic  factors. Environmental influences  explained the remaining variance. Significant resemblance between spouses was observed, which was best explained by phenotypic assortative mating, but it had only a small effect on the genetic variance . There was no effect of cultural transmission from parents to offspring. Borderline personality disorder (BPD) is characterized by emotional lability, impulsivity, interpersonal difficulties, identity disturbances, and cognitive impairments To date, genetic research on individual differences in BPD has been limited to non-twin family studies and classical twin studies. Family studies have consistently shown increased rates of BPD in family members of BPD patients Firstly, adding data from siblings to the classical twin model results in a considerable increase in power to detect non-additive genetic effects Secondly, the effect of assortative mating, meaning that spouses are more similar for a trait or disorder than expected under random mating Although the classical twin design offers information about the influence of shared environment, it is not informative about how much of the shared environment is transmitted from parents to offspring. By adding phenotypic data from parents to the classical twin design vertical cultural transmission, reflecting the non-genetic influence of the parents' BPD features on their offspring, can be tested. Because BPD features have a heritable component In this study, we examine the genetic and environmental influences on individual differences in BPD features using an extended twin-family design. We collected data on BPD in twins, their spouses, siblings and parents. Analyzing the data from family members simultaneously in one model allows for testing of additive and dominant genetic effects, individual specific environmental influence, assortment and cultural transmission N = 1,907) or from self-report answers to eight survey questions on physical twin resemblance and confusion of the twins by family members and strangers. Based on the answers to these items from all longitudinal surveys, zygosity was assigned. A total of 1,045 twins were of opposite sex and therefore classified as dizygotic. Agreement between zygosity based on survey questions and zygosity based on DNA typing was 97% Twins and their parents, siblings and spouses registered with the Netherlands Twin Register Personality Assessment Inventory-Borderline Features scale (PAI-BOR) false, slightly true, mainly true, very true). The items consist of statements concerning, for example, stability of mood and affects, emotionally responsiveness, anger control, self image, feelings of emptiness, intense and unstable relationships, loneliness, impulsivity, self harm and recklessness. Several studies have supported the reliability and the validity of PAI-BOR scores in indexing the degree to which BPD features are present BPD features were measured by a Dutch translation of the 24-item The classical twin design makes use of the different genetic relatedness of monozygotic (MZ) and dizygotic (DZ) twins to disentangle genetic and environmental influences on the variance in a trait. MZ twins are genetically (nearly) identical while DZ twins share on average 50% of their segregating genes, like non-twin siblings. The more similar MZ twins are relative to DZ twins, the more variability in a trait is caused by genetic effects. When there is no difference in resemblance between MZ and DZ twins, shared environmental influences are most likely the cause of the resemblance between twins. Genetic effects can act in an additive (A) or non-additive, or dominant  manner. Environmental effects can be common to members of the same family (C) or unique to an individual (E).Adding data from siblings, spouses and parents of twins to the classical twin study has several advantages. Firstly, it provides the information and statistical power to distinguish between A and D, which is poorly achieved with the classic twin design Secondly, the effects of assortative mating can be examined. In the classical twin design these may be confounded with the effects of the shared environment Thirdly, including parents of twins into a study can provide information about cultural transmission from parents to offspring. Cultural transmission increases the parent-offspring correlation as well as the correlation among their offspring. In the classical twin design, cultural transmission will be accounted for as C. In an extended twin design cultural transmission can be distinguished from other forms of C, assuming that vertical cultural transmission from parents to offspring is based on the measured phenotype of the parents s). The use of parental data entails the assumption that assortative mating, genetic and cultural transmission and gene-environment correlation remain constant from generation to generation g (genetic variance), r  and s (gene-environment covariance) in the parental generation are constrained in the model fitting as a function of the parameters in the offspring generation.In a first step, the resemblances between pairs of family members with different degrees of genetic relatedness were summarized by correlations. Correlations were estimated conditional on sex, for MZ and DZ twins, parent and offspring, sibling pairs, and for spouses (parents of twins and twins with their spouse). Simultaneously, means, variances and regression of BPD scores on age and sex were estimated. We tested for differences in correlations between DZ twins and siblings, for sex effects on twin and parent-offspring correlations and for regression effects of sex and age on the PAI-BOR scores. Next, the contribution of genetic and environmental factors to the variation in BPD features was estimated. Genetic modelling of the data was based on a re-parameterization of the model proposed by Fulker 2 is the heritability of a trait, the correlation (due to A) between parents and offspring and between siblings equals ½h2. Under assortative mating, there is an increase in the genetic variance, which will increase the resemblance between parents and offspring as well as between siblings, i.e. rg>0.5 i. The copath represents an extrinsic correlation that influences the covariance structure of the spouses' latent variables but does not contribute to their variance The additive genetic variance is perfectly correlated in MZ twins. For DZ twins and siblings the correlation between the latent A factors is 0.5. These coefficients are based on the assumption of random mating in the population 2 distribution and the degrees of freedom (df) for this test equals the difference in the number of estimated parameters in the two models. A non-significant p-value means that the constrained model is not significantly worse than the model and is kept as the most parsimonious and best fitting model. Because of the large sample size a p-value of 0.01 was chosen.Several models of familial resemblance were fitted to the data. We first estimated correlations between relatives and then fitted a series of genetic models to the data. In the first model (model I), A, D, E, cultural transmission and resulting genotype environment correlation are specified. Model II tests the significance of cultural transmission and genotype environment correlation, model III the significance of D and model V the significance of assortment. Finally, model IV tests the significance of A. Because the data showed a somewhat skewed distribution with a tail to the right, a square root transformation was applied. All analyses were performed in the software package Mx p<.001). The effects of sex and age on the PAI-BOR scores were therefore included in all genetic models as a regression coefficient. Variances were equal for men and women.p>.01), indicating that there were no sex differences in the heritability of BPD features, the same genes influence BPD features in men and women (test not shown in p>.01). The MZ twin correlation was .45 and the DZ/sib correlation was .19 suggesting that around 50% of the variance in BPD features can be attributed to genetic factors and that part of the genetic variance might be dominant. Resemblance between mothers and their offspring was equal to the resemblance between fathers and their offspring (p = .014). The parent-offspring correlation (r = .13) was somewhat lower than the DZ/sibling correlation which is consistent with the presence of dominance. There was a significant association between the PAI-BOR scores of twins and the score of their spouses (r = .19). The correlation between MZ twins and their co-twins spouse (r = .18) was higher than the correlation between DZ twins and their co-twins' spouse (r = .08) which suggests that non random mating is primarily based on phenotypic assortment. The spouse correlation in the parental generation was .24 indicating that in addition to phenotypic assortment, there may be some influence of marital interaction. The estimates for the familial correlations for pairs of family members with different degrees of genetic relatedness are summarized in The bottom part of a2 * g/total variance). The influence of assortment on A can be calculated by A - a2 showing that in this model 3.0% of the additive genetic variance (38.5%) is explained by assortment. Non additive genetic effects  explained 11.4% of the variance. Unique environmental effects  explained 55.3% and negative cultural transmission (r) explained 1.3% of the variance. Genotype-environment covariance  was estimated to be negative, resulting in a negative contribution of 6.4% of the variance in BPD features. In model II , additive genetic effects explained 21.3% (1.1% due to assortment) and dominant genetic effects explained 23.9% of the variance in BPD features. The remaining variance was accounted for by unique environmental influences. The fit