MAP4 gene region and on chromosome 3 with blood pressure. To prioritize variants across the genome for testing, variants were first functionally assessed using prediction algorithms and expression quantitative trait loci (eQTLs) data. Four set-based tests in the family-based association tests (FBAT) framework--FBAT-v, FBAT-lmm, FBAT-m, and FBAT-l--were used to analyze 20 pedigrees, and 2 variance component tests, sequence kernel association test (SKAT) and genome-wide complex trait analysis (GCTA), were used with 142 unrelated individuals in the sample. Both set-based and variance-component-based tests had high power and an adequate type I error rate. Of the various FBATs, FBAT-l demonstrated superior performance, indicating the potential for it to be used in rare-variant analysis. The updated FBAT package is available at: http://www.hsph.harvard.edu/fbat/.The revolution in next-generation sequencing has made obtaining both common and rare high-quality sequence variants across the entire genome feasible. Because researchers are now faced with the analytical challenges of handling a massive amount of genetic variant information from sequencing studies, numerous methods have been developed to assess the impact of both common and rare variants on disease traits. In this report, whole genome sequencing data from Genetic Analysis Workshop 18 was used to compare the power of several methods, considering both family-based and population-based designs, to detect association with variants in the  Both existing and novel methods incorporating family-based and population-based designs were compared in this report. All the methods we compare use a single test for a set of multiple single-nucleotide polymorphisms (SNPs) in a region (gene in our setting). This approach avoids the problem of needing large samples for testing rare variants individually.family-based association tests (FBAT) refers to a suite of family-based association testing methods that rely on an extension of the transmission disequilibrium test. We used 2 newly developed rare-variant association tests in the framework of FBAT, FBAT-v, FBAT-lmm, and 2 previously existing multimarker FBAT tests, FBAT-m and FBAT-l. Although the Genetic Analysis Workshop 18 (GAW18) sample size is large, it is made up of a small number of pedigrees with a large number of individuals per pedigree. The FBAT approach treats all nuclear families in a pedigree as independent, unless a trait locus is known to be linked to the markers under test. The Q1 variable, which was not simulated to be directly associated with any causal gene, was very highly heritable  was used to predict nonsynonymous, splice, and stop variants. Nonsynonymous variants were further classified using polyphen2 [MAP4 [10 p value from eQTL analysis) was used for eQTL filtering.Variants were filtered based on their predicted function. For coding variants, SnpEff  has been proposed as a test for association between both common and rare genetic variants in a region using either continuous or dichotomous traits ,7 for poWe used the complete set of 200 replicates for assessing type I error and power, using an alpha of 0.05 to determine statistical significance. In our analyses, we focused on 2 continuous phenotypes: systolic blood pressure (SBP) and diastolic blood pressure (DBP). Heritability estimates for SBP and DBP were both in the range of 20% to 30% . In total, 1443 genes were analyzed for their association with average residual of blood pressure over three time points  overlap with the results from SKAT.A whole genome scan was performed using FBAT-l for both family and population-based methods after adjusting for first 10 principal components generated by EIGENSTRAT . Only chMAP4 gene and on chromosome 3. This approach incorporated the use of functional prediction information to filter variants as would traditionally be done in most applied studies. Both SKAT and GCTA had high power and an adequate type I error rate. Of the various FBAT tests, FBAT-l demonstrated superior performance, indicating the potential to be used in rare-variant analysis. The lack of population substructure and availability of potential phenotypes contribute to the high performance of FBAT-l. Absent these conditions, the performance degrades. The relatively poor performance of FBAT-lmm could be a result of small sample size and concordant direction of effect size across SNPs. However, FBAT-lmm shows promise for the case where effect sizes within a test region vary in signs of risk. It does not currently have the capability to analyze extended pedigrees.Both family-based and population-based analyses of whole genome sequencing data were evaluated for their power to detect associations with a simulated phenotype with variants in the We also note that when analyzing extended pedigree data and highly correlated traits between relatives, the empirical variance estimator (-e) should be used to achieve the correct type I error. However, its use decreases the effective sample size so that it is closer to the number of independent pedigrees. Finally, our analysis demonstrates that using the average phenotype over 3 time points gives higher power compared to single-time-point phenotype analysis. This suggests the combination of the phenotypes from different time points, or even the combination of SBP and DBP, may achieve higher power.MAP4 and this could be due to some causal variants of MAP4 within the variants for analysis being common. Our population-based tests comparison suggests that in the absence of population substructure, the population-based association tests are more powerful.In this paper, we compared various FBAT region based tests and compared family based tests with population based tests. Our results show that FBAT -l outperformed FBAT -v0 when testing The authors declare that they have no competing interests.JJZ developed FBAT-lmm, ran analyses, and wrote the paper. WKY codeveloped FBAT-v and FBAT-v -e, and assisted in computing. MHC developed the functional screening algorithm for SNP reduction. DQ assisted in data cleaning and formatting, and running of principal components. MLNM edited and revised the manuscript; NML performed the overall design and edited the manuscript. All authors read and approved the final manuscript.


