While the importance of gene-gene interactions in human diseases has been well recognized, identifying them has been a great challenge, especially through association studies with millions of genetic markers and thousands of individuals. Computationally efficient and powerful tools are in great need for the identification of new gene-gene interactions in high-dimensional association studies.We develop C++ software for genome-wide gene-gene interaction analyses (GWGGI). GWGGI utilizes tree-based algorithms to search a large number of genetic markers for a disease-associated joint association with the consideration of high-order interactions, and then uses non-parametric statistics to test the joint association. The package includes two functions, likelihood ratio Mann–Whitney (LRMW) and Tree Assembling Mann–Whitney (TAMW). We optimize the data storage and computational efficiency of the software, making it feasible to run the genome-wide analysis on a personal computer. The use of GWGGI was demonstrated by using two real data-sets with nearly 500 k genetic markers.Through the empirical study, we demonstrated that the genome-wide gene-gene interaction analysis using GWGGI could be accomplished within a reasonable time on a personal computer . We also showed that LRMW was suitable to detect interaction among a small number of genetic variants with moderate-to-strong marginal effect, while TAMW was useful to detect interaction among a larger number of low-marginal-effect genetic variants.The online version of this article (doi:10.1186/s12863-014-0101-z) contains supplementary material, which is available to authorized users. The recent genome-wide association studies (GWAS) have made significant progress in finding single genetic variants associated with common complex diseases, with disclosure of regions of interest. Nonetheless, it is likely that a substantial proportion of genetic variants remain uncovered. Common complex diseases are likely caused by the interplay of multiple genetic variants, each with relatively modest marginal effects. A comprehensive genome-wide gene-gene interactions analysis (GWGGI) will take this complexity into account. By fully exploring all available genetic variants on the entire genome, GWGGI could yield novel interaction findings that can be investigated through later bench science research and clinical application for their functional importance and clinical usefulness.Software, such as the commonly used multifactor dimensionality reduction software (MDR) , has beeThe advance of high-throughput technologies generates millions of single-nucleotide polymorphisms (SNPs) that can be extensively explored for gene-gene interactions. Nevertheless, the search of interactions among millions SNPs is a daunting challenge and requires more computationally efficient and powerful statistical tools. We implement two modules, LRMW and TAMW, into GWGGI, for high-dimensional gene-gene interaction analyses involves thousands or even millions of SNPs.P(Gi|D) and Gi, in cases and controls, respectively. The MWU can then be formed based on the LR values,ND and Both LRMW and TAMW utilize the Mann–Whitney U-statistic (MWU) to evaluate joint association of multiple genetic variants with the consideration of possible interactions. Given the multi-locus risk groups formed based on the selected disease-susceptibility genetic variants , LRMW and TAMW assign likelihood ratio (LR) value for each individual belonging to a particular risk group, where LR measures the risk of an individual having disease rather than non-disease . For insBased on this definition, we can calculate the variance,ractions .G1={0}, G2={}), which gives the highest possible MWU. In step two, it searches for the second SNP, considering its possible interaction with the first SNP, to split the two existing risk groups into four risk groups }, G2={0, 2}, G3={, }, G2={, 2}), which gives the highest possible MWU. The whole splitting process continues until samples are divided into risk groups with a small number of samples. The 10-fold cross-validation is then used to choose the final model with the optimal number of risk groups. As we demonstrate elsewhere [LRMW and TAMW utilize different search algorithms, which make them useful to detect different types of gene-gene interactions. LRMW uses a forward selection algorithm to search all available genetic variants for important interactions among a small number of moderate-marginal-effect genetic variants . In steplsewhere , the forLRi,j is the LR value assigned to an individual i for the j-th time, and Ti is the total number of times that the individual i is included in the OOB samples. The overall MWU statistic can then be formed based on the assembling LR to test joint association of hundreds or thousands of genetic variants with diseases. Compared with LRMW, TAMW is more powerful when the underlying disease model involves a large number of genetic variants and their interactions. Nevertheless, it is computationally more intensive than LRMW, and the results from TAMW are less interpretable. Both LRMW and TAMW involve model selection procedure, so the p-value should be obtained by using permutation test. Alternatively, we can split the data to training dataset and testing dataset, and obtain the p-value on testing dataset [For complex diseases influenced by the interplay of hundreds genetic variants, LRMW can only identified those most significant interactions. To consider interactions among hundreds or even thousands genetic variants, most of which have low marginal effects, we also developed TAMW . TAMW usmentclass2pt{minim dataset , which cGWGGI is developed in C++, and is available for multiple platforms . The software is based on standard C++ and does not depend on other source codes or libraries. Researchers can download the source code, recompile and build it using different C++ compilers . Figure We implement both LRMW and TAMW into GWGGI, which can be called by using commands “--lmw” and “--tamw”, respectively. Users can decide which module to use based on the prior knowledge of the disease and their research purposes. LRMW is suitable for scenarios when the underlying disease model caused by a small number of moderate-marginal-effect genetic variants and interactions, while TAMW fits for disease models involving a large number of low-marginal-effects genetic variants and interactions.Data read in GWGGI can be either in Plink  binary fGWGGI also provides tuning parameters, so that users can use the software in a flexible and sometimes biologically meaningful way. For example, using “--hz”, users can determine whether to include a heterozygote effect (Aa v.s. AA/aa) in the analysis. In TAMW, researchers can also use “--td-burnin” to get the optimal size of trees from the first 50 bootstrap samples.In the output of GWGGI, both statistical significance of detected gene-gene interactions and the marginal contribution of each genetic variant are reported. In addition, GWGGI provides additional information regarding the joint association model . More detailed information, such as the tree structure in LRMW and individual LR values in TAMW, can be also obtained if needed.We demonstrated the use of GWGGI through the analysis of two datasets from the Wellcome Trust genome wide association study . The firThe optimal tree size from LRMW  was chosen based on 10-fold cross validation. The optimal tree size from LRMW was 7 for the T1D dataset and was 6 for the CAD dataset. For TAMW, we chose the optimal size of tree by using the first 50 bootstrap samples . The optimal size from TAMW was 4 for the T1D dataset and was 3 for the CAD dataset. The analyses were performed on a personal computer with 2.5GHz CPU and 4G memory. The analysis of the dataset with 2 k SNPs and 4901 samples was completed in a few minutes . Because not all of the packages were designed for genome-wide analyses, the comparison was made based on the T1D dataset with 2184 SNPs. Among these packages, Plink and BOOST can only consider two-way interactions, while MDR and RJ can explore high-order interactions like GWGGI. Another difference of these packages is how they deal with missing data. BOOST can’t handle missing data, therefore we imputed missing data for BOOST. MDR treats missing data as another category besides 0, 1, and 2, while Plink, RJ and GWGGI can directly handle missing data. MDR ran very slowly on a large number of SNPs, so we first applied a “RELIEFF” filter to select top 20 SNPs and then searched for interactions with order up to 5. Because RJ was built for the prediction purpose without providing p-values, we used a goodness-of-fit chi-squared test to calculate p-values. The results were summarized in Table We develop a C++ package, GWGGI, for high-dimensional gene-gene interaction analyses. It comprises of two major functions, TAMW and LRMW, each of which can be used for genome-wide gene-gene interaction analyses without requiring a filter algorithm. In addition, each approach has its own uniqueness. While LRMW is suitable for the identification of gene-gene interactions among a few moderate-marginal-effect genetic variants, TAMW is designed for detecting gene-gene interactions involving hundreds low-marginal-effect genetic variants. We further optimize the package so that the genome-wide gene-gene interaction analysis can be accomplished within a reasonable time on a personal computer.Project Name: GWGGIProject Home Page:https://www.msu.edu/~changs18/software.html#GWGGI or https://www.msu.edu/~qlu/Software.htmlOperating Systems: UNIX, WindowsProgramming Languages: C++Other Requirements: No other dependence librariesLicense: GNU GPLAny restrictions to use by non-academics: license needed