of model II is not significantly worse than the fit of model I (χ2(1) = .50, p = .480) which indicates that there is no significant effect of cultural transmission and resulting genotype environment correlation. Comparing the fit of model II with the fit of model III shows that removing D from the model results in a significant deterioration in the fit of the model (χ2(1) = 47.0,p<.001). Model IV (versus model III), shows that the influence of A is highly significant since removing it from the model results in a considerable worsening of fit (χ2(1) = 293.2, p<.001). Finally, comparing model V with model II shows that there is a significant effect of assortment (χ2(1) = 62.0, p<.001). Comparing the fit of the different models showed that the ADE model best explained the data.This is the first study that analyzes borderline personality data from twins and their family members simultaneously providing a powerful design to distinguish between additive and dominant genetic effects and to detect non-random mating, cultural transmission and genotype-environment correlation. A genetic model in which additive genetic effects , dominant genetic effects  and unique environmental influences  explained the variance in BPD features best explained the data. There was no evidence for shared environmental influences, which is a common finding for a range of personality traits and personality disorders. The effect of phenotypic assortment was included in the genetic model, but it had only a small effect on the genetic variance.The presence of significant dominant genetic effects is in line with what is often suspected for personality traits, but not detected due to a lack of statistical power in relatively small twin studies. Our results showed that BPD features are genetic in origin but only partly transmitted from parents to offspring because dominant genetic effects influence borderline personality only in combination with other genes. These combinations are not shared by parents and offspring. Keller et al. 2(1) = .011, p = .916). The MZ and DZ twin correlations of the younger and older age groups were .472 versus .247, and .459 versus .095, suggesting that broad-sense heritability might be larger in the older generation. However, constraining the MZ and DZ twin correlations to be equal across age groups did not lead to a significant worsening of model fit (χ2(1) = .051, p = .821 and χ2(1) = 2.618,p = .106). Thus, heritability may not change as a function of age. Secondly, to investigate whether different genes are expressed at different ages, we selected a group of siblings less then 4 years (190 pairs) and a group of siblings 4 years or more apart in age (212 pairs). The PAI-BOR correlations for siblings in these groups were .208 and .327 and the resemblance between siblings thus does not decrease as the age difference between them increases. The correlations in the two sibling groups could be constrained to be equal (χ2(1) = 1.69, p = .194). This suggests that the same genes influence BPD features at different ages.The finding of dominance for personality traits is not uncommon, but there may be alternative explanations for these data. The parent-offspring correlation for BPD features was lower than the DZ/sibling correlation which is indicative of the presence of dominance but might also suggest genotype by age interaction, i.e. the expression of different genes at different ages or a change in genetic variance as a function of age. Gene by age interaction can inflate estimates of dominance because it will decrease the correlation between parents and offspring as a result of their differences in age. To investigate this alternative we first divided the twin sample into a group with roughly the same age as the parents in the total sample  and a group with roughly the same age as the offspring in the sample . The total variance did not differ between the two groups . Several studies demonstrated that traumatic life events such as sexual and physical abuse, parental divorce or illness or parental psychopathology are important risk factors for the development of BPD


Longitudinal studies that collect repeated measurements on the same subjects over time have long been considered as being more powerful and providing much better information on individual changes than cross-sectional data. We propose a three-level linear mixed-effects model for testing genetic main effects and gene-age interactions with longitudinal family data. The simulated Genetic Analysis Workshop 16 Problem 3 data sets were used to evaluate the method. Genome-wide association analyses were conducted based on cross-sectional data, i.e., each of the three single-visit data sets separately, and also on the longitudinal data, i.e., using data from all three visits simultaneously. Results from the analysis of coronary artery calcification phenotype showed that the longitudinal association tests were much more powerful than those based on single-visit data only. Gene-age interactions were evaluated under the same framework for detecting genetic effects that are modulated by age. There is considerable evidence suggesting that genetic effects are modulated by age on some common complex traits. For systolic blood pressure, Rao and colleagues demonstrated age trends in familial effects -3. The eith individual from a family measured at the jth visit can be modeled in general asFor a quantitative trait, phenotype of the β0 is the mean after accounting for covariate and genetic effects, and Aij represents the age of the ith individual at the jth visit. The first three terms model the trait as a quadratic function of age at a population level, higher order terms or any other functional forms can also be applied if the phenotype so suggests. The fourth terms models the genetic main effect, where the measured genotype gi can be coded as dominant, additive, or recessive according to different biometric model assumptions. The fifth and sixth terms are the linear and quadratic interactions between age and genetic effects. The random effect term aij accounts for familial as well as inter-visit correlations, and the last term stands for the residual, which is assumed to be independent and identically normally distributed. In longitudinal family-based studies, repeated measurements taken within a pedigree are correlated in a more complicated fashion compared with cross-sectional family studies or longitudinal studies of unrelated individuals. Repeated measurements for the same individual are temporally correlated; measurements on related individuals at each time are subject to familial correlation. More generally, measurements of related individuals at different time points are correlated as well, mostly due to the familial correlation.where MN × MN for a family with M individuals and N repeated measurements. To model the variance-covariance matrix efficiently, we can exploit the structure of longitudinal family data from two distinct perspectives. One is to generalize the two-level linear mixed-effects model for cross-sectional family data [M × M and N × N, respectively. The first one models the correlation across family members and the other across visits. This is mathematically equivalent to modeling the random effect aij such thatAssuming independence among families, the variance-covariance matrix of marginal distribution of phenotypes is of dimension ily data  and treaaij} to form a long vector, and Σvisit and Ωfamily represent temporal and familial variance-covariance matrices, respectively.where vec stacks the columns of {aij could be modeled as the sum of two random effect termsAlternatively, we could view the repeated measurements first cluster at the individual level and individuals as further cluster within families. Three-level mixed-effects models have been developed to model data with such hierarchical structures . In thisb represents familial effect and cj models the visit effect within a family. The second order moment of random effects aij is then modeled aswhere MN and 1M are matrices with 1 as elements and of dimension MN × MN and M × M, respectively.where 1p-values of Hardy-Weinberg equilibrium test were smaller than 10-6, or call rates less than 95%, SNPs were removed.With the simulated GAW 16 Problem 3 data sets we focused on the coronary artery calcification (CAC) phenotype for methodological evaluations. PROC MIXED in the computer program SAS was applied for likelihood-ratio tests. More details and examples of modeling individual growth within clusters using linear mixed-effects models may be found in Singer . CAC pheβ3gi in the model using likelihood ratio approach without any gene-age interaction terms. For additive model, it tests whether β3 = 0, and for genotype model it tests a factor with three levels. Akaike information criterion (AICs) were computed with subjects that have no missing genotype data. The -log and AICs are presented in Table p-Values of the tests with the two models are in general comparable, while hierarchical three-level model tends to yield slightly more significant results. In terms of computational complexity, the three-level model took about three seconds for each model fitting on a Pogo Linux sever with two AMD Opteron 270 2.0-GHz dual core central processing units and 4 GB memory, and the Kronecker model took about five minutes. Unless specified, all results are based on the three-level mixed-effects model in the rest of the paper.To evaluate the two linear random-effects models, we applied the first replication of the simulated phenotype data. No structure on temporal correlations were assumed for both the models with Kronecker and hierarchical three-level structures , and a compound symmetric structure was assumed for the familial correlations. The tests of main effects were based on testing the fourth term p-value