Over the last decade, high-throughput genotyping and sequencing technologies have contributed to major advancements in genetics research, as these technologies now facilitate affordable mapping of the entire genome for large sets of individuals. Given this, genome-wide association studies are proving to be powerful tools in identifying genetic variants that have the capacity to modify the probability of developing a disease or trait of interest. However, when the study’s goal is to evaluate the effect of the presence of genetic variants mapping to specific chromosomes regions on a specific phenotype, the candidate loci approach is still preferred. Regardless of which approach is taken, such a large data set calls for the establishment and development of appropriate analytical methods in order to translate such knowledge into biological or clinical findings. Standard univariate tests often fail to identify informative genetic variants, especially when dealing with complex traits, which are more likely to result from a combination of rare and common variants and non-genetic determinants. These limitations can partially be overcome by multivariate methods, which allow for the identification of informative combinations of genetic variants and non-genetic features. Furthermore, such methods can help to generate additive genetic scores and risk stratification algorithms that, once extensively validated in independent cohorts, could serve as useful tools to assist clinicians in decision-making. This review aims to provide readers with an overview of the main multivariate methods for genetic data analysis that could be applied to the analysis of cardiovascular traits. The interaction of several genetic and environmental factors modulates the clinical expression of common cardiovascular diseases (CVDs), such as coronary artery disease (CAD), cerebrovascular disease, peripheral arterial disease, and stroke. Poor diet, physical inactivity, smoking, and harmful use of alcohol have all been established as key risk factors that can affect the clinical expression of many CVDs . While pp-value <1 × 10−8), single genetic variants identified by GWASs only explain a small proportion of the disease risk or phenotype variability  successfully identified more than 1,100 associations of genetic markers with cardiovascular traits, such as stroke, CAD, peripheral arterial disease, variability of the human electrocardiogram, and monogenic cardiac diseases . Althougiability –6. As aniability  induce eiability . FurtherIn the following sections, this review will address the main multivariate approaches to perform genetic variants selection from GWAS or candidate region studies, how the deriving findings could be modeled to define specific risk profiles and risk stratification algorithms and how to evaluate the prediction accuracy of the defined models.Identifying informative genetic markers among millions of candidates generated by microarrays or next generation sequencing (NGS) platforms has historically been a process of ranking variants according to their level of statistical association with a specific trait. This is first estimated by one-SNP-at-a-time testing approaches, and then a subset of these associated variants is selected based on a defined significance threshold . More reMultivariate approaches of feature selection allow researchers to identify a subset or a combination of informative common genetic variants and non-genetic covariates that underlies the risk of developing a trait . These aA distinction has then to be made between multivariate methods for the analysis of binary traits  and methods for quantitative traits analysis .The analysis of binary traits offers several alternatives that draw from both frequentist and Bayesian methods Table . In ordeThe Least Absolute Shrinkage and Selection Operator (LASSO)  is a shrBayesian methods, such as the binary outcome stochastic search (BOSS)  and bagsClassification and regression trees (RTs) methods  fall undRandom forests (RFs)  are baseABACUS is an Algorithm based on a BivAriate CUmulative Statistic, which allows identifying combinations of common and rare genetic variants associated with a disease by focusing on predefined SNPs-sets  . ABACUS Specific implementations of LASSO, elastic net, CTs, RFs, and stepwise Cox proportional hazard regression  have beeMany of the feature selection methods for binary traits derive from algorithms originally established for quantitative traits analyses Table . Linear The LASSO and the elastic net shrinkage algorithms for regression problems work similarly for classification. Warren and colleagues  used LASThough largely similar to CTs, RTs differ from CTs in that the dependent variable is continuous, and a regression model is fitted to each node to perform the task of prediction. Additionally, RFs for regression problems are also widely employed and implemented in specific analytical packages.Demographic, clinical, and genetic risk factors identified by the previously described methods or selected based on prior knowledge can be combined in order to define specific predictive models, which could assist clinicians during the decision make steps of the clinical practice –49. Suchvia traditional regression-based statistics and standard metrics are used to estimate its predictive power , gender, and QT interval duration (≥500 or <500 ms), which are known independent risk predictors in LQTS. Three risk groups were identified based on the observed probability of an adverse cardiac event: low risk (probability <30%), intermediate risk (30–49%), and high risk (≥50%). Based on the published risk stratification algorithms for LQT1, LQT2, and LQT3 patients . Similar results were obtained from the case–control analyses.Ripatti et al.  tested 1Once multivariate sets of SNPs, PRSs or risk stratification algorithms are defined on an initial cohort (training set), their accuracy in predicting the condition of new examples must be assessed on independent populations (test set). In the absence of independent cohorts, it is possible to rely on resampling strategies like K-Fold Cross Validation (K-Fold CV) , holdoutThe goal of this review is to provide readers with an overview about the main multivariate methods that can be applied to the identification of informative genetic variants and to the definition of risk prediction tools in the context of CVDs. It is important to note that some methods described have been applied to intermediate phenotypes that could be considered precursors to their manifestation as cardiovascular traits, but these methods have not yet been applied to the analysis of cardiovascular traits. Their application to large