Pre-eclampsia is a major cause of maternal and fetal mortality in pregnancy. The identification of genetic variants which predispose to pre-eclampsia demands large DNA collections from affected mothers and babies and controls, with reliable supporting phenotypic data. The InterPregGen study has assembled a consortium of researchers from Europe, Central Asia and South America with the aim of elucidating the genetic architecture of pre-eclampsia. The MoBa collection is playing a vital role in this collaborative venture, which has the potential to provide new insights into the causes of pre-eclampsia, and provide a rational basis for novel approaches to prevention and treatment. The InterPregGen consortium, a multinational collaboration between research groups from Europe, Central Asia and South America, is seeking to identify genetic factors which predispose to pre-eclampsia, a quest which has proved challenging to investigators from around the world for decades. Pre-eclampsia is the most serious of the hypertensive disorders of pregnancy, with an incidence ranging from 2-5% of pregnancies in Western Europe and North America to as high as 18% in parts of Africa . Exact fth week of gestation; these are manifestations of widespread vascular endothelial dysfunction. It is possible that this is a common end point to diverse pathogenetic mechanisms, but the two-stage theory is a useful model, supported by observational and experimental evidence [The clinical features of pre-eclampsia are maternal hypertension and proteinuria developing after the 20evidence . In the evidence . For theEpidemiological studies over the past five decades have provided robust and consistent support for the clinical observation that pre-eclampsia runs in families. First degree relatives of affected women have a 2- to 3-fold increase in risk of pre-eclampsia -10. FurtThese observations justify the search for genetic variants in mothers and babies which confer susceptibility to pre-eclampsia. Genetic studies offer an important advantage in the identification of novel pathogenetic mechanisms in diseases of pregnancy, as they circumvent the practical and ethical challenges of obtaining suitable maternal and fetal tissue early in pregnancy, when trophoblastic invasion of maternal tissues occurs; investigation of genetic variation in mother and offspring can be conducted on DNA obtained at any time. Furthermore, in a disorder such as pre-eclampsia with a rapidly progressive pathophysiology it is often difficult to distinguish between causal factors and secondary phenomena resulting from disease processes. Genetic variation which proves to be associated with disease is guaranteed to predate the disease process.Genome-wide linkage studies of pre-eclampsia, analysing families with two or more affected women from Australasia, Iceland, Finland and Holland, have each identified loci which appear to show linkage with pre-eclampsia in their populations, but these results have not been independently replicated -18. ManyA major cause of the lack of success in identifying susceptibility genes has been the limited statistical power of the majority of studies performed to date. It is now apparent that many common genetic variants which predispose to complex disorders have individually small effect sizes. These variants are therefore difficult to detect by linkage analysis but can be detected with much higher power using genetic association study designs . InteresThe InterPregGen consortium was formed to address these deficiencies, aiming firstly to include a sufficiently large number of subjects with rigorously defined pre-eclampsia to provide adequate statistical power for association studies to detect genetic variants with small effect sizes; secondly, to use genome-wide association screening (GWAS) to scan both the maternal and fetal genomes for variants that predispose to pre-eclampsia. Also, the majority of larger published genetic studies in pre-eclampsia have been conducted in women of European ancestry, where the incidence of pre-eclampsia is amongst the lowest in the world. Therefore a further objective of the InterPregGen study was the inclusion of populations from different ethnic backgrounds in Europe, Central Asia and South America.InterPregGen is making use of several large biobanked DNA collections for studies of pre-eclampsia in Western Europe. These include the Norwegian Mother and Child Cohort Study (MoBa) ,25; the th week of gestation [The diagnosis of pre-eclampsia is based on an international definition, requiring new-onset hypertension , associated with proteinuria (≥ 300 mg/L) after the 20estation . RecruitThe majority of control subjects are women with no history of hypertension (blood pressure <140/90 mm Hg) recruited during pregnancy. For Icelandic and UK subjects control data is provided by extensive existing GWAS data from population cohorts of respectively 36000 and 6000 individuals. Population control data have been used successfully for the identification of genetic associations with many complex disorders ; providiAll participants in the study have provided informed consent for the use of their samples, or those of their babies, in genetic studies. Approval for use of the samples and associated clinical data has been obtained from Research Ethics Committees in their country of origin, and over-arching approval for the InterPregGen study has been provided by the University of Nottingham Research Ethics Committee.The study is using genome-wide association screening as the primary strategy for discovery of genetic variants which are associated with pre-eclampsia. The principles of GWAS have been well-described elsewhere : case anTo maximise the statistical power of the study in a cost-effective way, InterPregGen is making use of GWAS data generated in the course of earlier studies in maternal and control samples from Iceland, the UK and Colombia. Additional GWAS is being undertaken using Illumina genome-wide arrays on offspring of pre-eclamptic pregnancies from Iceland and the UK, and also on newly collected maternal-fetal cases and controls from Central Asia. GWAS data is therefore available from a total of 7600 maternal cases and 4000 fetal cases .−8 is applied for genome-wide significance . For each study population with GWAS genotypes from pre-eclamptic mother-baby pairs, SNPs are also tested for evidence that maternal-fetal genotype interaction increases susceptibility to pre-eclampsia. Allelic odds ratios (OR) provided for each population by logistic regression analysis are combined in a meta-analysis to generate an overall OR for each SNP. The selection of SNPs for subsequent replication genotyping is based on the results of meta-analysis, with priority given to those with the lowest p-values. To adjust for the multiple statistical tests conducted in the course of GWAS, a meta-analytic p-value below 5×10nce  effects. The approach for examining parent-of-origin effects in Icelandic data will differ, due to the richness of existing Icelandic whole-genome data, providing two independent approaches to test for imprinting effects. Through whole-genome sequencing of Icelandic individuals, long-range haplotype phasing and parental-origin determination the deCODE dataset provides complete information of the parental-origin of each allele, without additional genotyping of paternal samples.We anticipate that the research effort will identify functional DNA variants, or their proxies, which pre-dispose to pre-eclampsia and its complications, leading to enhanced understanding of the underlying disease process. InterPregGen will explore the potential for translating this information into clinical benefits through risk-profiling and the development of novel predictive markers. Currently the prediction of women at high risk of pre-eclampsia depends on clinical criteria, including the identification of risk factors at antenatal booking . These iMoBa is a unique collection of samples and data gathered prospectively at the time of pregnancy. For researchers into the genetics of complex disorders of pregnancy such as pre-eclampsia MoBa offers the advantages of a searchable database of reliable clinical information which can be used to identify cases and controls which fulfil the inclusion criteria of the study with a high degree of confidence. The well-managed biobanking facility ensures that DNA of dependable quality is available for genotyping studies from large numbers of cases and controls, a vital requirement for adequately powered genetic association studies. In contrast to many case-control collections, MoBa includes data and DNA samples from the partners and babies of pregnant women, which will enable InterPregGen to explore both maternal and fetal genomes, the interactions between maternal and fetal gene variants, and the contribution of paternal genes to pre-eclampsia. The biobanking expertise of MoBa partners in the InterPregGen study is proving invaluable in the discussion of ethical policies, and in the development of procedures for the newly formed biobanks in Uzbekistan and Kazakhstan.The identification of genetic factors which predispose to pre-eclampsia is a large undertaking, in which MoBa has a key role. InterPregGen is conducting the largest ever genome-wide association screen of maternal and fetal genes and their interactions in this disorder, and is also the first with adequate power to investigate the role of genetic imprinting (parent-of-origin effect). The ability to compare the genetic architecture of pre-eclampsia in subjects from three continents may give insights into the source of variation in the frequency of the condition across different ethnic groups. The prospects are good for novel findings which will ultimately translate into a better understanding and management of a condition which remains one of the major killers of pregnant women and their babies throughout the world.