of 7.05 × 10-7), which is also the only one that passes the Bonferroni-adjusted significance level (10-6). This SNP is one of the five major-gene SNPs of CAC known as τ2, while other major-gene SNPs were not detected. The most significant SNP from the genotype test is rs213952 , which is also a major gene SNP of CAC (τ5). The second significant SNP, rs17714718, also the top SNP from additive model test, has a p-value of 3.76 × 10-6, which is slightly larger than the Bonferroni adjusted significance level. A plot of the -log for the additive model test is shown in Figure Genome-wide association tests were conducted based on the first replication of CAC phenotype data set and 50 k genotype data set. Longitudinal data with three visits were applied to genotype test and test assuming additive disease model. The most significant finding from the additive model test involved SNP rs17714718 (τ5) passed the significance level in all three cross-sectional tests. A few SNPs appeared to be genome-wide significant in the genotype test, which are likely false-positive results. For example, SNP rs213952 has a p-value of 2.65 × 10-7 and rs9616496 has a p-value of 7.23 × 10-7 when tested with the second visit data set. In Table p-values) for testing rs17714718 (τ2) and rs213952 (τ5) under different scenarios. Results from the longitudinal tests are generally more significant than those from cross-sectional tests.To compare the longitudinal analysis with cross-sectional ones, a two-level mixed-effects model , which mτ2) with all 200 replications of phenotype data sets provided in the GAW16 Problem 3. Receiver operating characteristic (ROC) was plotted with empirical power as the y axis and nominal type 1 error as the x axis, where the latter was derived from thresholds and nominal distributions of the test statistics. Figure To further compare the power of the two types of tests, we tested rs17714718 τ with allWe examined quantile-quantile (QQ) plots of the genome-wide test statistics against their nominal distributions, which were shown in Figure In the two linear mixed-effects models, familial correlations were assumed to have a compound symmetric structure, which is appropriate for pedigrees with first-degree relative pairs only. For pedigrees with more general relationships, such models may not be accurate and can be further generalized by introducing kinship matrix. Comparing the two linear mixed-effects models with Kronecker and hierarchical structures, the first implicitly treats each family as a single subject and phenotypes are repeatedly measured across time as well as across family members. In the three-level mixed-effects model, individuals are the subjects and measurements are repeated only across time while individuals are nested in the familial clusters.τ2) was detected only when using the longitudinal data . SNP rs213952 (τ5) were found to be significant with both longitudinal and cross-sectional data, and the former yielded the most significant result . None of the other major-gene SNPs were found to be significant. According to the answer to GAW 16 Problem 3 [τ1 was simulated to display only a minimal main effect, τ2 displays a measurable additive main effect, and τ3 and τ4 were simulated to be purely epistatic SNPs. Hence τ1, τ3, and τ4 were not significant when testing of their main effects only.Results from the longitudinal analysis of the three-visit phenotype data were found to be more significant than those from cross-sectional ones. Out of the five major-gene SNPs of CAC, association with rs17714718 (p-value may indicate possible defects in statistical analysis, e.g., population substructure, loose genotype quality control, or inappropriate statistical method. One underlying assumption of the argument is that the number of true positives is small if there will be any, hence test statistics from a genome-wide scan should represent an empirical distribution of test statistics under the null hypothesis. Inflation of the distribution should only happen in the tail due to the true-positive results, not for the whole distribution. In GAW16 Problem 3, no effect of population substructures was simulated in any phenotypes; inflated QQ plots, however, were still observed. For a complex trait like CAC, which has 17 major-gene SNPs involved directly or indirectly and 2000 polygenes spread all over the 22 chromosomes, such assumption may be worth examination. The effect sizes of all of these 2017 SNPs are so small that they may not be able to stand out at the tail of the distribution. On the other hand, the SNPs are true signals, and hence are more likely to have smaller p-values than other null markers. Considering further that each of these SNPs may be in linkage disequilibrium with some other SNPs, it is possible that empirical distributions may not align to their nominal distributions simply due to the complexity of the phenotype itself. In a recent genome-wide association study of dyslipidemia [QQ plots are widely used in genome-wide association studies to measure credibility of the results. An inflated distribution of the test statistic or ipidemia  in whichCAC is probably the most complex phenotype in the simulated GAW16 data set. All the major genes and polygenes of high-density lipoprotein, low-density lipoprotein, and triacylglyceride affect this phenotype simultaneously. Medication, diet, gene-gene, and gene-age interactions make it even more complex. In the tests of linear and quadratic gene-age interactions, no interactions were detected for any major or polygenes at a Bonferroni-corrected significance level. This may due to small marginal effects of those major gene SNPs. Also, some major gene SNPs have pure epistatic effects only, which could significantly reduce the power of test of genenotype-age interactions. In addition, because the gene-age interaction was simulated in a piece-wise linear fashion , this suWe applied two linear mixed-effects models to analyze longitudinal family data provided by GAW16 Problem 3. The models with Kronecker and hierarchical structures yielded comparative performance in terms of goodness of fit and significance of theirs results. Longitudinal test that jointly analyze repeated phenotypes were found to be much more powerful than tests based on cross-sectional data only. Complexity of the trait itself could be a reason for inflated distribution on QQ plot, and using the correct null phenotype is suggested when evaluating distribution of test statistic under the null hypothesis.AICs: Akaike information criterion; BMI: Body mass index; CAC: Coronary artery calcification; GAW: Genetic Analysis Workshop; QQ: Quantile-quantile; ROC: Receiver operating characteristic; SNP: Single-nucleotide polymorphism.The authors declare that they have no competing interests.GS developed the concept, carried out the analysis, interpreted the data and drafted the manuscript. TKR conducted phenotype adjustments, interpreted the data, and revised the manuscript critically. CCG acquired the data, interpreted the data and revised the manuscript critically. DCR developed the concept, interpreted the data, revised the manuscript critically, and gave final approval for publication. All authors read and approved the final manuscript.


Recent developments in SNP discovery and high throughput genotyping technology have made the use of high-density SNP markers to predict breeding values feasible. This involves estimation of the SNP effects in a training data set, and use of these estimates to evaluate the breeding values of other 'evaluation' individuals. Simulation studies have shown that these predictions of breeding values can be accurate, when training and evaluation individuals are (closely) related. However, many general applications of genomic selection require the prediction of breeding values of 'unrelated' individuals, i.e. individuals from the same population, but not particularly closely related to the training individuals.Accuracy of selection was investigated by computer simulation of small populations. Using scaling arguments, the results were extended to different populations, training data sets and genome sizes, and different trait heritabilities.e*L and the number of markers was 10*Ne*L, the breeding values of unrelated individuals could be predicted with accuracies of 0.88 – 0.93, where Ne is the effective population size and L the genome size in Morgan. Reducing this requirement to 1*Ne*L individuals, reduced prediction accuracies to 0.73–0.83.Prediction of breeding values of unrelated individuals required a substantially higher marker density and number of training records than when prediction individuals were offspring of training individuals. However, when the number of records was 2*NeL requires about ~30,000 training records, but this may be reduced if training and evaluation animals are related. A prediction equation is presented, that predicts accuracy when training and evaluation individuals are related. For humans, 1NeL requires ~350,000 individuals, which means that human disease risk prediction is possible only for diseases that are determined by a limited number of genes. Otherwise, genotyping and phenotypic recording need to become very common in the future.For livestock populations, 1N An important result from these sequencing efforts is the detection of 100,000's to millions of SNP markers for each of the sequenced species. The availability of all these SNP and recent innovations in high-throughput SNP-chip genotyping technology have made the routine genotyping of huge SNP panels feasible. For example, in human genetics, assays with > 500,000 SNP are routinely used, and in cattle, pigs and sheep ~50,000 SNP chips are commercially available.The Human Genome Project and related projects for other species have generated the complete DNA sequence of many