CVD cohorts could lead to interesting findings.Multivariate methods allow the identification of complex additive effects due to the presence of multiple genetic variants on specific loci or complex interactions among genetic and non-genetic risk factors able to modulate the probability of developing a specific disease or its severity.Still, the task of identifying informative combinations of genetic variants by multivariate search strategies can be extremely computationally intensive due to the high number of models to be explored and, in many cases, to the impossibility of parallelizing the analyses. Missing values represent a common limitation to these approaches, although it could be partially solved by resorting to multivariate imputation methods. Furthermore, large sets of samples thoroughly characterized in terms of phenotype characteristics are needed in order to avoid overfitting issues and to increase the probability of defining models whose predictive performances can be confirmed in independent cohorts.AM and GG conceived the study and drafted the manuscript. RB and CN conceived the study and revised the manuscript critically for important intellectual content. All authors approved the final version of the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Malus × domestica Borkh.) phenotypes using relationship matrices constructed from genome-wide dense single nucleotide polymorphism (SNP) markers; and compare the accuracy of genomic predictions using genomic best linear unbiased prediction models with or without including nonadditive genetic effects. A set of 247 clonally replicated individuals was assessed for six fruit quality traits at two sites, and also genotyped using an Illumina 8K SNP array. Across several fruit quality traits, the additive, dominance, and epistatic effects contributed about 30%, 16%, and 19%, respectively, to the total phenotypic variance. Models ignoring nonadditive components yielded upwardly biased estimates of additive variance (heritability) for all traits in this study. The accuracy of genomic predicted genetic values (GEGV) varied from about 0.15 to 0.35 for various traits, and these were almost identical for models with or without including nonadditive effects. However, models including nonadditive genetic effects further reduced the bias of GEGV. Between-site genotypic correlations were high (>0.85) for all traits, and genotype-site interaction accounted for <10% of the phenotypic variability. The accuracy of prediction, when the validation set was present only at one site, was generally similar for both sites, and varied from about 0.50 to 0.85. The prediction accuracies were strongly influenced by trait heritability, and genetic relatedness between the training and validation families.The nonadditive genetic effects may have an important contribution to total genetic variation of phenotypes, so estimates of both the additive and nonadditive effects are desirable for breeding and selection purposes. Our main objectives were to: estimate additive, dominance and epistatic variances of apple ( The main goal of most fruit breeding programs is to identify the best performing individuals (or genotypes) as potential commercial cultivars, and the secondary goal is to identify genotypes that can be used as parents in future crosses. The genetic value (GV), which includes both additive and nonadditive genetic effects, predicts a genotype’s performance for a trait when asexually propagated plants are used for production  is incorporated through the use of the additive relationship matrix derived from pedigree records  between individuals in the pedigree. Nonadditive performance of relatives could also be included in BLUP analysis through nonadditive relationship matrices derived from the pedigree. However, partitioning of total genetic components into additive and nonadditive parts, using standard pedigree-based models, requires specific family structures involving mating designs . Furthermore, clonally replicated progeny trials enable the estimation of individual-level BV and GV, as well as the magnitude of genotype-by-environment interaction (G × E) .In best linear unbiased prediction (BLUP) of BVs, information from performance of relatives ( records . This ma (G × E) . BLUP ane.g., dominance, epistasic) have also been developed  are particularly advantageous when pedigree relationships are not available for some individuals and/or when the recorded pedigree information may contain errors . StudiesAn approach termed genomic BLUP (GBLUP), which directly estimates genomic breeding values (GEBV) using additive GRM, is now commonly used in genomic selection (GS) studies of animal and plant species , and oneAlthough numerous studies on estimation of genetic parameters of apple fruit phenotypes have been conducted  families, involving 25 advanced selections as parents, was used as the source of budwood for this study. Based on pedigree records, the average coefficient of relationship between the 25 parents was 0.15 , resulting in varying degrees of relationships between the 17 full-sib families. Budwood from each of the 255 randomly selected genotypes (15 from each of the 17 families) was collected in the winter (June and July) of 2010. This budwood was held in cold storage before chip-budding eight lateral buds from each of the 255 genotypes onto nursery-grown 1-year-old ‘M9’ rootstocks in spring (September 2010), making eight clonal replicates of each of the 255 genotypes. In the following winter (July 2011), all successfully propagated seedlings were planted (3.0 × 0.5 m spacing) at two orchard sites, one in each of the key apple production regions in New Zealand, namely Hawkes Bay  and Motueka . Generally, HB is warmer during winter, spring, and autumn than MOT. Rainfall and humidity are higher in MOT than in HB, particularly during spring. Comparing the soil types of the two sites, MOT has a more fertile soil than the HB orchard, thus trees are more vigorous at the former site. The initial goal was to plant four replicates of each genotype at each of the two sites; however, because of problems in the propagation survival, the number of plants available for each genotype varied. Ninety percent of the genotypes were represented by at least three clonal replicates at each site. There were only five individuals with only one replicate at each site. All trees received standard commercial management for nutrition, pesticide, fruit hand-thinning, and irrigation.A field trial consisting of 17 full-sib apple  during 2013 and 2014, began when fruit from each tree were judged to be mature, based on a change in skin background color from green to yellow, and when the starch