Genomic prediction (GP) allows breeders to select plants and animals based on their breeding potential for desirable traits, without lengthy and expensive field trials or progeny testing. We have proposed to use Dissimilarity-based Partial Least Squares (DPLS) for GP. As a case study, we use the DPLS approach to predict Bacterial wilt (BW) in tomatoes using SNPs as predictors. The DPLS approach was compared with the Genomic Best-Linear Unbiased Prediction (GBLUP) and single-SNP regression with SNP as a fixed effect to assess the performance of DPLS.Eight genomic distance measures were used to quantify relationships between the tomato accessions from the SNPs. Subsequently, each of these distance measures was used to predict the BW using the DPLS prediction model. The DPLS model was found to be robust to the choice of distance measures; similar prediction performances were obtained for each distance measure. DPLS greatly outperformed the single-SNP regression approach, showing that BW is a comprehensive trait dependent on several loci. Next, the performance of the DPLS model was compared to that of GBLUP. Although GBLUP and DPLS are conceptually very different, the prediction quality (PQ) measured by DPLS models were similar to the prediction statistics obtained from GBLUP. A considerable advantage of DPLS is that the genotype-phenotype relationship can easily be visualized in a 2-D scatter plot. This so-called score-plot provides breeders an insight to select candidates for their future breeding program.DPLS is a highly appropriate method for GP. The model prediction performance was similar to the GBLUP and far better than the single-SNP approach. The proposed method can be used in combination with a wide range of genomic dissimilarity measures and genotype representations such as allele-count, haplotypes or allele-intensity values. Additionally, the data can be insightfully visualized by the DPLS model, allowing for selection of desirable candidates from the breeding experiments. In this study, we have assessed the DPLS performance on a single trait. At the same time, however, many real associated variants may be missed. The success of GWAS relies on the underlying trait architecture [Genome wide association studies (GWAS) have been widely applied in human, plant and animal studies to identify genetic variants associated with complex traits –3. In GWitecture , heritabitecture –7, effecitecture , 9. Theritecture . In addiitecture . Breederitecture . It has itecture –14 and aitecture –17. The itecture . Severalitecture –15. For The accurate prediction of a complex trait can be extremely challenging, as the trait may be affected by multiple loci that interact. Another major challenge is the fact that the number of SNPs in GP studies greatly exceeds the number of samples leading to the so-called ‘large-p - small-n’ problem. Because of this, many traditional statistical approaches are not applicable to such data. Deriving an accurate prediction of complex traits by the high-density SNPs, while at the same time taking into account possible interactions between multiple loci, requires powerful feature reduction methods. A variety of methods such as Bayesian regression –21, GenoMost of the suggested statistical models differ in their assumptions of the distribution of the SNPs effect. For example, the GBLUP model assumes that the SNPs effect size is drawn from a common Gaussian distribution and the variances of SNPs effect are equal. This unrealistic assumption of GBLUP corresponds to use of a single random effect term in the model, which is a severe and unnecessary limitation. Whereas the Bayesian methods , 26 assuMultiple Linear Regression (MLR) is an often used quantitative technique for prediction from predictors , 30. HowRalstonia solanacearum and is considered as one of the most destructive diseases for a wide range of crops, including tomato [Therefore, we propose to use Dissimilarity-based Partial Least Squares (DPLS) to predict one or multiple traits from a large set of SNPs. In DPLS, measurements of the dissimilarity between the accessions (instead of the raw SNPs) are used for prediction. Because of this, DPLS may also be used for GP, when the method is used in combination with a suitable measure of the genomic distance between genotype accessions. Note that, during the dissimilarity calculation (between accessions), SNPs information is lost, which means effect of SNPs on the traits cannot be directly calculated from DPLS. However, there is a pseudo-sample technique proposed in literature to extract variables interaction effect from DPLS model . Unlikelg tomato . In thisThe prediction quality (PQ) of the DPLS model was measured in term of R2 estimated from observed and predicted trait values in a cross validation (CV) setup. Furthermore, we have compared the prediction performance of DPLS with a prediction based on SNPs found as significant in a Univariate association analysis (where SNP was used as fixed effect) and GBLUP (where SNP was used as random effect). We demonstrate GP with DPLS on a single trait. The method can however be applied to simultaneously predict multiple, possibly correlated traits.The differences in information captured by various genomic distance measures for GP have not been explored. Therefore, we first explored the properties of the eight genomic distance measures of interest to this study by the Mantel test, heatmap visualization, and their application in Multi-Dimensional Scaling (MDS) before we studied their application in DPLS.r) statistics. The pair-wise correlation results obtained from the comparison of genomic distance measures by the Mantel test are presented in Table The Mantel test was used to compare the relation between two distance matrices in terms of correlation  were used to visualize the relations between the tomato accessions in a scatter plot Fig. . The MDSIn both plots the observed clusters do not clearly relate to the phenotype. We conclude that the two groups of distance metrics represent different structures within the genotype data, neither of which can be strongly associated to the phenotype measures by MDS. However, this insight could only be obtained from the MDS score plot that represents the relative differences and similarities between all accessions used in the study.In this study, DPLS was used to relate genomic information captured by the distance measures indicated in Table 2 estimated on testset), model error measured in terms of Root Mean Square Error (RMSE) and the optimal number of LVs used for building prediction models. PQ range from 0.59 to 0.64 for analyzed genomic distance measures. The resulting RMSE was found to be similar for each genomic distance measure. These results . The phenotypic variance predicted from each SNP ranges from ~0.04 to ~50 %, which is lower than the variance explained by DPLS (59–64 %). This analysis clearly shows DPLS prediction has edge over single-SNP regression approach. The analysis clearly indicates that BW is a complex trait, which should be analyzed by multivariate methods that observe all SNPs within all accessions.The results obtained from the proposed DPLS method indicate that its prediction performance is on par with that of GBLUP. Together with that DPLS provides some other beneficial characteristics. It can be applied to dataset of any dimension. DPLS reduces the dimensionality drastically and can handle missing values while computing distances or dissimilarities. It can handle the multi-colinearity that is omnipresent in genomic data and can be easily implemented using widely available software and methodology for conventional PLS. A major advantage of DPLS over other methods is the DPLS score plot, which represents arrangement of tomato accessions in DPLS space. This visualization provides a tool for the breeders to select the optimal candidates for their future breeding program. For instance, breeders can select the specific tomato accessions from the right panel of the score plot presented in Fig. The other advantage of DPLS is that, it is flexible to various genotype representations. For Example, SNPs are usually encoded as discrete variables  and many models uses this encoding as standard input for GP. The DPLS prediction model does not rely on such standard genotype representation since a distance matrix between accessions is used as input for the model. This makes it more flexible to data representation and may possibly be better applicable for GP in diploid or polyploid crops. The approach can also be very useful for analyzing complex phenotypes which are often collected in form of multiple traits to gather more information . These tIn this study DPLS, a novel approach for genomic prediction, is proposed for dealing with genomic data. This method employs the strengths of multivariate partial least squares (PLS) based prediction with the expression of genomic distances  between individual accessions. This way, problems in the data such as the categorical nature of the variables, the large number of variables and their multi-collinearity are avoided. It was found that DPLS performs on par with GBLUP and better than Univariate prediction approach for GP. The prediction performance of the proposed method was close to the biologically imposed upper limit boundary set by the heritability of the trait. DPLS allows for visualization of the accessions with respect to the trait of interest, which may be invaluable for selection of specific candidates in agricultural breeding programmes.329 tomato breeding accessions were genotyped for 7321 SNPs using “SolCAP” array. The data was kindly provided by Bezo Zaden and East–west Seed. The SNPs are distributed across 12 chromosomes of tomato genome. A quality check (QC) was performed on the genotype data to exclude low quality SNPs and accessions from the analyses. SNPs were excluded if minor allele frequency (MAF) <0.01, proportion of missing value (PMV) > 0.10 or both. Tomato accessions with genotypes, but not phenotyped were excluded from the analyses. 242 tomato accessions and 6517 SNPs remains after the quality filtering and were used for GP.Ralstonia solanacearum bacteria. It is one of the most destructive crop diseases in tropical, subtropical and some warm temperate regions of the world [BW disease is caused by the he world . BW is an = total number of observation, yi = percentage wilted plat at the ith observation and t = time at the ith observation.Where Eight dissimilarity measures , where for the BW- tomato data example X is the genotype matrix and Y is disease trait or response vector [The aim of this study is to determine if DPLS is a viable method for genomic prediction from whole genome marker data. The DPLS method employs the strengths of PLS based prediction with the expression of genomic distances  between individual accessions. The general goal of PLS is to predict a set of response (dependent) variablese vector . This pre vector , 55. TheWhere,T = X-factors scores U = Y-factors scoresP = X-factors loadings andC = Y-factors loadingsE and F = matrices of residualsX to Y is obtained by:The regression coefficient that relates Where,W = X-factors weights i.e., projections of the objects of X-space onto Y-factor scores. The decomposition of X and Y are made so as to maximize the covariance between T and U.X (genotype matrix) is replaced by dissimilarity matrix D (distance between tomato accessions). A summarized overview of genomic distance measures used to fit a DPLS prediction model in this study are given in Table In DPLS , the oriD matrix is a square matrix. A double centering  has to be applied to matrix D. This means for DPLS the score matrix is same as the loading matrix (linear combination of predictors in D matrix), up to a scaling constanαt α to identify the model.The B obtained from DPLS model is based on D matrix and not on X matrix as in PLS. The DPLS method also calculates scores for each accession. These scores are linear combinations of the predictor variables and are calculated in similar fashion as presented in equation (W), which reflects the covariance structure between predictors and response variables. We have used the R-package ‘pls’ [The regression coefficient from the DPLS model can be calculated in similar equation as in classical PLS (see equation ). Howeveequation . In DPLSge ‘pls’  and a cuge ‘pls’ .Three steps are critical when building a PLS/DPLS prediction model of 1) selection of optimal number of latent variables (LVs), and model building 2) the assessment of the overall model quality (or model reproducibility) 3) assessing significance of prediction model (model transportability).Several approaches including cross-validation (CV) setups are recommended for selection of LVs –60. Herep-value was obtained by combining all obtained statistics (mean and standard deviation RMSE) to assess the significance of difference between statistics (mean and standard deviation of RMSE) from original and permuted dataset.Permutation analysis is often used for validation of PLS-based classification or regression , 61, 62.Genomic BLUP  is consiy is a vector of phenotype, μ is the overall mean, Z is design matrix corresponding to g, g is the vector of SNP effects and e is the vector of residuals. It was assumed that g ∼ N where σg2 is additive genetic variance and Gis genomic relationship matrix derived from SNP markers. These analyses were performed using the R-package rrBLUP [Where, e rrBLUP .2) was calculated for each individual SNP and compared with the R2 value obtained from multivariate approach DPLS.In an unpublished study, 29 SNPs were found to be significantly associated with bacterial wilt s resistance. These SNPs were extracted from the BW-tomato data and fit in a univariate linear model. The SNPs were treated as fixed effect in this univariate model. The predictive ability (RNo human or animal samples were used in this study. As far as applicable, all experiments have been performed according to legal guidelines.The authors would like to thank Bejo Zaden and East-west Seed for access to the tomato dataset and to publish these results.The distance matrices to perform genomic predictions can be provided upon request. The raw genotyping data cannot be shared due to the fact that the authors are not the owners of this data. Therefore the main contribution of this paper is on the methodological part of genomic prediction.