animal, plant, and microbial genomes 2 = 1, where R2 is the square of the correlation between the allele frequencies at two loci. Habier et al. )r et al.  have demet al. [The ideal of having a marker in perfect LD with each QTL is complicated by the fact that recently, it has been shown in human genetics studies, that nearly all the genetic variation of quantitative traits is due to genes with a small effect . This imet al.  for heiget al. ).In the step estimating marker effects, the estimation of effects of very many markers is hampered by the LD, i.e. collinearity, between the marker effects. Fortunately, similar combinations of marker alleles will be found in the evaluation data set (step (ii)), especially if the individuals of steps (i) and (ii) are related (e.g. parents and offspring as in ). The lae) argument from coalescence theory [The aim of this study is to assess whether the breeding values of unrelated individuals could be predicted with high accuracy, and what resources are required in terms of marker density and number of records in the training data set. The results are based on computer simulations of relatively small populations, but will be generalised using the scaling by effective size , compared to a population with Ne = 1000 and 10,000 SNPs per M, i.e. for both populations, the marker density is 10 * Ne /M [From the coalescence theory it is well known that, for a population in recombination-drift equilibrium, the LD between marker and QTL and amongst markers is a function of N * Ne /M .However, the second population requires the estimation of 10 times as many markers, which may be achieved with a similar accuracy if we have 10 times as many training data. The latter is also seen from recent predictions of the accuracy of selection :r is accuracy of selection; N is the number of phenotypic training records; h2 is the trait heritability; L is genome size in Morgan; 4 NeLν is the effective number of QTL loci in the genome, which each equals the effective number of segments in the genome when the infinitesimal model is assumed (i.e. BLUP is used for the estimation of SNP effects). In the latter case, ν may be interpreted as the ratio of the effective number of segments and the actual number of segments, which is expected to be 4 NeL. Goddard [i is the size of chromosome i.where  Goddard  derived e = 100 and 1000, respectively.From this scaling argument and Equation (1) it is also seen that as genome size doubles, we need twice as many training records (N) to achieve a similar accuracy of predicting breeding value, assuming a constant marker density. Whether the latter expectation holds will be tested in the Results and Discussion section. Also, the LD structure between the QTL is equivalent if the number of QTL per M is 100 and 1000 in populations with Ne = 100), but the scaling argument makes it possible to extend the results to bigger population sizes. The use of a relatively low Ne does not only reduce the population size to be simulated, but also the number of generations needed to reach equilibrium between mutation, drift and recombination. This is because lineages coalesce faster in small populations.In order to reduce computer time, the effective size used in the simulations described here will be quite low  within 200 (= 2Ne) generations. Any mutations before this MRCA lived do not cause a polymorphism . Preliminary simulations showed that an approximate mutation-drift balance was reached before 400 generations (result not shown). Recombinations were sampled according to the Haldane mapping function. The genome consisted of 10 chromosomes of 50 cM each, i.e. the total genome size was 5 M.In general, the model for the population history mimics that of coalescence simulations , howevere/M. For humans, this density corresponds to a total of ~2.3 million markers . Smaller marker densities of 20/x Ne/M were obtained by taking every x-th marker from the original set of 10,000 markers, where x = 2, 4, 10 or 20.After these 400 generations, SNP with a Minor Allele Frequency (MAF) < 0.02 were discarded. From the remaining SNP, 12 were randomly selected per chromosome to become a QTL, which resulted in a total of 120 QTL. From the remaining, non-QTL SNP, the 1000 SNP per chromosome with the highest MAF were selected to become a marker. This resulted in a total of 10,000 markers, and a density of 20 N of 38 M , and Ne e ~3,000 ), and foi.e. they were genotyped and phenotyped. The 100 G2e individuals are only genotyped, and their genetic value is to be predicted. The G0e, G0t, G1e, G1t, G2e and G2t individuals were pedigree recorded, i.e. for the pedigree recording the parents of G0 were treated as founders. The 'training' individuals (G2t) had neither parents nor grandparents in common with the evaluation individuals (G2e) due to the separation of the two lines. The results were based on 16 replicated simulations, which was computationally advantageous, since the 16 replicates could be run in parallel. Figure After these 400 generations, the population was increased to 1000 by sampling parents from the previous generations for 1000 individuals, which formed generation G0. Generation G0 was split into 500 G0t and 500 G0e individuals . The 500 G0e-individuals were used for the sampling of parents for 500 G1e individuals, and similarly the G0t-individuals were used for the sampling of parents for 500 G1t individuals. Setting up different lines for the sampling of the G1e and the G1t individuals ensured that these two groups of individuals shared no close relationships. Subsequently, parents of 100 G2e individuals were sampled at random (with replacement) from the 500 G1e individuals. Similarly, parents of N G2t individuals were sampled from the 500 G1t individuals, where N was 500, 1000 or 2000. The G2t individuals were used for the estimation of marker effects, j, was sampled from the exponential distribution, and uj was given a negative sign with probability 0.5. The total genetic value of individual i was calculated as:An additive genetic model was assumed, and the allelic effect of the mutant QTL allele at locus j, uij is the number of mutant alleles  that individual i carries at locus j. At the end of the 400 generations of simulation, the allelic effects were standardised so that the total genetic variance was 1. Phenotypes for the G2t individuals were obtained by adding an environmental effect sampled from N to their genetic value. This resulted in a high heritability of 0.8. The effect of a lower heritability is investigated in the Results and Discussion section.where qQTL/Nm of markers), whilst the remaining markers did not have an effect at all, where NQTL is the number of QTL and Nm is the number of markers fitted. However, in the BayesB model implemented here, the prior distribution assumed that the majority of the markers (i.e. the fraction 1- NQTL/Nm) did have a small effect, the variance of which was assumed equal and was estimated in the model, instead of assuming that these markers had no effect at all (as in [Estimation of marker effects was performed using three models: (i) BLUP of marker effects, which assumes that every marker effect has a constant variance (G-BLUP); (ii) BayesB, which estimates the variance of every marker using a prior distribution and Bayesian methodology ; and (iil (as in ). The laThe statistical model used to estimate the marker effects by G-BLUP, BayesB, and MIXTURE was:y is a Nx1 vector of phenotypes; aj is the effect of marker j; Xj is a Nx1 vector denoting the genotype of the individuals for marker j, where 0 denotes homozygous for the first allele; 1/√Hj denotes heterozygous; 2/√Hj denotes homozygous for the second allele, and Hj is the marker heterozygosity. The √Hj term in Xj standardises the variance of the marker genotype data to 1. The variance of aj is assumed to be 1/Nm for G-BLUP, is estimated by BayesB, and, in MIXTURE it equals σ12 or σ22, depending on whether the marker effect is small or large. The probability of a small or large marker effect is estimated together with the variances of the small and large distribution of marker effects, σ12 and σ22.where Given the estimates of the marker effects and the marker genotypes, genetic values for the individuals in set G2e are predicted as:ij is the marker genotype of individual i for marker j coded the same as above; and gi and where XTraditional BLUP (T-BLUP ) breedine/M.From Equation (1) it may be expected that a doubling of the genome size requires twice as many records. To test this expectation, we compared the situation of a genome with 5 chromosomes with N = 500 G2t individuals, to 10 chromosomes with N = 1000, and to 20 chromosomes with N = 2000. Marker density was kept constant at 20 Net al. [Following Habier et al. , the accG-BLUP (rT-BLUP) is the accuracy using G-BLUP (T-BLUP), (1-rT-BLUP) denotes the inaccuracy of rG-BLUP, and ρG-BLUP is the proportion of the inaccuracy that could be explained by G-BLUP. Since, rG-BLUP and rT-BLUP are known, ρG-BLUPcan be calculated from the simulation results and Equation (2). Using these ρG-BLUP values, a method to predict the accuracies from traditional BLUP , and EqTo test these predictions, a simulation was conducted where the training data set was composed of G1t individuals, the number of which was increased to N, and the evaluation individuals originated from G1e. Hence, the training and evaluation individuals were two generations less separated (one generation in each of the lines).G-BLUP2, then it can be seen from Equation (1) that the E(PEV-1) = 1+β*N, where -1 on N is linear, and the regression coefficient is a function of h2, which is known, and the effective number of segments, 4NeLν.By combining the simulation results and Equation (1), the effective number of segments can be derived as follows. Let PEV = 1-ret al. [2 = 1/(4Ned+1) [e/M