pattern index was between 2 and 3 using a scale from 0 (full starch) to 7 (no starch). Phenotypes of each individual were collected in both years. One sample of six fruit from each clonal replicate of each genotype were stored for 70 days at 0.5°, followed by a further 7 days at 20° before evaluation. Fruit firmness (FF) was determined on opposite sides of each fruit after peel removal using a Fruit Texture Analyzer (GÜSS) fitted with an 11-mm diameter probe tip. A list of visual, sensory, and instrumental traits assessed following A total of 247 (out of 255) individuals were genotyped using the IRSC apple 8K SNP array v1 , with dey is a vector (ns × 1) of adjusted phenotypes (BLUEs) on a trait; n is the number of individuals (247) and s is the number of sites (2); b is a vector of fixed effect ; a ∼ N, d ∼ N are the vectors (n × 1) of random additive, dominance, and additive-by-additive epistatic effects respectively; Ga, Gd, and Gaa are the additive, dominance, and epistatic relationship matrices (n × n) respectively; e ∼ N is a vector of random residual terms and I is an identity matrix (ns × ns); t1 ∼ N of random interactions of a, d, and i with site, respectively; Is represents an identity matrix with order equal to the number of sites; ⊗ denotes the Kronecker product operation; Z1 – Z3 are incidence matrices (ns × n) for the main genetic effects, and Z4 – Z6 are incidence matrices (ns × ns) of interaction of main genetic effects with site, respectively.A two-step approach was used to estimate genetic parameters and make genomic predictions. The first step consisted of calculating best linear unbiased estimates (BLUEs) to account for fixed effects such as replicates and year, so that each individual had a single phenotypic value for each trait at each site. These estimates were then used as ‘phenotypes’ for estimation of variance components and BLUP of additive, dominance, and epistatic effects using the following linear mixed model:Ga, Gd, and Gaa) were constructed using SNP marker information according to methods from previous studies  representing genotypes at each locus. The coefficient of ith column of the M matrix are (0–2ip), (1–2ip) and (2–2ip) for genotypes AA, AB and BB respectively; ip and iq are the frequencies of allele A and B at ith SNP locus, respectively. Similarly, Gd = H is a n × m matrix of heterozygosity coefficients with elements (0–2iqip) and (1–2iqip) for homozygous  and heterozygous (AB) individuals at ith SNP locus, respectively. The epistatic genomic relationship matrix (Gaa) was obtained as G#G, where # denotes the Hadamard product operation . BLUP-GV (= a + d + i) of all 247 individuals were obtained from h2) and broad-sense (H2) heritability, as the ratio of additive  was evaluated by the log-likelihood value. The superiority of an alternative model over an additive model, obtained using all available data, was tested using a likelihood ratio test.In the subsequent text, a + d + i), (a + d), and a for the models ADE, AD, and A, respectively. The observed BLUP-GVs were linearly regressed on the GEGV, where the regression coefficient reflected the degree of bias of the GEGV, and a regression coefficient of one indicated no bias.To account for the family structure of our data, we applied a cross-validation scheme by using each full-sib family in-turn as a validation population (VP) and the remaining 16 families as a training population (TP), resulting in a 17-fold cross-validation. Prediction accuracy of a model was estimated as the correlation between genomic GV (GEGV) and the observed BLUP-GV of individuals in the VP. GEGV was defined as  have not been field tested at any of the two sites (HB and MOT) of this study, i.e., individuals in the VP were treated as missing at both sites. Thus, the prediction accuracy of a model in the first validation strategy was based solely on the performance of individuals in the TP. The second validation strategy considers a scenario where individuals in the VP are tested at one site  but missing at the other site . The prediction accuracy in this strategy relies on the performance of TP in the target environment (MOT) and the performance of all individuals (VP and TP) from the test site (HB). This process was repeated so that all 17 families at both sites were predicted.Two different validation strategies were used to address practical situations. The first strategy mimics a scenario where a set of individuals  at the HB and MOT sites were 183 g and 192 g, respectively, with a coefficient of variation (CV) of 23% at both sites . StatistFile S4). Results in A plot of the first two principal components of the SNP data matrix grouped seedlings largely according to their familial relationships . In almoFile S5). On average (across traits), the additive, dominance, and epistatic effects contributed about 30%, 16%, and 19% to the total phenotypic variance. The pedigree-based average estimates of additive and nonadditive variance were 22% and 25%, respectively (results not shown). For various traits, the magnitude of variance due to interaction of genetic effects with site varied between 0 and 3%, 0 and 4%, and 0 and 8% for additive, dominance, and epistatic effects, respectively. Estimates of between-site genotypic correlation varied between 0.87 (GRE) and 0.95 (WT), and the interaction of genetic effects with site collectively accounted for less than 10% of the total phenotypic variance (The additive variance (variance .h2) estimate was low (< 0.20) for JUI and FIN, moderate (0.20 – 0.40) for GRE and CRI, and high (>0.40) for WT and FF (H2) was 0.34 for FIN and >0.60 for other traits, reflecting a substantial amount of nonadditive genetic variance. h2 from different models varied between 0.39 and 0.70 when the epistatic effect was dropped , and between 0.47 and 0.82 when dominance and epistatic effects were excluded  from File S6 for details). These are much higher than h2 estimates (0.11 – 0.52) of various traits obtained using the model ADE. The likelihood ratio test showed that model ADE had relatively low –2 log likelihood compared with model A (File S7), but the goodness of fit was not improved significantly .The narrow-sense heritability  was essentially the same for the additive model (model A) and for the model including additive and nonadditive effects (model ADE), and varied from about 0.15 (for JUI) to 0.35 (for FF) (File S8). These results suggested that the degree of bias is higher for the additive model than for the model ADE. For the second validation strategy , the accuracy of predicted GEGV was generally similar for both sites, and varied from about 0.50 (for FIN) to about 0.83 (for WT and FF) (r = 0.44) with the degree of genetic relatedness to the training families (File S9). Prediction accuracy also showed strong relationship (r = 0.81) with trait heritability (File S10).Prediction accuracies for the first validation strategy  are shown in (for FF) . The coe and FF) . Predictvs. 