The positive predictive value of high score was much higher for affected FCH individuals than for similar sporadic cases in the population. FCH is highly polygenic, supporting the hypothesis that variants across the whole allele frequency spectrum contribute to this complex familial trait. Polygenic SNP panels improve identification of individuals affected with FCH, but their clinical utility remains to be defined.Familial combined hyperlipidemia (FCH) is a complex and common familial dyslipidemia characterized by elevated total cholesterol and/or triglyceride levels with over five-fold risk of coronary heart disease. The genetic architecture and contribution of rare Mendelian and common variants to FCH susceptibility is unknown. In 53 Finnish FCH families, we genotyped and imputed nine million variants in 715 family members with DNA available. We studied the enrichment of variants previously implicated with monogenic dyslipidemias and/or lipid levels in the general population by comparing allele frequencies between the FCH families and population samples. We also constructed weighted polygenic scores using 212 lipid-associated SNPs and estimated the relative contributions of Mendelian variants and polygenic scores to the risk of FCH in the families. We identified, across the whole allele frequency spectrum, an enrichment of variants known to elevate, and a deficiency of variants known to lower LDL-C and/or TG levels among both probands and affected FCH individuals. The score based on TG associated SNPs was particularly high among affected individuals compared to non-affected family members. Out of 234 affected FCH individuals across the families, seven (3%) carried Mendelian variants and 83 (35%) showed high accumulation of either known LDL-C or TG elevating variants by having either polygenic score over the 90 Familial combined hyperlipidemia (FCH) is a familial dyslipidemia and the most common familial risk factor for premature coronary heart disease. Its genetic architecture is poorly understood. Rare high-impact variants have been identified in some patients, but have not explained a substantial portion of the trait. FCH has previously been speculated to be a polygenic disorder, but genetic data supporting this hypothesis have so far been incomplete. We provide experimental evidence for the polygenicity and heterogeneity of FCH in a large set of affected families using comprehensive genome-wide variant data. Approximately a third of the affected FCH individuals in our sample had high polygenic burden, and only a minority carried high-impact variants identifiable by genotyping. We show that the polygenic burden of affected FCH family members is comparable to that observed in individuals with similar lipid phenotypes in the general population. Genetic variants identified in large-scale population studies can also underlie the typical phenotypes observed in complex familial diseases such as FCH. Advances in genetic diagnosis based on population samples may thus also benefit FCH families. Families without high polygenic burden are good candidates for sequencing studies to identify rare variants not observable with genotyping. Familial combined hyperlipidemia (FCH), classically defined by elevations in serum total cholesterol (TC), triglycerides (TG), or both, in two or more first degree relatives, displays a prevalence of greater than 1% in Western populations . It is tHere, we present a comprehensive evaluation of the genetic background of FCH using a dense-marker genotyping panel. We hypothesized that FCH risk could derive in part from a combination of common variants associated, in population cohorts, with LDL-C and/or TG as well as uncommon variants in genes that have been implicated in Mendelian lipid syndromes. To test our hypothesis we evaluated Finnish FCH families to determine if they demonstrated an enrichment of known lipid-associated variants, compared to Finnish general population samples, and assessed whether such variants could account for differences in lipid levels and degree of aggregation of disease observed between the FCH families. Additionally, following the logic of recent studies that have demonstrated the combined impact of multiple small effect variants (polygenic scores) on risk for familial hypercholesterolemia (FH) and other lipid disorders –11, we mth age- and sex-specific population percentile) TC without elevated TG, 76 (32%) had elevated TG without elevated TC, and 80 (34%) had both lipids elevated. FCH probands  and other FCH affected individuals showed higher mean levels of both LDL-C  and TG  compared to all FCH family members  and to the general Finnish population   . The medctively) .p = 0.0025 for LDL-C and p = 0.0016 for TG). We included in this analysis all SNPs with at least one affected carrier (194 of the 212 SNPs previously associated with either LDL-C or TG in population genome-wide association (GWA) studies or with monogenic dyslipidemias). In total, 60 out of 95 LDL-C elevating SNPs were more common in EUFAM than in population samples, and 57 out of 99 of LDL-C lowering SNPs were less common. Similarly, 61 out of 96 TG elevating SNPs were enriched and 57 out of 98 TG lowering SNPs were depleted , could at most explain only 7 (3.0%) of all 234 affected FCH individuals, thus being of minor importance in our FCH family sample.We then examined if high-impact variants implicated in monogenic dyslipidemias would be enriched and contribute to FCH. ous form , was 1.8y of 95% . The APOhenotype , 15. It variants . As the th percentile in the population  showed high accumulation of known LDL-C or TG elevating variants, having either one or both polygenic lipid scores over the 90pulation . Three apulation . In six pulation .th population percentile) for either LDL-C or TG had a positive predictive value (PPV) of 0.45 in the FCH families and 0.23 in the general population. Negative predictive values (NPV) were 0.71 and 0.89, respectively.Finally, we evaluated how well the high polygenic scores predicted FCH affectedness in the families or among hyperlipidemic individuals in the population . Having In summary, we observed enrichment of both common and uncommon lipid-elevating variants in the FCH families. Only a minority  of affected individuals were carriers of high-impact variants of Mendelian dyslipidemias. The polygenic lipid scores contribute to FCH in over one third of 234 FCH subjects in these families, with considerable heterogeneity between families. In more than half of the families we did not observe either an increased load of common variants or carriers of high-impact variants.th percentile of the population for LDL-C and TG, respectively. In 13 families three or more affected individuals had high polygenic score and in 22 families none of the affected individuals had polygenic score above the 90th percentile of the population.Our results demonstrate an enrichment of many known lipid-level elevating variants in FCH families. This enrichment was observed for both uncommon and common variants known to affect either LDL-C or TG levels in populations. When the known variants were combined into polygenic lipid scores for each individual, 17% and 25% of the affected individuals had polygenic scores that were higher than the 90APOE, LIPC and APOA5, whose role in dyslipidemias is already established, but also include several genes whose function in lipid metabolism is not yet clear .Our results allow us to draw several conclusions about the genetic background of FCH. First, variants across the whole frequency spectrum were enriched and contribute to the high LDL-C and/or TG levels in the affected FCH individuals. This emphasizes the polygenic nature of FCH and is in line with previous results with familial hypercholesterolemia demonstrating that this less prevalent syndrome has a polygenic component . Genes iSecond, the majority of the enriched variants were originally identified in random population samples. This finding confirms that variants identified in population screens play a considerable role also in the complex familial disease FCH, and highlights the potential of using variants identified in population-based GWA studies to characterize familial dyslipidemia cases genetically.APOA1-C3-A4-A5 cluster, showing the central role of genetically driven TG in FCH , 22th Fircentile .For analyses of continuous lipid traits, individuals using lipid-lowering or estrogen medication at the time of sampling were excluded. Samples from the Finnish National FINRISK study were used as a Finnish population-specific comparison group, and individuals with known diabetes or cancer were excluded from the analyses . For then = 20,626) were genotyped with the HumanCoreExome BeadChip  using standard methods  and the FINRISK samples , or SNPs catalogued in the Online Mendelian Inheritance in Man (OMIM) database as located in genes implicated in primary and secondary monogenic dyslipidemic syndromes  was associated with the SNPs’ effects on the lipid in question (elevating or lowering).We estimated allele frequencies for all 212 SNPs in the 234 affected FCH individuals and in 18,715 FINRISK samples after excluding individuals with known diabetes or cancer similarly to the EUFAM exclusion criteria. The minor allele in FINRISK was designated as the effect allele. We then calculated enrichment ratios by dividing the effect allele frequencies in affected FCH individuals with the effect allele frequencies in the FINRISK samples. Under the null hypothesis of no enrichment, we estimated the null distribution for enrichment testing by calculating the enrichment statistic (enrichment ratio) for all variants with MAF > 0.001%  across the genome excluding regions within 50 000 base pairs from the lipid-associated SNPs. We estimated the null distribution in MAF bins across the genome while keeping the family structure fixed ; [0.5%,1%); [1%,1.5%); [1.5%,2%); [2%,2.5%), [2.5%,5%); [5%,10%); [10%,15%); [15%,20%); [20%,25%); [25%,30%); [30%,35%); [35%,40%); [40%,45%); and [45%,50%)). The observed lipid SNP allele frequency enrichment ratios were compared to the null distribution to provide one-sided We applied linear mixed models to test for differences in metabolic and clinical characteristics between FCH affected and unaffected individuals . An empiS1 TextThe recruitment, assessment, and genotyping of study subjects, the calculation of polygenic lipid scores, and the statistical analyses performed are described in more detail.