hardly increased the accuracy of selection . For G-BLUP, the slope of the increase with increasing density was clearly smaller, which indicates that the superiority of BayesB increases with increasing density. This may be expected since with increasing density it becomes more important to filter the SNP that are in strong LD with the QTL from all the others, instead of spreading the effects over all SNP as G-BLUP does, which results in very small effects for the single SNP.Figure et al. ). The li(4Ned+1) , where de/M) G-BLUP yielded only a 0.02–0.06 fold lower accuracy than BayesB.The differences between BayesB and MIXTURE are very small Table , but sliFor T-BLUP, the accuracies varied between 0.19 and 0.23 as N increased from 500 to 2000 (result not shown elsewhere). Thus T-BLUP was much less accurate than BayesB (varied from 0.83 – 0.93) because (i) it does not make use of the marker data; and (ii) it uses pedigree-based relationships to predict the EBV of the evaluation individuals from the phenotyped of the training individuals which were generally low, on average 0.01.The accuracy of G-BLUP increases more than that of BayesB when the number of records increases Figure . Thus, GTable Table e/M and 2000 G4t individuals, the accuracy reduced to 0.920 and 0.868 for BayesB and G-BLUP respectively (result not shown elsewhere). These accuracies compare to those in Table The effect of even more distant relationships between training and evaluation individuals was investigated by continuing the breeding of the lines in Figure e/M, the regression of PEV-1 on N was calculated as suggested in section 'Estimation of the effective number of segments'. For G-BLUP, the estimates of the intercept (α) and slope (β) were 1.388 and 1.551*10-3, respectively. For BayesB, these figures were 1.859 and 2.649*10-3, respectively. This results in estimates of the effective number of QTL of 516 and 302 for G-BLUP and BayesB, respectively. This value is expected to be lower for BayesB, since it concentrates on the loci with substantial effects whereas G-BLUP gives equal weight to all loci. The actual number of QTL was 120, which indicates that BayesB had to use several SNP to estimate the effect of each QTL. The derivation of Goddard [e argument') predicts that there are effectively 189 segments, which is considerably lower than the estimate of 516 by G-BLUP. Possibly the estimate of G-BLUP is biased by the deliberate exclusion of close relationships between the training and evaluation individuals. The estimates of the regression coefficients α and β can also be used to predict PEV, and thus rG-BLUP and rBayesB for different sizes of the training data set, N, than those used here.Using the results of Table  Goddard  (see Sece/M results). This could be due to the training and estimation individuals being less related than when they were randomly sampled from the population.Using the prediction of 189 effective segments from , Equatio2 remains the same, which is approximately the case for N = 1000 and h2 = 0.8, and yielded accuracies of 0.817 and 0.882 (Table 2 reduces. The latter may be because Equation (1) predicts basically the accuracy of a single (effective) locus, whereas, if accuracy is high, all other loci are also predicted accurately. If heritability, and thus accuracy is reduced, the accuracy of the other loci reduces as well and the overall accuracy reduces more than expected from single locus predictions.The effect of a reduced heritability was tested using a heritability of 0.5 instead of 0.8. For N = 2000, this yielded accuracies of 0.789 and 0.859 for G-BLUP and BayesB, respectively (result not shown elsewhere). Equation 1) predicts that accuracy does not change if N*h predictsThe number of simulated QTL was quite large: 24 per Morgan, i.e. 720 for a 30 Morgan genome. In addition, the effective size was quite small, such that the expected LD between the QTL is substantial, i.e. from :many QTL .et al. [e/M, the accuracy of selection reduced to 0.914, 0.916 and 0.879 for BayesB, MIXTURE and G-BLUP, respectively (result not shown elsewhere). Thus, the effect of normal vs. exponentially distributed QTL effects was small, but larger for BayesB than for G-BLUP as might be expected. Although the difference is small and may well be due to sampling, the MIXTURE model seems to yield the highest accuracy when QTL effects are normally distributed, which may be expected since it attempts to estimate the prior distribution from the data, and the normally distributed QTL effects may be more in accordance with the assumptions underlying the MIXTURE model.This genetic model with many, small QTL will especially be a disadvantage for BayesB, which attempts to estimate the variance of individual QTL, whereas G-BLUP a priori assumes that every marker has equal variance. Therefore, the results in Table et al.  found, we*L SNP markers and ~2*Ne*M genotyped and phenotypes training individuals for the estimation of SNP effects. The former requirement is likely to be achieved in species where the genome sequence is available, but the latter will be challenging. If we accept accuracies of 0.7 – 0.8, ~1*Ne*L training individuals is sufficient. For humans, this still implies ~350,000 training records, which makes the risk prediction for truly polygenic diseases and for unrelated individuals probably impossible unless genotyping and phenotyping for such diseases becomes very common in the future.The results presented here imply that the accurate prediction of breeding values of unrelated individuals requires a set of ~10*NeL implies N = 30,000. Using Holstein dairy bulls, VanRaden et al. [For cattle, 1Nn et al.  found ac1. Accuracies of ~0.9 for unrelated individuals require 10*Ne*L SNPs and 2*Ne*L training records. For related individuals these requirements can be substantially lowered.2. Accuracy increases approximately linearly with marker density, when expressed as |R| between adjacent markers.3. The superiority of BayesB over G-BLUP increases with marker density.4. BayesB yielded more persistent estimates of SNP effects over generations.5. As the size of the training data set increases, the difference between G-BLUP and BayesB decreases.6. To take advantage of high marker densities, large training data sets are needed.-1) on the number of training records (N) is linear, and the regression coefficients can be used to predict the accuracy for different N.7. The regression of the inverse of the prediction error variance  hold approximately, but they over-predicted the accuracies found here, perhaps because the training and evaluation individuals were less related than expected.The author declares that they have no competing interests.THEM performed the computer simulations and wrote the manuscript.


Genetic association studies have been used to map disease-causing genes. A newly introduced statistical method, called exhaustive haplotype association study, analyzes genetic information consisting of different numbers and combinations of DNA sequence variations along a chromosome. Such studies involve a large number of statistical calculations and subsequently high computing power. It is possible to develop parallel algorithms and codes to perform the calculations on a high performance computing (HPC) system. However, most existing commonly-used statistic packages for genetic studies are non-parallel versions. Alternatively, one may use the cutting-edge technology of grid computing and its packages to conduct non-parallel genetic statistical packages on a centralized HPC system or distributed computing systems. In this paper, we report the utilization of a queuing scheduler built on the Grid Engine and run on a Rocks Linux cluster for our genetic statistical studies.Analysis of both consecutive and combinational window haplotypes was conducted by the FBAT  and Unphased  programs. The dataset consisted of 26 loci from 277 extended families (1484 persons). Using the Rocks Linux cluster with 22 compute-nodes, FBAT jobs performed about 14.4–15.9 times faster, while Unphased jobs performed 1.1–18.6 times faster compared to the accumulated computation duration.Execution of exhaustive haplotype analysis using non-parallel software packages on a Linux-based system is an effective and efficient approach in terms of cost and performance. Genetic association studies are a gene-discovery strategy that compares the frequency of genetic variation at a chromosomal position (locus) between cases and controls to assess whether they contribute to the disease phenotypes. Association studies are categorized into ether population-based or family-based with case-control studies being the former. The family-based association test (FBAT) is an extension of the case-control study to family trios consisting of a father, a mother and an affected child . A uniqun are:Exhaustive window haplotype analysis requires high computational power because of the larger number of haplotypes and window sizes. Indeed, the number of haplotypes in ConsWH and CombWH analysis for the window size respectively. Unfortunately, most of commonly-used software packages for statistical genetics are not written in parallel code and rewriting them for parallel analysis requires the reliability testing of the new code. To circumvent these obstacles and still achieve higher performance, we used a queuing system to sequentially submit jobs in a parallel manner on a Linux cluster.The FBAT and Unphased programs were utilized to analyze both ConsWH and CombWH , the summation of the amount of time required to detect process termination by Grid Engine and fork a new process by the Linux kernel was not negligible when high numbers of processes were involved. Therefore, Unphased-CombWH-uncertain analyses sharing smaller window sizes 1, 2, or 3 were bundled into single processes. The Unphased-CombWH