0.34) reflected that there were perhaps many more ancestral relationships not captured by the pedigree records. Different kinds of relationships  along with permanent environmental or maternal effects shared by siblings make it challenging to partition nonadditive variance from the additive variance using traditional methods (vs. 30%), suggesting that nonadditive effects are as important as additive effects for various apple phenotypes. Genetic relationship matrices, constructed using genome-wide SNP markers, were fitted using a GBLUP approach to estimate nonadditive genetic variation. The difference between the pedigree-based and SNP-based additive coefficient of relationship  in this study was very similar to those in some other reports (h2 of FIN (0.11) was similar to that reported by h2) of CRI and JUI has been reported to vary between 0.15 and 0.40 (H2 in our study varied between 0.34 (FIN) and 0.79 (FF), with an average of about 0.65 . The ratio of nonadditive , in contrast to unbalanced datasets with little or no clonal replication of individuals  in the parents of a population, a covariance between the additive and nonadditive effects would be introduced . Moreover, the large family sizes and a random cross-validation scheme in File S4). Genetic relatedness between the training and validation families, and trait heritability were positively correlated with the prediction accuracy (File S9 and File S10), which is consistent with previous studies  and FIN (0.52). Although the G × E variance components for JUI and FIN were similar to those for other traits , the lowThe prediction accuracy of the second validation strategy  was at lThis study showed that nonadditive genetic effects are important sources of genetic variation for apple phenotypes, so there is a good case to account for these effects when selecting individuals as potential cultivars. For selection of individuals as parents for new crosses the additive effects is probably more relevant as the nonadditive effects do not transfer very effectively to the next generation. The GBLUP approach is relatively simple to implement to estimate additive and nonadditive variances and to predict GEBV and GEGV. GBLUP models fitting only the additive effects can predict phenotype with similar accuracy to models fitting both the additive and nonadditive effects, but the degree of bias will be lower for the latter. Also, GBLUP models ignoring nonadditive effects will provide an overestimated additive variance that will exaggerate the expected genetic gains in breeding. The high correlation between the additive and nonadditive effects may be due to the genetic relatedness between samples, so including nonadditive genetic effects in GBLUP models may still improve prediction accuracy in populations of less-related individuals—this hypothesis needs to be tested.


The goal of genome-wide prediction (GWP) is to predict phenotypes based on marker genotypes, often obtained through single nucleotide polymorphism (SNP) chips. The major problem with GWP is high-dimensional data from many thousands of SNPs scored on several thousands of individuals. A large number of methods have been developed for GWP, which are mostly parametric methods that assume statistical linearity and only additive genetic effects. The Bayesian additive regression trees (BART) method was recently proposed and is based on the sum of nonparametric regression trees with the priors being used to regularize the parameters. Each regression tree is based on a recursive binary partitioning of the predictor space that approximates an unknown function, which will automatically model nonlinearities within SNPs (dominance) and interactions between SNPs (epistasis). In this study, we introduced BART and compared its predictive performance with that of the LASSO, Bayesian LASSO (BLASSO), genomic best linear unbiased prediction (GBLUP), reproducing kernel Hilbert space (RKHS) regression and random forest (RF) methods.Tests on the QTLMAS2010 simulated data, which are mainly based on additive genetic effects, show that cross-validated optimization of BART provides a smaller prediction error than the RF, BLASSO, GBLUP and RKHS methods, and is almost as accurate as the LASSO method. If dominance and epistasis effects are added to the QTLMAS2010 data, the accuracy of BART relative to the other methods was increased. We also showed that BART can produce importance measures on the SNPs through variable inclusion proportions. In evaluations using real data on pigs, the prediction error was smaller with BART than with the other methods.BART was shown to be an accurate method for GWP, in which the regression trees guarantee a very sparse representation of additive and complex non-additive genetic effects. Moreover, the Markov chain Monte Carlo algorithm with Bayesian back-fitting provides a computationally efficient procedure that is suitable for high-dimensional genomic data.The online version of this article (doi:10.1186/s12711-016-0219-8) contains supplementary material, which is available to authorized users. The concept of genome-wide prediction (GWP) was introduced by Meuwissen et al.  and refeentclass1pt{minimaaccuracy . Two popaccuracy .2 population derived from crosses of inbred lines. They found that the parametric methods predicted phenotypic values less accurately when the underlying genetic architecture was entirely based on epistasis, whereas the parametric methods resulted in only slightly better predictions than nonparametric methods when the underlying genetic architecture was additive. However, they did not evaluate any regression tree method.Several studies have evaluated the predictive abilities of different statistical and machine learning methods in genome-wide selection situations e.g. , 6, but The classification and regression trees (CART) method was developed by Breiman et al. . A regreThe random forest (RF) method  is a colChipman et al.  introducThe purpose of this study was to review regression trees and RF, establish a connection between these methods and traditional genetics, introduce the BART methodology, and compare the prediction properties of BART with those of the LASSO, Bayesian LASSO (BLASSO), genomic BLUP (GBLUP), reproducing kernel Hilbert space (RKHS) and RF methods. We used simulated data as well as real pig data to compare methods.j, τ). ⨅ is the structure of the tree with a finite collection of nodes where each