(DOCX)Click here for additional data file.S1 FigThe number of genotyped affected (black) and unaffected individuals (white) is presented for each FCH family. The families are sorted by the number of affected individuals in each family, but the family numbers on the x-axis correspond to those presented in (PDF)Click here for additional data file.S2 Fign = 53). Vertical lines represent the range of values within the families. The families are sorted by the medians of LDL-C and TG levels, respectively, but the family numbers on the x-axis correspond to those presented in Median values of (a) LDL-C and (b) TG for genotyped individuals in all families ((PDF)Click here for additional data file.S3 Fign = 48, (a), (b)), or in all FCH family members , (d)), to allele frequencies in the Finnish FINRISK population cohort  and d); n = 18,715 in a) and b) after excluding individuals with diabetes and cancer). Under the null hypothesis of no enrichment, a 95% credible interval (shaded area) was estimated by calculating the enrichment statistic (enrichment ratio) for all variants with MAF > 0.001% across the genome excluding the loci of the 212 SNPs. Variants are designated as either lipid level elevating (red) or lowering (blue) for LDL-C ((a), (c)) and TG ((b), (d)) based on β estimates from linear regression in the FINRISK samples. Point size and color intensity reflect the magnitude of the effect. Only SNPs with at least one heterozygous carrier are shown . FINRISK, The National FINRISK Study. *The enrichment ratio for LPL rs1801177 fell within the 95% credible interval.Enrichment ratio is the ratio of effect allele frequency in FCH probands ((PDF)Click here for additional data file.S4 FigAPOA5 rs3135506 predisposes to hypertriglyceridemia and homozygosity for (b) APOE rs7412 predisposes to type III hyperlipoproteinemia, which typically presents in elevated levels of VLDL and TG species. Only individuals without diabetes and other relevant confounders were included in this comparison. In (b) the y-axis is log-scaled.Homozygosity for (a) (PDF)Click here for additional data file.S5 Fign = 51), we calculated mean empiric genetic correlation of all combinations of pairs of affected subjects. Families are ranked on the x-axis as in For each family with at least two genotyped affected members ((PDF)Click here for additional data file.S1 TableP-values were calculated using Wald test by a linear mixed model correcting for sample relatedness. FCH, familial combined hyperlipidemia.(PDF)Click here for additional data file.S2 Table†Global minor allele. ‡MAF in non-Finnish Europeans calculated from the public ExAC data set (version 0.3) for coding SNPs (those present in the ExAC data set), and from the public 1000 Genomes Phase 3 data set for non-coding SNPs Click here for additional data file.S3 Tablep-values were estimated from the null distribution. Enrichment ratios are presented for the affected individuals. The carrier counts were calculated from all genotyped FCH family members who passed exclusion criteria and did not have diabetes or other relevant confounders (n = 661), and did not account for non-independence within family. The + and—symbols denote elevating and lowering effects on the lipid in question, respectively. FCH, familial combined hyperlipidemia; FINRISK, The National FINRISK Study. J.A.K, J. A. Kuivenhoven; C.J.W., C. J. Willer; T.M.T., T. M. Teslovich; I.S., I. Surakka  for coding SNPs (those present in the ExAC data set), and from the public 1000 Genomes Phase 3 data set for non-coding SNPs  to the Finnish population .Under the null hypothesis of no enrichment, we established the null distribution for enrichment testing by calculating the enrichment statistic (enrichment ratio) for all variants with effect allele  frequency > 0.001% across the genome excluding the loci of the 212 SNPs. Enrichment ratios were calculated for each of the 212 SNPs if at least one carrier was identified , and one-tailed  Surakka . †Effecting SNPs . ‡Effect(PDF)Click here for additional data file.S4 TableIn the EUFAM study, dyslipidemia was established based on levels of total cholesterol, triglycerides, or both that were ≥ 90th Finnish age- and sex-specific population percentile. The population percentiles were derived from FINMONICA, a large population survey performed in 1992. The percentile estimates and a description of the polynomial regression analyses used to establish them have been reported in detail previously .(PDF)Click here for additional data file.


Several methods have been proposed to account for multiple comparisons in genetic association studies. However, investigators typically test each of the SNPs using multiple genetic models. Association testing using the Cochran-Armitage test for trend assuming an additive, dominant, or recessive genetic model, is commonly performed. Thus, each SNP is tested three times. Some investigators report the smallest p-value obtained from the three tests corresponding to the three genetic models, but such an approach inherently leads to inflated type 1 errors. Because of the small number of tests (three) and high correlation  among these tests, the procedures available for accounting for multiple tests are either too conservative or fail to meet the underlying assumptions .eNOS -786T>C which was shown to be associated with breast cancer risk.We propose a method to calculate the exact p-value for each SNP using different genetic models. We performed simulations, which demonstrated the control of type 1 error and power gains using the proposed approach. We applied the proposed method to compute p-value for a polymorphism Our findings indicate that the proposed method should be used to maximize power and control type 1 errors when analyzing genetic data using additive, dominant, and recessive models. Genome-wide association studies (GWAS) and candidate gene association studies are commonly performed to test the association of genetic variants with a particular phenotype. Typically, hundreds of thousands of single-nucleotide polymorphisms (SNPs) are tested for association in these studies. Associations between the SNPs and the phenotypes are determined on the basis of differences in allele frequencies between cases and controls. Severalα by utilizing the Bonferroni adjustment corresponding to each of the models are as follows: additive model: t = , dominant model: t = , and recessive model: t =  for genotypes AA, Aa, and aa, respectively. Let the three test statistics corresponding to the additive, dominant, and recessive models be T1, T2, and T3, respectively.where the weight, T1, T2 and T3, has an asymptotically normal univariate distribution. Therefore, the p-values for each of these tests can be obtained from their asymptotic distributions. However, reporting the smallest p-value obtained from testing T1, T2 and T3, individually leads to an inflated type 1 error rate. If the exact joint distribution of the three tests is known, one can compute the exact p-value for the SNP that will account for the multiple correlated tests. We proceed to derive the joint distribution of the three test statistics, T1 = (RYX2−RXY2) + 2(RYX3 − RXY3), and T2 = (RYX2 − RXY2) + (RYX3 − RXY3), and T3 = (RYX3 − RXY3). As T3 = T1 − T2, we only need to derive the joint distribution of T1 and T2. It is reasonable to assume that the three genotype counts in cases  and the three genotype counts in controls  follow a multinomial distribution, with probabilities  and  respectively. LetT = AX + BY, whereT1, T2 is given byEach test statistic, fx, fy are trinomial probability mass functions and h = B−1T − B−1AX. The derivation of the joint pmf of T1, T2 is detailed in the Appendix. The p-value corresponding to the test statistic  can be computed by summing up the probabilities of the test statistics that are equally or less probable than the observed test statistic, which can be written aswhere RX and RY counts  = 1, 2. GCD = RX = RY and 3. 