analysis of short windows, comprised by all possible combinations of 1–5 loci out of 26 total, involves > 80,000 haplotypes and results in a large number of output files. Combining analyses of all combinations for each window size made data management much more efficient, resulting in only five files, albeit with lower acceleration. Analysis with larger window sizes may require file compression, file archiving or database management softwares to optimize acceleration. Although our HPC cluster system consists of retired PCs and regular network appliances, the system was sufficient to meet our substantial statistical genetics demands. This may explained by the minimal memory required and the low network traffic between nodes by either program.The small-scale cluster developed in this study effectively accelerated the efficiency of statistical genetic analysis, saving years of time. Today, the necessity of intensive computational power is increasing at the individual and small group level. Here we show that at minimal cost, off-the-shelf hardware, open source software, and existing non-parallel statistical packages can be configured to bring HPC into the realm of small groups. version 4.3 with the SGE roll for supporting the Grid Engine job queuing system . The cluster consisted of one PC for frontend-node, and 22 PCs for compute-nodes. All the computers had Intel Pentium 4 (1.7 GHz) CPUs. The frontend-node and each compute-node was connected each other by 100BASE-T network through a switching hub.The Linux HPC cluster was build using the Rocks Cluster Distribution Whole blood samples were collected from 277 extended families . Subsequently, DNA was extracted from these samples, and genetic variations of single nucleotide polymorphisms (SNPs) at 26 genetic loci were characterized for each individual. The results obtained 172k-byte pedigree data file for following analysis. For the FBAT program, the original Linux executable was installed on the cluster. The hbat -e interactive command of FBAT was used for ConsWH and CombWH analysis, and the -e option was implemented to account for the bias introduced by studying multiple members from the same family. For the Unphased program, its version 3.0.10 source code was recompiled with the GNU C compiler with the option -march = pentium4 -O2 for the CPU-specific optimization. Unphased was used with -uncertain and -certain options from the command-line instead of its graphical user interface written in Java. The former option includes ambiguous genetic data to increase the sensitivity, whereas the later option evaluates only known genetic data, resulting in much quicker analysis.start: end submitter.sh, whereupon the Grid Engine assigned sequential array job IDs to the SGE_TASK_ID environment variable using the range defined by start and end. Subsequently, Grid Engine invoked the shell script submitter.sh to initiate the FBAT and Unphased statistical packages. For FBAT, submitter.sh invoked the expect command, which automatically provides commands according to the expect script in interactive manner, a requirement of FBAT. The expect script invoked FBAT and inputs the run interactive command to read a FBAT batch file. The FBAT batch file containing hbat interactive commands indicating the subject haplotypes were prepared by a Ruby script. To avoid memory allocation problems, we restricted the number of hbat commands for a FBAT process to 500. For Unphased, submitter.sh read a line indicated by SGE_TASK_ID from a text file seed.txt. The seed.txt file prepared by a Ruby script contained command lines for Unphased indicating haplotypes to analyze. FBAT and Unphased output their results into the Unix standard output. Grid Engine redirected them into the directory indicated in submitter.sh with the filename applying the rule of "results.ojob_ID.array_job_ID ".Haplotype analysis was separated into multiple processes and submitted into a Grid Engine queue as array jobs to distribute each compute-node. Figure The window sizes for CombWH analysis were limited to 1–5 loci because the results of larger window sizes were divergent. The maximum number limit of array jobs (max_aj_jobs) was changed from default 75000 to zero by the qconf -mconf command. To increase the efficiency of job distribution, the flush time of Grid Engine (reporting_params/flush_time) was also optimally decreased by the the qconf -mconf command from default 15 sec to 5 sec.The authors declare that they have no competing interests.HM conceived the study, built the Linux HPC cluster, and wrote scripts for data acquisition and computation. ACL designed the genetic study, coordinated collection of the human biological samples and conducted genetic analysis. JN built the Linux HPC cluster, and conducted computational performance evaluation. All authors contributed to writing the manuscript.


PTPN22, STAT4, and TRAF1-C5, have been identified. However, it is presumed that some genes may interact to have a significant effect on the disease, while each of them only plays a modest role. We propose a new combinatorial association test to detect the gene-gene interaction in the rheumatoid arthritis data using multiple traits: disease status, anti-cyclic citrullinated peptide, and immunoglobulin M. Existing gene-gene interaction tests only use the information on a single trait at a time. In this article, we propose a new multivariate combinatorial searching method that utilizes multiple traits at the same time. Multivariate combinatorial searching method is conducted by incorporating the multiple traits with various techniques of feature selection to search for a set of disease-susceptibility genes that may interact. By analyzing three panels of markers, we have identified a significant gene-gene interaction between PTPN22 and TRAF1-C5.Rheumatoid arthritis is inherited in a complex manner. So far several single susceptibility genes, such as  PTPN22 [STAT4 [TRAF1-C5 [K-mean clustering method to reduce the dimension, as well as the Akaike's information criterion (AIC) to select models.Rheumatoid arthritis (RA) has a complex mode of inheritance that involves the interaction of several genes and environmental factors. So far, several genes have been identified as conferring high to modest level of risk to RA, including PTPN22 , STAT4 [TRAF1-C5 . Due to TRAF1-C5 , but theTRAF1-C5  methods,TRAF1-C5 , our tesPTPN22, 41 consecutive SNPs (from rs10858004 to rs11485101) in and around the PTPN22 gene were included. The recently reported SNP rs2476601 (encoding R620W) is the center of the 41 markers that span an interval of more than 400 kb. rs2476601 is well known to be associated with multiple autoimmune diseases, including RA [We selected 151 single-nucleotide polymorphisms (SNPs) from the three genes which are mentioned above. For STAT4, we selected 51 SNPs (from rs883844 to rs6744978) in STAT1-STAT4 region [For 4 region  covering4 region  conducteTRAF1-C5 region on chromosome 9, we tested 59 SNPs (from rs10739575 to rs4837820) that span a region of about 400 kb covering all the SNPs genotyped by Plenge et al. [TRAF1-C5 region.In the p-value of HWE test <0.001. Finally, 137 SNPs remained.We removed the SNPs that have only one type of genotype or with genotype missing rate ≥ 5%. After genotype imputation (see below "Genotype and phenotype imputation"), the data were further filtered based on minor allele frequency (MAF) < 5% and the We also discarded the diseased individuals with missing anti-CCP or IgM measures. To minimize the effect of outliers, we removed individuals with anti-CCP ≥ 500 or IgM ≥ 800. After the above data trimming, 1860 individuals (1194 controls and 666 cases) remained for analysis.Missing genotypes for each SNP were randomly imputed based on the marginal distribution of the genotypes in all other individuals.Because all anti-CCP and IgM values are missing in controls, we imputed these two values for each control from a bivariate normal distribution whose means (11.1 for anti-CCP and 12 for IgM) and variances (58.5225 and 0.4) are taken from the existing literatures . The corK SNP loci are genotyped. Consider the subsets of the K SNPs, there are L from K) different locus-sets that involve L SNPs (1 ≤ L ≤ K). L is a pre-specified number, and in our implementation, we only consider single-locus sets (L = 1) and two-locus sets (L= 2). For the N individuals, the ith individual has a trait vector yi = T, i = 1, ..., N. Let The goal of the multivariate combinatorial searching method (MCSM) is to identify a set of loci that are associated with the multiple traits. Suppose that, within one or several genes, L-locus sets  and use a filter to retain those sets that can explain a significant proportion of the total variation in the multiple traits. For a L-locus set  let g1, ..., gm+1 denote all the distinct multi-locus genotypes observed in the sample, where m+1 is the total number of distinct multi-locus genotypes in this sample. For example, if L = 1, then m = 2. The ith individual has corresponding genotypic coding as Xi =  whereIn Step 1, we search all Consider a multivariate linear regression model:βj = T, j = 1, ..., m, and εI = T, i = 1, ..., N is a three-dimensional random vector, independent of the genotypic score Xiwhere the coefficient Equivalently, Eq. (1) can be rewritten asY is denoted as above, X = T and J is a vector whose elements are 1's, B = T and ℑ = T.where R2-like measure of association between Y and X : Syy is the sample covariance matrix of the y values, Sxx is the sample covariance matrix of x values, and Sxy is the matrix of sample covariance between y values and x values. However, r, the square root of the maximum eigenvalue of Y and X. Within all L-locus sets, after calculating the r value for each set, we retain the top 10 sets that have the largest r values for future validation (step 2).Based on the multivariate model in Eqs. (1) or (2), a natural choice of filter for screening out the insignificant SNP loci is an m becomes large rapidly as L increases, K-mean clustering method is used to reduce the high dimension [k groups, denote G1,...,Gk to be the k genotype groups found by the K-mean clustering method and then redefine a numerical code for the genotype of the ith individual as Xi = , whereIn Step 2, we validate and compare those locus sets retained in Step 1. Because imension . Then foimension . After pIn this way, we construct a new multivariate regression model for each retained locus set, which is similar to Eqs. (1) or (2). The AIC of the multivariate model is a measure that indicates the reliability of the model. The small value of AIC means that the model or the locus set is reliable. For a specific locus set, the AIC value for each partition is calculated, and the smallest AIC is chosen as the final value of the objective function of that locus set:T.At the end of Step 2, the best locus set is chosen as the one that has the smallest value of the objective function T) value of the best locus set as T0. In each permutation, the trait vectors y = T of the individuals are randomly permuted, then Step 1 and 2 are repeated on the randomized data. A objective function (T) value is obtained for each permutation. For 1000 permutations, denote values of the objective function (T) by T1, T2, ..., T1000. The overall p-value of the test for association between the final locus set and the multiple trait is To assess the statistical significance of the best locus set chosen from Step 2, we perform a permutation test. Denote the objective function ; the phenotype data is the same as the one used in GAW16. To evaluate the power of MCSM, we generated both genotype and phenotype data based on the dichotomous trait in GAW16. Here we simulated the checkerboard model [When the level of significance is 0.05, the type I errors of the MCSM are 0.05 for an MAF of 0.1 and 0.5, respectively, and power was 100% for both MAF of 0.1 and 0.5. Thus, when combining multiple traits, the power of the MCSM is very high.TRAF1-C5) and rs2476601 (PTPN22) with a p-value of 0.031. Table p-values. As we can see, no single-locus set is significant, and even the T value of the best single-locus set is still greater (worse) than the T values of all retained two-locus sets, which could be evidence of the dominance of joint (gene-gene interaction) effects upon marginal effects of the candidate genes.After implementing MCSM on 1860 individuals with 137 SNPs, we located the best set as a two-locus set: rs7037673 (PTPN22) is also top-ranked when only considering marginal effect  when considered jointly with another SNP. Three SNPs in TRAF1-C5, rs17611, rs993247, and rs1951784, are not significant in single-locus sets, but stand out when interacting with rs2476601 in two-locus sets. rs7037673 (TRAF1-C5) is as active as rs3761847 (TRAF1-C5) in both single- and two-locus sets. However, we did not get any evidence supporting rs7574865 (STAT4).From Table TRAF1-C5 and PTPN22 interact significantly, with the best two-locus set being rs7037673 and rs2476601. In the gene TRAF1-C5, we discovered SNP rs7037673, which is as active as rs3761847 in both single-locus and two-locus sets. However, we did not detect any significant role for rs7574865 (STAT4).In summary, considering three genes together, The primary advantage of MCSM is that it utilizes multiple traits at the same time to detect gene-gene interactions. However, the computations become intensive due to the trait matrix instead of a trait vector, so we only considered one-locus and two-locus sets in our current analysis. To reduce the computational burden, certain efficient screening statistic or any machine-learning methods could be used.The other concern is the validity of our simulated phenotypes in controls. From the statistical point of view, we could impute them by empirical parameters, and our method works well as long as the traits' distributions in cases and controls largely differ from each other. However, whether such imputated phenotypes are reasonable and meaningful in the biological view still needs further discussion.AIC: Akaike's information criterion; Anti-CCP: Anti-cyclic citrullinated peptide; GAW16: Genetic Analysis Workshop 16; IgM: Immunoglobulin M; MAF: Minor allele frequency; MCSM: Multivariate combinatorial searching method; RA: Rheumatoid arthritis; SNP(s): Single-nucleotide polymorphismThe authors declare that they have no competing interests.XC carried out the data cleaning, evaluated the algorithm, performed the simulation and analysis, and drafted the manuscript. QS and SZ participated in the development of the algorithm. H-SC initiated and designed the study, helped develop the algorithm, guided the overall study, and helped with the manuscript. All authors read and approved the final manuscript.


TRAF1-C5 locus, were examined by conducting Armitage's trend tests. Examining the two-sided alternative hypothesis shows that SNPs rs12380341 (p = 9.7 × 10-11) and rs872863 (p = 1.7 × 10-15), along with six SNPs across the TRAF1-C5 locus, rs1953126, rs10985073, rs881375, rs3761847, rs10760130, and rs2900180 (p~1 × 10-7), are significantly associated with anti-cyclic citrullinated peptide-positive rheumatoid arthritis. But examining the one-sided alternative hypothesis that the minor allele is positively associated with the disease shows that only those six SNPs across the TRAF1-C5 locus are significantly associated with the disease (p~1 × 10-8), which is consistent with the results from the combined sample of the NARAC and the EIRA.The importance of considering confounding due to population stratification in genome-wide association analysis using case-control designs has been a source of debate. Armitage's trend test, together with some other methods developed from it, can correct for population stratification to some extent. However, there is a question whether the one-sided or the two-sided alternative hypothesis is appropriate, or to put it another way, whether examining both the one-sided and the two-sided alternative hypotheses can give more information. The dataset for Problem 1 of Genetic Analysis Workshop 16 provides us with a chance to address this question. Because it is a part of a combined sample from the North American Rheumatoid Arthritis Consortium (NARAC) and the Swedish Epidemiological Investigation of Rheumatoid Arthritis (EIRA), the results from the combined sample can be used as references. To test this aim, the last 10,000 single-nucleotide polymorphisms (SNPs) on chromosome 9, which contain the common genetic variant at the  N1 = 868) and controls (N0 = 1194) after removing duplicated and contaminated samples [The Genetic Analysis Workshop 16 (GAW16) rheumatoid arthritis (RA) dataset is the initial batch of whole genome-wide association study (GWAS) data for the North American Rheumatoid Arthritis Consortium (NARAC) cases  dominant score: x0 = 0, x1 = 1, and x2 = 1; 3) recessive score: x0 = 0, x1 = 0, and x2 = 1. Here, the names of scoring systems are in favor of the minor allele "m".Under the null hypothesis, it is approximately distributed with Armitage , whateveFrom the rationale of the genetic association analysis , it is Hereafter, we concentrate on the alternative hypothesis that the minor allele is positively associated with the disease. To this aim, one-sided can be defined asN. Similarly, those three scoring systems can also be used here. It is shown in Knapp [F is the Wright's coefficient of inbreeding, and Z is the test statistic simply comparing the frequencies of minor allele "m" in the case and control groups. Here the value of F automatically corrects the population stratification to some extent.Under the null hypothesis, it is approximately distributed with in Knapp  that if TRAF1-C5 locus. The same analysis can be extended to the whole genome of approximately 550,000 SNPs.For simplicity of interpretation, we only consider the last 10,000 SNPs on chromosome 9, which contain the common genetic variant at the 10 p) of the test Z2, which simply compares the frequencies of the minor allele in both groups, the Armitage's tests F; only those SNPs with LOD > 6 are reported. The SNPs across the TRAF1-C5 locus are marked with asterisks.For the two-sided alternative that the genotypes at a SNP are associated with the disease, Table F (<0.03), and this explains why their Z2 in the second column. Also, for these six SNPs, In Table rs12380341 and rs872863, have extreme large LOD scores for Z2, ZA1 is the statistic ZA with co-dominant score, ZA2 dominant score, and ZA3 recessive score. From Table Another thing learned from Table The question of whether the two-sided alternative or the one-sided alternatives should be considered is intractable, but this manuscript attempts to raise the question and address it to some extent. Table But if we do not want to believe that the minor allele is positively associated with the disease and do not want to miss any SNPs related to the disease, we had better consider the two-sided alternative.More information can be gained from GWAS by using multiple scoring systems in the Armitage's trend tests and examining both the one-sided and the two-sided alternative hypotheses.EIRA: Epidemiological Investigation of Rheumatoid Arthritis; GAW16: Genetic Analysis Workshop 16; GWAS: Genome-wide association; NARAC: North American Rheumatoid Arthritis Consortium; RA: Rheumatoid arthritis; SNP: Single-nucleotide polymorphism(s).The authors declare that they have no competing interests.YF conceived the idea, performed the statistical analysis, and drafted the manuscript. YW and NS helped to perform the statistical analysis and draft the manuscript. All authors read and approved the final manuscript.