node Consider a response vector ion tree . Each leA regression tree for two SNPs and one phenotype, the genetic interpretation and response surface are described in Additional file Single regression trees are easy to construct and still relatively flexible, but there are some limitations. First, regression trees tend to have a high variance because of the binary splits and because the errors in the higher nodes are propagated downwards. Hence, a small change in the data may result in a very different tree structure, i.e. trees can be instable. Second, the terminal node surface is not smooth. This is a minor problem for SNP predictors that only have three possible values. However, it can be challenging in situations where other continuous predictors are included in the model. Third, the binary splits will favor a non-additive structure , RF (uslidation ) methodsλ path (minMSE + 1SE), i.e. the largest λ-value such that the error is within one SE of the minimum, were used as stopping criteria for LASSO [LASSO and RF analyses were run with the default settings of the glmnet and randomForest packages. The minimum mean squared error (minMSE) and minMSE + 1 standard error of minMSE backwards along the regularization parameter or LASSO , 40. Thec values .The bandwidth parameter of the radial basis function (RBF) of the RKHS method was optimized by evaluating OOB) is recorded. Each predictor variable is then randomly permuted and j new MSPEOOB are calculated. The difference between the two are then averaged over all trees, and normalized by the standard deviation of the differences [It is possible to obtain different variable importance measures (VIMP). In the RF approach, there are several measures of variable importance. One common approach for regression trees is to calculate the decrease in prediction accuracy from the OOB data. For each tree, the OOB portion of the data is passed through the tree and the prediction error , including nine known genes and 28 random genes. All QTL were modelled as additive effects, except for two pairs of epistatic QTL and three paternal imprinting QTL. The known genes were selected based on their high level of polymorphism and high linkage disequilibrium (LD) with SNPs. All known QTL had an additive effect of +3 . The random genes were drawn from the simulated SNPs (excluding those on chromosome 5) and their effects were sampled from a truncated normal distribution, y-values.In order to also evaluate if BART can detect various forms of dominance and epistasis, a second simulated dataset was created based on the QTLMAS2010 data by adding effects at different loci on chromosome 5: (1) SNP 9212 was a dominant locus by setting a value of 5 and 5.01 for the effect of the heterozygous (Aa) and homozygous states (AA) , respectively; (2) SNP 9404 was an over-dominant locus by assigning values of 5, −0.01 and 0.01 to the heterozygous (Aa) and homozygous (aa) and (AA) states, respectively; (3) SNP 9602 was an under-dominant locus by assigning values of −5, −0.01 and 0.01 to the heterozygous (Aa) and homozygous (aa) and (AA) states, respectively; and (4) two SNPs 9694 and 9695 that had no additive effects were chosen to create an epistatic effect by assigning values of −0.01 and 0.01 to the homozygous aa and AA states, and a value of 5 to both AA homozygous states. Finally, the values of these new SNPs were summed to the original Cleveland et al.  publisheGenotyped animals had phenotypes for five purebred traits (phenotypes from a single nucleus line), with heritabilities ranging from 0.07 to 0.62. For this study, we chose the trait that had a heritability of 0.38. This phenotype was corrected for environmental factors and rescaled by correcting for the overall mean. Individuals with missing phenotype data were removed and a final number of 3141 individuals was used.For the original QTLMAS2010 dataset, the LASSO with the minMSE option was found to produce a The analysis of the QTLMAS2010 dataset when dominance and epistatic effects are added resulted in an The regression coefficient and variable importance plots in Fig. Analyses of the QTLMAS2010 dataset for which the phenotype was constructed with additional dominance and epistatic loci are in Fig. Analysis of the five random cross-validation partitions of the real pig dataset of Cleveland et al.  also sho.9 Table . The secPenalized regression coefficients of the LASSO and BLASSO methods, back-calculated regression coefficients of the GBLUP and RKHS methods, and variable importance measures of the RF and BART methods averaged over the five cross-validation partitions are in Fig. The partitioning of genetic effects into additive and non-additive (dominance and epistasis) contributions has a long history in quantitative genetics . The addThe RF methodology has been used in several genome-wide association studies (GWAS) and GWP studies. Cabras et al.  showed hThe LASSO method sets unimportant variables to exactly zero and therefore provides an automatic variable selection procedure . Bayesia Alvares  proposed Alvares  suggeste Alvares  describe Alvares . Recentl Alvares  suggeste Alvares .It should also be noted that since ensemble regression tree methods are black-box approaches, it is rather difficult to evaluate the genetic effect of a given SNP. However, some tools are available to investigate how SNPs influence the prediction. Partial dependence plots provide a useful approximation to visualize non-linearity within and interaction between important variables . The ideThe number of statistical machine learning methods has increased dramatically over the recent years , 37 and This study shows how the Bayesian additive regression tree method (BART) can be applied to large-scale genome-wide SNP data for the prediction of unknown phenotypes and detection of the SNPs that contribute information for the prediction. Since BART is based on an ensemble of regression trees, it is a non-parametric and non-linear method that has the important feature of being able to handle all types of genetic effects of SNPs in a very sparse way. Comparison of BART with the LASSO, BLASSO, GBLUP and RKHS methods using simulated data showed that the prediction error of BART under additive gene action was equally good or lower, and considerably better in the presence of dominance and epistasis. BART outperforms RF under all settings. Moreover, BART has the lowest prediction error of all methods for the analysis of real pig data, which indicates that non-additive gene action contributes to the analyzed phenotype. To date, no GWP applications have used BART. Hence, there is a need for further applications and evaluations of BART using data from different species.