1 < GCD < min. In scenario 1 the triangles do not overlap, therefore the p-value can be evaluated most efficiently . Briefly, the CA trend test statistics form a system of constrained linear Diophantine equations. The computational optimizations presented in the Appendix are based on exploiting the properties of the linear Diophantine equations with trinomial constraints. The solution space of these equations corresponds to the discrete space of nonzero probabilities for the joint pmf. This discrete space has a pattern of overlapping triangles that can be enumerated based on Figures . In thislogit(P(Z = 1)) = β0 + β1X, where X is the indicator for genotype, Z is the disease status, β0 is the intercept, and β1 is the log odds ratio for the SNP. The genotype data for a SNP were simulated using a minor allele frequency (MAF) of 40% for the null hypothesis and two MAFs of 40% and 20% for the power comparisons. For the type 1 error comparisons, we simulated 1000 replicate datasets from the null hypothesis , with β0 = − 2.5 and β1 = log (1). For the power comparisons, we simulated 1000 replicate datasets for 40% and 20% MAFs from the alternate hypothesis  for each of the three scenarios: (1) additive model with odds ratio of 1.2, (2) dominant model with odds ratio of 1.3, and (3) recessive model with odds ratio of 1.3. The methods we compared were as follows: performing only additive analyses (additive-only), performing only dominant analyses (dominant-only), performing only recessive analyses (recessive-only), using the p-value based on reporting the smallest p-value of the three genetic models (min-p), using the Bonferroni correction approach, and using the proposed exact p-value method.We performed simulations to evaluate the performance of the proposed method and compared our approach with standard approaches used in the literature. All the simulation results were based on 1000 replicate data sets. Each replicate dataset comprised 1000 cases and 1000 controls. The disease status for each data set was obtained using the logistic regression model The type 1 errors based on 1000 replicates from the null hypothesis are shown in Table The power comparisons based on 1000 replicates for the SNP data simulated using 40% and 20% MAFs for the three scenarios when the data were simulated using the additive, dominant, and recessive models, respectively, are shown in Table When the data were simulated using the dominant model  and included 421 breast cancer cases and 423 cancer free controls. The first panel in Table eNOS -786T>C. The second panel in Table eNOS -786T>C computed using the 5 different approaches: additive-only, dominant-only, recessive-only, Bonferroni and the proposed exact p-value method. The additive-only, dominant-only and recessive-only approaches had p-values of 0.0045, 0.0148 and 0.0313, respectively, and the Bonferroni adjusted p-value was 0.0135. For this SNP, the p-value computed using the proposed exact p-value method was 0.0021, which was more significant than the smallest of the three p-values obtained using the additive-, dominant-, and recessive-only analyses . The software to compute exact p-values is available atIn genetic association studies, three genetic models--additive, dominant, and recessive--are generally used to test each SNP using the Cochran-Armitage trend test. Reporting the minimum p-value of the three genetic models leads to inflated type 1 errors. We proposed an approach to compute the exact p-value when genomic data is analyzed using the three genetic models. The proposed approach leads to higher power while controlling the type 1 error.X1, X2, X3 and Y1, Y2, Y3 are the number of individuals with genotypes AA, Aa, and aa in cases and controls, respectively, with X1 + X2 + X3 = RX and Y1 + Y2 + Y3 = RY. The three genotype counts in cases  and the three genotype counts in controls  follow a multinomial distribution with probabilities  and , respectively. The probability mass function (pmf) of  isY1, Y2, Y3) isT1 = (RYX2 − RXY2) + 2(RYX3 − RXY3) , T2 = (RYX2 − RXY2) + (RYX3 − RXY3), and T3 = (RYX3 − RXY3) respectively. As T3 = T1 − T2, we only need to derive the joint distribution of T1 and T2. LetT = AX + BY, whereRecall that G with pmf fG. Suppose we have a transformation from G → H. The pmf fH of the transformed variables H can be expressed as follows:[Consider an n-dimensional discrete random vector follows:G and H are different, i.e., the transformation from  → T is a linear transformation of the form T = AX + BY. The pmf of T is given byThis can be extended to the case where the dimensions of This can be simplified as:T1, T2) is prohibitively time consuming. Computational optimizations can be used to speed up the computations of the probability mass function. We list several optimization techniques below. The first optimization is to transform the pmf to be symmetric in , which reduces the computational burden by half. The original test statistics T1 and T2 are T1 = (RYX2 − RXY2) + 2(RYX3 − RXY3) and T2 = (RYX2 − RXY2) + (RYX3 − RXY3), respectively. The joint pmf of  is a one-to-one function of the joint distribution of any two orthogonal linear combinations of T1 and T2. So if we transform the test statistics T1 and T2 intoComputing this pmf on all the possible values of  is a one-to-one function of the pmf of . Hence, the p-value obtained will be the same when using  instead of . The resulting pmf of  can be derived using the same method as with .the resulting pmf of . The number of values  can take are finite and represented by the solution space of the equationsThe next computational optimization is to identify the values that can be taken by  of RX and RY. If RX and RY are co-prime (GCD=1), only three triangles overlap at a single point  which requires no additional computation. When RX and RY are not co-prime, the triangles overlap at multiples of the GCD of RX and RY. In this scenario, multiple values of X3, Y3, X2, and Y2 contribute to the same .Another important fact is that these triangles may overlap, reducing the solution space, which is depicted in Figures Z1, Z2) isRX = 1000 and RY = 1000 using a computer with a 3.4-GHz processor and 8 GB of RAM. However, the amount of storage required for the solution space far exceeds the hardware capabilities available. In light of this limitation, computational optimizations should be employed to avoid storing the whole solution space. This limitation leads to three possible scenarios:In an ideal scenario, the total number of computations required to compute the pmf of  = 11. GCD = RX = RY2. GCD < min3. RX and RY are co-prime, the triangles only overlap at a single point ; therefore, we can independently evaluate each of the possible values of the solution space. The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, so we evaluate the probabilities of each of the possible values of the test statistics one at a time. Hence, the p-value is the sum of all the probabilities of test statistics that are lower than the probability of the observed test statistic. Using this procedure there is no need to store any data, which leads to faster computation of the p-value from the joint distribution.When RX and RY are equal, most of the triangles overlap with each other. But a pattern has been observed in this scenario, which is shown in Figure RX = 10 and RY = 10. As seen in Figure RX apart. So if we condense the possible solution space, the solution space is as shown in Figure When Algorithm:RX = RY = R. The solution space can then be constrained to a matrix with 2R + 1 rows and 2R + 1 columns. Let the center of the matrix correspond to the test statistic .2. Now, as we can see from Figure1. Let i = 1: R start at (Z1 = − (R − i), Z2 = − 1). Find the possible combinations of X3, Y3, X2 and Y2 that contribute to the cell corresponding to (Z1 = − (R − i), Z2 = − 1). Compute the probabilities for the cells along the diagonal path in quadrant 3, until Z1 = 0. Here X3 and X2 remain the same; hence, it is trivial to compute the probabilities for each cell.3. For Z1 = R − (i − 1); here X3 remains the same and Xnew2 = X2 + Z2.4. Then in quadrant 4, compute the probabilities for the cells along the horizontal path until Z2 = 0; here X3 and X2 remain the same.5. Then continue vertically until X3, Y3, X2 and Y2 that contribute to all the cells only R times, as opposed to computing once for each cell (approximately 4R2 times).This algorithm reduces the computational burden by computing the possible combinations of GCD < min. Several patterns that can be used to reduce the computational burden that could be applied for a particular GCD were found, but these could not be generalized to all the possible situations. We instead use a straightforward approach to determine the p-value for each of the possible solutions for . The algorithm is as follows:This is the general scenario where Z1, Z2) compute the triangles that contribute to this particular point.1. For each possible .2. Add up the probabilities of each of the elements of these triangles to compute the p-value of that particular (We declare that there are no competing interests.RT and SS conceived and designed the study. RT implemented the method. RT and JW performed simulations. RT and SS wrote the paper. All authors read and approved the final manuscript.