Fifteen known type 2 diabetes (T2D) gene variants were assessed for their associations with T2D status in 228 T2D families from the Framingham Heart Study (FHS) Original, Offspring, and Children Cohorts. Bayesian approach was used to test single-single-nucleotide polymorphism (SNP) association followed by logistic regression. Bayesian and logic regression approaches were used to test multiple SNP association searching for the best combinations of variants followed by logistic regression reconfirmation. The significant variants for T2D risk were also tested for their main and interacting effects on triglyceride (TG)/high-density lipoprotein (HDL) ratio change derived from four point measures across time. This slope phenotype was made available using mixed model growth curve approach from 155 T2D families in the FHS Offspring Cohort.CDKN2B rs10811661 (p = 0.042), TCF7L2 rs4506565 (p = 0.004), and JAZF1 rs864745 (p = 0.04) were individually associated with risk of T2D . CDKN2B and TCF7L2 were found with significant main  and interacting (p = 0.05) effects for increased (OR = 3.0) risk of T2D. CDKN2B and JAZF1 were found with significant main (p = 0.0002 and 0.034) and interacting (p = 0.001) effects on increased (β = 0.42) TG/HDL ratio longitudinal change. These interacting effects were independent of effects of age and sex with effect sizes of 0.3-0.4% for risk of T2D or TG/HDL ratio longitudinal change.CDKN2B and TCF7L2 interacting effect for T2D risk and CDKN2B and  JAZF1 interacting effect on TG/HDL ratio increase over time among  T2D families in the FHS. These interacting effects were consistent  in conferring risk of T2D or progressive insulin resistance with  modest effect sizes.  These synthetic approaches allowed for successful detection of   Fifteen replicated gene variants for type 2 diabetes (T2D) have been assessed . While m2, average TG was 83.7, 108.5, 134.0, and 135.5 mg/dl, average HDL was 51.6, 52.6, 51.6, and 54.5 mg/dl, and average TG/HDL ratio was 1.9, 2.5, 3.1, and 3.0, at Visit 1, 3, 5, and 7, respectively. Every study subject provided written informed consent. The study was approved by Boston University Institutional Review Board.All participants in the FHS were Caucasians. Their characteristics were described elsewhere . In brieAffymetrix 100 k single-nucleotide polymorphisms (SNPs) and genotype annotation resources were described elsewhere . Identic2, and sex. BIMBAM (Bayesian imputation-based association mapping) [p-value . This was followed by logistic-GEE  single-SNP test under general and additive assumptions. BIMBAM output corrected p for multiple testing. BIMBAM was further used to identify the best multiple-SNP combination with the highest BF. LOGREG [Covariates included age, agemapping)  was used. LOGREG  was alsoCDKN2B rs10811661 (p = 0.0011), TCF7L2 rs4506565 (p = 0.0043), and JAZF1 rs864745 (p = 0.0402). Multiple SNP test results are also given in Table CDKN2B rs10811661 and TCF7L2 rs4506565 was significantly detected using the logistic-GEE model . For the slope trait, single-SNP test results were non-significant for CDKN2B rs10811661 (p = 0.4621), but significant for TCF7L2 rs4506565 (p = 0.0379) and JAZF1 rs864745 (p = 0.0349) in the mixed sandwich estimator additive model. Interaction between CDKN2B rs10811661 and TCF7L2 rs4506565 variants were significant , and it was associated with high slope values, which may be expressed as an increase in insulin resistance across ages.Single-SNP test results are presented in Table TCF7L2 intron 3 variant for T2D is in line with a previous FHS genome-wide association study report [CDKN2B near/promoter and JAZF1 intron 1 variants for T2D risk was also found. We thought the T2D families in FHS may contain an enriched genetic component for SNP association assessment of T2D gene variants. Currently, functions of these two genes are yet not clear, but as is the case for TCF7L2 and other confirmed T2D genes [β-cell failure, insulin resistance, and lipid toxicity. Our finding of interactions among the three variants for T2D risk was interesting and novel, which may help disentangle underlying gene pathways and further our understanding of T2D etiology and pathophysiology.Our finding of Correction for multiplicity to minimize the false-positive declaration rate seems to be less sensitive for this analysis for two reasons. First, we aimed to identify and evaluate the best combination of SNPs from confirmed T2D variants. Second, the FHS T2D status information was obtained at the initial visit of the study, and 'new' T2D cases may have remained in the 'non-diabetic' control group after decades of follow-up. This would bias our association findings towards reduction of type 1 error. The results of BIMBAM were consistent with those of logistic-GEE analyses for the single-SNP main effect; likewise, BIMBAM and logic regression results for multiple-SNP joint/interacting effect were also consistent. These synthetic approaches apparently worked well in association detection for both main and joint effects of candidate gene variants with prior knowledge.This 500 k SNP genotype data allowed us to examine 15 of the 18 confirmed exact variants (genotypic imputation was not applied). While reproducibility may be cohort-specific and sensitive to sample heterogeneity and size, it was a bit surprising that we could only identify three meaningful variants. It is very possible that this was due to the presence in the control groups of persons with diabetes who had not received a clinical diagnosis. We did not use a transmission-disequilibrium test-like FBAT program for this analysis simply because we wanted to maximize the sample size by using all available family information. We did not correct the data for potential effect of body max index because obesity coexisting with T2D is very likely rooted in the same pathway genes among most T2D patients, at least in most Western countries.TCF7L2 variant was only associated with β-cell function failure but not insulin resistance [TCF7L2, together with JAZF1 variants, may indirectly impart insulin resistance through joint modulation of lipid metabolism.We were excited to find that the identified interacting variants also affected the TG/HDL ratio. Using the ROC/AUC (receiver operator characteristic/area under the curve) model, we found that it was an imperfect predictor of T2D with best sensitivity and specificity of approximately 75%. Applying a mixed growth curve approach to model longitudinal multiple measures of the TG/HDL ratio proved useful. The derived slope phenotype represented the TG/HDL ratio change across decades of observation time. This approach is advantageous in handling missing data points, as well as remote values, especially in intervention and interaction studies. Genetic heritability of the slope phenotype was 20%, and these three variants were individually and interactively associated with an increase of the slope phenotype. Previously, it was thought that the sistance . Our curTCF7L2, CDKN2B, and JAZF1 genes were independently and interactively associated with increased T2D risk and the TG/HDL ratio change across ages. For the remaining T2D risk conferring gene variants, we did not find significant association evidence in this analysis.In conclusion, using the FHS T2D family data and different statistical approaches, we found variants in the AUC: Area under the curve; BF: Bayes factor; BIMBAM: Bayesian imputation-based association mapping; GAW16: Genetic Analysis Workshop 16; GEE: Generalized-estimating equations; HDL: High-density lipoprotein; TG: Triglyceride; T2D: Type 2 diabetes; FHS: Framingham Heart Study; ROC: Receiver operator characteristic; SNP: Single-nucleotide polymorphism;The authors declare that they have no competing interests.PA, MF, IB, and MP drafted the manuscript. SK, AA, and SL performed the statistical data analysis. All authors read and approved the final manuscript.