Genome wide association study (GWAS) was conducted for 14 agronomic traits in wheat following widely used single locus single trait (SLST) approach, and two recent approaches viz. multi locus mixed model (MLMM), and multi-trait mixed model (MTMM). Association panel consisted of 230 diverse Indian bread wheat cultivars . Three years phenotypic data for 14 traits and genotyping data for 250 SSR markers  was utilized for GWAS. Using SLST, as many as 213 MTAs  were identified for 14 traits, however, only 10 MTAs  qualified FDR criteria; these MTAs did not show any linkage drag. Interestingly, these genomic regions were coincident with the genomic regions that were already known to harbor QTLs for same or related agronomic traits. Using MLMM and MTMM, many more QTLs and markers were identified; 22 MTAs  using MLMM, and 58 MTAs  using MTMM were identified. In addition, 63 epistatic QTLs were also identified for 13 of the 14 traits, flag leaf length (FLL) being the only exception. Clearly, the power of association mapping improved due to MLMM and MTMM analyses. The epistatic interactions detected during the present study also provided better insight into genetic architecture of the 14 traits that were examined during the present study. Following eight wheat genotypes carried desirable alleles of QTLs for one or more traits, WH542, NI345, NI170, Sharbati Sonora, A90, HW1085, HYB11, and DWR39 (Pragati). These genotypes and the markers associated with important QTLs for major traits can be used in wheat improvement programs either using marker-assisted recurrent selection (MARS) or pseudo-backcrossing method. Arabidopsis thaliana also, in one of the several GWA studies, MTAs for 107 phenotypes were detected [Ae. tauschii, the donor of the wheat subgenome D [Genetic analysis of quantitative traits (QTs) mainly involves either the linkage-based interval mapping or the linkage disequilibrium (LD)-based genome-wide association studies (GWAS). GWAS utilizes diverse germplasm (representing most of the genetic variability), which is the product of hundreds of recombination cycles, thus providing higher resolution of QTL regions . This apdetected –12, kerndetected , HMW gludetected , diseasedetected –17, earldetected , droughtdetected –21, and detected –24, etc.genome D .Earlier, in our laboratory, we used SSRs for QTL analysis in wheat using both, interval mapping and single locus single trait (SLST) association mapping , 26–27. The association mapping panel comprised 230 Indian wheat cultivars , reThe data on mean values for each of the 14 traits of the above 230 Indian common wheat cultivars  was procured from ICAR-IIWBR, Karnal, India ; the datDescriptive statistics including frequency distribution, mean values, coefficient of variability (CV) and Pearsons’s correlation coefficients were obtained using SPSS version 17.0. Model-based cluster analysis of association mapping panel was conducted during an earlier study in our lab  to infer2 (%) and the probability values for determining relationships between the phenotypic traits and population structure [Multiple regression analysis was carried out to estimate rtructure . Based otructure . Followihttp://www.maizegenetics.net) was used to conduct SLST association mapping—involving associations of individual markers with each of the 14 traits, employing one of the following four models for individual traits: (i) general linear model (GLM: naive model), (ii) GLM including Q-matrix derived from STRUCTURE (Q-model), (iii) the mixed linear model (MLM) based on the kinship matrix (K-model) and (iv) the MLM based on both the Q-matrix and the kinship matrix (Q+K-model)  were used. In MTMM, following three tests were applied: (i) full test that compared the full model including the effect of a marker genotype and its interactions, with the model that included neither, (ii) interaction effect test that compares the full model to one, which does not include interactions, and (iii) common effect test that compares a model with a marker genotype to the model that does not include marker genotype [In addition to SLST analysis, GWAS using MLMM  and MTMMgenotype .In each of the above approaches, corrections were made using false discovery rate (FDR) criteria earlier suggested  to reducinteractionPval available in SNPassoc package of R-software [For each trait, two dimensional epistatic interactions were also examined using MTAs detected through SLST, MLMM and MTMM. This analysis was carried out using the function software . In ordeQTLs that were detected by all the three methods or by at least two methods were considered to be relatively more important. However, QTLs that were detected by SLST alone and qualified FDR or those reported in earlier literature were also considered important. For identification of desirable QTL alleles, for each trait, a set of 20 genotypes with their superior phenotypic performance was selected. Marker allele for individual marker loci and pairs of alleles for the interacting epistatic loci present in maximum number of genotypes (out of 20 superior genotypes) were taken to be associated with desirable QTL allele for the trait concerned. The corresponding genotypes carrying desirable QTL alleles and a desirable trait value were treated as superior genotypes for individual traits.2 ≥ 0.25) correlations, making these pairs to be suitable for MTMM  for all the 14 traits involving 230 genotypes are presented in for MTMM .2) (i) 0% to 5% = poor relationship; (ii) 