Rare genetic variants are thought to be important components in the causality of many diseases but discovering these associations is challenging. We demonstrate how best to use family-based designs to improve the power to detect rare variant disease associations. We show that using genetic data from enriched families (those pedigrees with greater than one affected member) increases the power and sensitivity of existing case–control rare variant tests. However, we show that transmission- (or within-family-) based tests do not benefit from this enrichment. This means that, in studies where a limited amount of genotyping is available, choosing a single case from each of many pedigrees has greater power than selecting multiple cases from fewer pedigrees. Finally, we show how a pseudo-case–control design allows a greater range of statistical tests to be applied to family data. Our results will enable us to inform future study design and how best to analyse existing family-based genetic data.We are interested in the effect on the power of statistical tests for rare variants when using family-based genetic data. The main question that we address in this paper is: Genome-wide association studies (GWAS) are powerful tools for locating common genetic variants that affect heritable traits, such as disease susceptibility, but these variants do not explain the majority of the heritability of most traits. The remaining heritability is likely to arise from genetic interactions or rare genetic mutations Maher,  and it iMost GWAS are based on unrelated subjects, particularly case–control studies in which allele frequencies in the affected subjects are compared to those in the unaffected. An alternative is to utilise information from the family structure of the samples and measure the difference in transmission and nontransmission frequencies of minor alleles to the affected subjects from their parents  cause single nucleotide polymorphism (SNP) association analyses, such as those used in GWAS, to be underpowered to detect their effects  disease status and measured genotypes for a set of variants for each subject. We assume that no data are missing and that the variants may occur anywhere in the autosomes. We do not consider covariates although some of the tests have the capability to include them. The question of disease association we are answering with respect to these data is:To answer this question all of the tests employ the same null hypothesis, namely that none of the SNPs have any effect on the individual’s susceptibility to the disease. This leads to the alternative hypothesis that one, or more, of the SNPs in the group do have an effect on disease susceptibility. The definition of the alternative hypothesis implicitly includes two important points: we do not assume a deleterious effect and we are not testing individual variants for association but the group as whole. This then puts us in a position to compare single SNP analyses with multiple test correction with the grouped analyses used in current rare variant tests.We have devised five new family-based score statistics derived from the well-known score statistics. These new statistics are calculated from the heterozygous parental transmission frequencies to affected offspring, in a similar manner as the transmission disequilibrium test (TDT). We consider independent nuclear families consisting of both parents and a number of full siblings; here we restrict attention to parent-child trios and parent–sib-pair families. We assume that we are not working under a prior hypothesis of linkage so that we may treat transmissions to each sib as independent, and therefore treat sib-pair families as two independent trios.n to be the number of trios in the data and m to be the number of variants then we define two ith trio, we let jth variant. Similarly, we define B and C takes the values 0, 1 or 2. The transmission disequilibrium found across the trios over all the variants is measured by We define B and C, we calculate the family-based transmission disequilibrium as U and its covariance matrix V asX.Combining 2 distributions  less than 1%] that affect disease susceptibility are hard to detect with single SNP association tests. These tests are underpowered unless the sample size is large enough to provide enough subjects with the minor allele present. To overcome the low minor allele counts of rare variants a number of tests have been devised that pool (or collapse) a group of variants into one “super” variant , consisting of two affected full siblings and their two parents. There, any causal alleles will be enriched over those found in a trio  creates a data set containing an equal number of cases and controls. We create only one of the three possible pseudo-controls per trio, which is the one based on the two untransmitted alleles, as this corresponds to the unmatched case–control design assumed by the tests we consider  but maintains independence of the new samples enabling the case–control tests to be applied successfully. Of course this will affect the power, as we will see in the Results section. This approach is equivalent to calculating U and V in the New Family-Based Score Tests section using families as the sampling unit rather than individuals.To assess the performance of the various combinations of family structures, data transformations and statistical tests we perform a simulation study. We use simulated data, the transformed data and familial relationships as inputs to each of the statistical tests defined above. We repeat these simulation and statistics steps 1000 times. The power and type I error for each statistical test is determined by the proportion of times that the statistic reports an association at G, c is a background chance of being affected for a subject with no minor alleles, i and ith variant. The background chance of being affected with a disease represents the probability of affection from unmeasured factors such as other causal SNPs and environmental factors.The overall process is given by the flowchart in Figure S3. When simulating subjects we must determine their affection status. To do this, we employ a logistic model. In the logistic model the chance of being affected by the disease for any given genotype is determined from the following equations:Firstly the six family-based tests (the single SNP TDT and the five new family-based score tests) are applied to the original family data. Next, the nine case–control tests  are applied to the PCC format genetic data. Finally, the same nine tests are applied to the UCC data. These tests are summarised in Table S1. The nonindependence of cases when derived from ASP data, as discussed above (in the Family Data and Transformations section), led to four tests being inappropriate in the UCC setting for ASP derived data. The type I error rates results are presented in the Results section. For the score tests on UCC/ASP data clustering was used. In addition, the asymptotics of the C-alpha test failed due to the low MAF so permutation testing was used and this test is denoted Cα-P.The parameter space for the simulations includes the familial structure, the number of variants, the MAF at each variant and the number and effect size of any causal variants. To fully explore this parameter space we take a systematic approach to the choices of these simulation parameters. We firstly see how each test performs under the null scenario of no association with all OR equal to 1 for each familial structure. Next, we define three baseline scenarios that provide a starting point for our analysis into the trio, ASP and enriched trio family structures.The baseline scenarios all contain 10 variants with MAF of 0.5% and a baseline prevalence of 1% [We then examine perturbations from these baseline parameters. In the first set of scenarios we change the number of causal variants from one to ten. We alter the OR at the same time to maintain approximately 90% power for the most powerful test. This set of scenarios alters the proportion of causal variants within a fixed total number of variants. The next set of scenarios alters the proportion of causal variants by keeping the baseline four causal variants and increasing the total number of variants. For the following two sets of scenarios we fix the number of causal variants at one and four, out of ten, and vary the effect size with the OR ranging from 1.0 to 3.0. The fifth and sixth sets of perturbations on the simulation parameters examine the effects of having nonequal OR causal effect sizes. In the fifth, we include protective variants and in the sixth we fluctuate the OR by up to ±20%. In the seventh, we investigate population stratification by simulating cases from two populations with MAF and OR given in Table S2. Finally, we examine the effect of reducing the sample size. In all the previous scenarios, we have kept the number of cases at 1200; in this set of scenarios we test subsets of size 100 to 1100 for changes in power.dwarf tool  their type I error rates drop to those presented in With only one exception for a Cα-P test, the trio and enriched trio false positive rates are all within a strict bound (⩽5.5%) and relaxing this bound does not alter the conclusions below. The single SNP tests  are shown to be consistently conservative (⩽4%). We found the analytic Recall that the baseline scenario consisted of 10 variants with MAF of 0.5% and four causal variants of equal OR dependent on the pedigree structure . The power estimates for these scenarios are given in The family-based statistical tests and the PCC statistical tests give very closely the same power for every test in each of the family structures  we see confirmation of the extra power of UCC tests. We also see a consistent but small reduction in power for the SKAT test compared to the SSU and Cα-P. As the SKAT is a parametrisation/generalisation of these other two tests we conclude that it is the parameters that may need adjusting. Any adjustment may improve the SKAT performance but not by any significant amount to warrant differing conclusions throughout our work.We use these relationships to clarify the presentation of our results in the subsequent scenarios. From each group and family structure combination we will select one statistic with one data format to be indicative of them all. This gives five statistics to consider for each of the family structures and 15 in total. As there is no significant difference between any of the statistics used in each box for the trio data we select the UminP, SSU, score, sum and KBAC tests with UCC data. This enables our results to be directly compared to those in other work. For enriched trios we make the same selections. The tests on UCC data have a large increase in power throughout.The results for ASP derived data are not so clear cut. The increase in power when using UCC data is, as for the enriched trios, pronounced but this is at the expense of potentially higher type I errors. We make the same choices as for the trio and enriched trio settings with UminP, SSU, score and sum tests with UCC data and use the KBAC test with PCC as well. The SSUw and score tests that have high type I errors do not perform as well as the SSU and sum tests that have acceptable type I errors. At no point in the analyses below do tests with type I error greater than 5.5% perform optimally.In the second and third set of scenarios, In these results, the SSU test shows optimal power throughout unless the proportion of causal variants is over 20%. The KBAC test demonstrates greater power when the number of causal variants rises above this level but is penalised in the ASP tests. This lack of power has two potential sources: the lack of independence in the cases and the lack of relative genotypic variation found with pseudo-controls.As we increase the total number of variants in our data, keeping only four causal, we observe in Figure S1B a similar result to The fluctuation tests involving perturbations of the effect sizes showed no deviation from the main results and are omitted.P-value calculations. The stratified populations, that are stratified by MAF, OR and baseline prevalence, give the same optimal tests as the baseline scenarios. For all family data using an UCC format is best, with the KBAC test optimal for independent cases (trios and enriched trios) and the SSU test for ASP family data.In Table S3 the type I error rates for a stratified population lead to the same conclusions as the baseline tests c.f. , namely An important consideration when choosing appropriate study designs and statistical tests to apply is the amount of data available. In Figure S1C, the power of each statistical test is presented for a subset of the 1000 cases used in each of the baseline scenarios. The power drops off almost linearly in each case. The order of tests by performance in the main results holds, with the exceptions that the sum test outperforms the SSU test at less than 500 cases and the KBAC test for ASP PCC data overtakes both the SSU and sum tests.In Family-based designs have had appeal for detecting association of rare variants because such variants are more common within families with multiple affected subjects. Here, we have compared some basic but key types of family-based design to case–control studies with the same number of cases, using a range of current methods for detecting rare variants. We demonstrate unequivocally that combining cases from enriched families with unrelated controls gives the greatest power to detect rare variants. In particular, when cases with a family history are used, it is more powerful to study these cases in a case–control rather than a case–parent trio or ASP design. In contrast, when unselected cases are used there are no differences in power between family-based and case–control designs.It may seem surprising that the case–control design has a significant increase in power over the family-based design when the cases have a family history, but not otherwise. The reason is that, under multiplex ascertainment, pseudo-controls constructed from untransmitted haplotypes are not typical of the general population Thomson, . TherefoTransmission statistics calculated though specific family-based formulae or by using pseudo-controls with case–control methods are shown to have equivalent power. As there are many well-researched and designed case–control statistics to test for rare variant disease associations, the PCC data format provides a larger set of tests to apply than for the original family-based format. For example, while we could easily adapt the SSU  and KBAC statistics consistently perform the strongest over the battery of scenarios applied. The equivalencies seen in our results and in analytical work . We show the equivalence of TDT, association and UminP statistics for trios and UCC. These contradict the assertions of Laird & Lange (Laird & Lange, In the baseline scenario  and the We have presented results that indicate future studies should use unrelated controls with cases but what is the implication for existing family-based data? We have shown that when cases are selected from families with multiple affected individuals, it is more powerful to analyse them with unrelated controls than by using transmissions within their families, so a solution might be to identify previously genotyped controls from a matching population and discard the transmission information in the family. Using a statistical test that can incorporate principal components to control for population stratification and admixture, like SKAT, would provide a potential solution. Of course, any study could be improved in this way by adding repository control genotypes, so a more considered view is that the reduced power of such families could be alleviated by combining their transmission data, via pseudo-controls, with repository control genotypes.We have just touched upon an important point. Family-based statistics, such as those presented here and elsewhere (Lake et al., The genotypes of related individuals are not independent therefore those case–control studies that contain related individuals have to contend with nonindependent data as well. These problems are manageable in the case–control setting. As mentioned above, using principle component analysis can control for population stratification and clustering algorithms remove any independence issues when applying case–control statistics to multiple affected individuals in a family.In conclusion, the use of enriched families is recommended for detecting rare variant disease association, provided this is within a case–control rather than a family-based design. Selecting unrelated rather than family-based controls greatly increases the power of statistical tests and their sensitivity to variants with smaller effect sizes. When cases are not selected for a family history, we found no advantage to using family-based designs compared to case–control studies and the usual concerns of population stratification (Mathieson & McVean,


Hip structural analysis based on DXA to analyze 17 strength and geometrical phenotypes of the hip. All the femoral properties had highly significant heritability, ranging from 0.252 to 0.586. The most significant correlations were observed at the genetic level (ρG). Osteoporotic fracture status (Affected 2) and, particularly, low bone mass and osteoporotic condition (Affected 3) had the highest number of significant genetic correlations with diverse femoral properties. In conclusion, our findings suggest that a relatively simple and easy to use method based on DXA studies can provide useful data on properties of the Hip in clinical practice. Furthermore, our results provide a strong motivation for further studies in order to improve the understanding of the pathophysiological mechanism underlying bone architecture and the genetics of osteoporosis.Femoral neck geometry parameters are believed to be as good as bone mineral density as independent factors in predicting hip fracture risk. This study was conducted to analyze the roles of genetic and environmental factors in femoral properties measured in a sample of Spanish families with osteoporotic fractures and extended genealogy. The “Genetic Analysis of Osteoporosis (GAO) Project” involved 11 extended families with a total number of 376 individuals. We studied three categorical phenotypes of particular clinical interest and we used a  Hip fracture is recognized as the most serious osteoporotic fracture due to its association with increased morbidity and mortality, and decreased functional capacity with a one-year mortality of approximately 20% , 2. It iA standard method of measuring proximal femur strength is bone biopsy. However, because biopsy is to invasive to be used in routine clinical practice, a series of alternative methods have been developed. By far, the most common method is measuring bone mineral density (BMD) at different skeletal parts, as this correlates sufficiently with the risk of developing osteoporotic fractures –6.h2) ranging from 0.37 to 0.62 [Femoral neck geometry parameters (FNGPs) that measure bone structural properties such as shape and size are believed to be as good independent factors in predicting hip fracture risk as BMD is . There i to 0.62 –12. In a to 0.62 –19 and g to 0.62 , 20.The best non-invasive approach to determine FNGPs requires imaging technologies and computational methods such as using quantitative computed tomography that are prohibitively expensive or require an unacceptably high radiation dose , 22. In In this study, we aim to analyze the relative importance of genetic and environmental factors in FNGPs measured by means of DXA-based HSA in a set of extended Spanish families characterized by osteoporotic fractures. One of the strengths of our study is precisely its extended design, which provides reliable estimates for the genetic contribution to the studied phenotypes. Unlike twin studies, family-based designs leverage different degrees of kinship allowing for a smaller sampling variance. However, at the same time, the inclusion of many members of the same family makes the separation of genetic from common environmental effects more challenging from a computational perspective .The patients included in the analysis are from the Genetic Analysis of Osteoporosis (GAO) Project. The GAO Project is a genetic study based on extended pedigrees from Spain and the selection, recruitment and methodology have been described in detail elsewhere , 28. In A medical history was obtained from all the participants and it included information about menstrual period, history of all clinical fractures (traumatic and atraumatic) and current medication with a known negative  or positive  effect on bone remodeling. Coffee, alcohol and smoking habits, dietary calcium intake, sun exposure and physical activity were also recorded.Spine, femur and whole-body DXA scans were performed on all participants using a Discovery dual energy X-ray absorptiometry (DXA) system with the APEX v2.3 software , following the manufacturer’s recommendations and analyzed by one expert technician. We used the HSA software to analyze strength and geometrical properties of the hip . This prOur study focused on 17 structural phenotypes that we considered of high clinical relevance. h2, as well as genetic and environmental correlations (ρG and ρE) among the studied phenotypes. Any significant correlation ≥ 0.70 was considered strong and of clinical interest.Statistical analysis was based on a variance component analytical framework in which maximum likelihood techniques were used to assess i) as a linear function using the following formula:In more detail, we used a mixed linear model to determine the contribution of genetic and individual-specific environmental factors to the variation of the quantitative and the categorical osteoporotic phenotypes. We modeled the measurement of a trait y for individual i , age of menopause for post-menopausal women, alcohol intake, smoking status and use of osteoporosis-related medication, as well as interactions of age and age2 with gender. The remaining variables, gi, and ei, represent the random deviations from μ for individual i that are attributable to additive genetic and residual non-genetic effects, respectively. The effects of gi, and ei were assumed to be independent and normally distributed with mean = 0 and variances σg2 and σe2.Covariates included age, ageThe statistical software SOLAR v4.3.1  was usedTo study the genetic relationships between categorical and quantitative phenotypes, we used a modified variance component method for mixed discrete/continuous traits  incorporSummary statistics of interest for the studied pedigrees, as well as a description of the probands used in the recruitment have been described elsewhere . In brieHeritability of each of the structural phenotypes is shown in G) and environmental (ρE) level. The majority of the correlations were negative. This is in accord with the expected negative correlation between osteoporotic phenotypes and cortical thickness (CT), cross-sectional areas (CSA), cross-sectional moment of inertia (CSMI) and section modules ((Z). On the contrary, the correlations were in general positive, as expected, between osteoporotic phenotypes and buckling rations (BR), a measure of cortical instability in buckling. Supporting information contains the full list of correlations among all combinations of phenotypes on the phenotypic, genetic and environmental level for the interested reader G). The highest genetic correlations were found between IT-BR and all different osteoporotic phenotypes (Affected 1–3), ranging from 0.775 to 1.000. Moreover, IT-CT showed high and significant genetic correlations (from -0.758 to -0.954) with Affected 1 and 3. NN-CSMI had also significant genetic correlations, ranging from -0.701 to -0.748, with Affected 1 and 3. Osteoporotic fracture status (Affected 2) and, particularly, low bone mass and osteoporotic condition (Affected 3) had the highest genetic number of significant correlations with diverse femoral properties. In the latter, the correlations were significant in eight over ten femoral traits. Finally, only two significant correlations were observed on the environmental level (ρE), involving Affected 3 and NN-BR (0.847), as well as IT-BR (0.732).None of the two structural traits (HAL and NSA) showed strong correlation with any of the three osteoporotic phenotypes analyzed. Regarding the femoral properties representing intermediate structural phenotypes, the most significant correlations were observed on the genetic level . A similar explanation is plausible for Affected 2 (patients with an osteoporotic fracture) including as few as 24 subjects.RTP3 gene [CT, CSA and CSMI are related with bone axial compression strength and structural rigidity. The association of low values of such parameters with a higher risk of hip fracture has already been described previously in the literature , 47. AlsTP3 gene .In relation to the contribution of environmental factors, the correlations were only relevant for IT-BR and NN-BR in Affected 3 again the group with the highest number of individuals. From our findings, it seems that environmental factors have, on the whole, much less influence on FNGPs than genetic factors do.Our study is inevitably not free from limitations, the most important of which being the small number of individuals with fragility fractures (Affected 2). These patients provide the most relevant information for uncovering the factors contributing to osteoporotic fractures. Even though this number is low, it is legitimate to assume that Affected 3 (low bone mass) and Affected 1 (osteoporotic) include patients at risk of developing fractures in the future and, thus, at various stages behind Affected 2.In our analysis, the mean phenotypic correlation of HAL and NSA with six BMD measurements was 0.48 and -0.05, respectively Click here for additional data file.S2 Table(DOC)Click here for additional data file.S3 Table(DOC)Click here for additional data file.S4 Table(DOC)Click here for additional data file.S5 Table(DOC)Click here for additional data file.S1 File(XLS)Click here for additional data file.