6% to 10% = moderate relationship; and (iii) >10% = strong relationship. Population structure showed poor relationship with HW (r2 = 4.3%) and DTH (r2 = 5.0%); moderate relationship with AL, DTM, GPC and TGW (r2 = 7.9% to 10.0%), and strong relationship with the remaining eight traits   .Values for mean square differences (MSD) for all the four models for each of the 14 traits along with the best fit models are summarised in Results of significant MTAs detected following SLST for each of the 14 traits are summarized in Twenty two (22) MTAs (after FDR correction) for seven traits  were identified following MLMM . These MMTMM analyses allowed identification of 58 MTAs (after FDR correction) representing 29 QTLs) for 11 pairs of correlated traits. These 58 MTAs involved 18 of the 21 wheat chromosomes with the exception of 2D, 5A and 6D. As many as 32 MTAs were identified using full test, 43 were identified using interaction test and 9 were identified using common marker test (a number of MTAs were identified using more than one method). Nine pleiotropic QTLs for the following three pairs of correlated traits were identified using common marker test: PH-TGW (1 MTA), PH-SV (5 MTAs) and DTH-DTM (3 MTAs). Out of 58 MTAs, eight MTAs were common with SLST , and nine MTAs were common with MLMM analyses (Tables As many as 63 epistatic interactions were identified for 13 (out of 14) traits , FLL, beDuring genotyping of 230 cultivars, 250 SSRs exhibited a total of 1124 alleles; 316 of these alleles (representing 165 SSRs) were rare alleles, each with a frequency of 5% or less. The genotypes carrying these rare alleles are described as rare variants for individual traits. For individual SSRs, these rare alleles ranged from 1 to 9 with a mean of 1.26 alleles per SSR. For individual traits, these rare alleles were carried by 1 to 11 rare variants . The rare variants were examined for each individual trait to identify the specific rare variants, which carried a desirable state of the phenotype for each trait. Such important and desirable rare variants carried only 78 of the 316 rare alleles belonging to 55 SSRs ; these 7Using the criteria mentioned earlier, 56 MTAs involving 38 SSRs for 11 traits were considered important; some of these SSRs were involved in more than one traits ; for theThe 38 desirable QTLs (associated with 38 associated SSRs) included 12 main effect QTLs that were not involved in epistatic interactions; the remaining 26 QTLs were also involved in epistatic interactions. A set of 17 superior genotypes carrying desirable alleles for important QTLs for 11 traits were also identified . Some ofDwarf4 gene of maize [The present association mapping study (GWAS) has the following important/novel features of interest. Firstly, it addresses the problem of trait-related population structure, secondly it provides improvement upon SLST analysis through the use of MLMM and MTMM, thirdly it includes identification of epistatic interactions, which are seldom included in GWAS, and finally effort has been made to highlight the problem of rare alleles and rare variants, which is currently one of the most widely debated issues in GWAS. It is known that during GWAS, confounding arises due to population structure, particularly if it is correlated with the trait under study . In the of maize –39. Keepof maize –41. Thusof maize , arbitraFDR corrections were also used in the present study. It may be recalled, that during SLST analysis, only nine markers involved in 10 MTAs, out of 213 MTAs, could qualify after FDR corrections; all these 10 MTAs fall within the genomic regions earlier reported to be associated with the corresponding or related traits in wheat, placing higher level of confidence in these MTAs . HoweverThe problem of genetic background affecting the detection of QTL was addressed during the present study through the use of MLMM , since eThe use of MTMM during the present study also allowed identification of 9 MTAs involving QTL that are associated with three pairs of correlated traits (out of 19 pairs of correlated traits examined). This suggested that the remaining correlations were either due to environmental effect or due to LD rather than due to pleiotropy/linkage. These 9 MTAs may also prove useful for simultaneous improvement of correlated traits. Further, out of 9 SSRs involved in above mentioned 9 MTAs, only one SSR (gwm44) was found to be associated with corresponding traits (DTH and DTM) in SLST analysis. The remaining MTAs involving 8 SSRs could not be detected using SLST and MLMM suggesting higher power of AM through MTMM. However, we speculate that power of AM may be further increased by using combined multi-locus multi-trait analysis.MTMM, however, also has certain limitations. For instance, unlike joint analysis of QTL Cartographer, which examines more than two traits simultaneously, MTMM allows analysis of only pairs of correlated traits, so that pleiotropic QTL controlling more than two traits cannot be identified, although correlation studies do suggest that more than two traits may be correlated with each other in all possible combinations . We recoNone of the three approaches  discussed above deals with epistatic interactions during routine analysis. Estimation of epistasis, however, is important to understand genetic architecture –56 and aImportant MTAs and QTLs were also examined for their utility in MAS. Since genes/QTLs need to be transferred/pyramided in different genetic backgrounds using MAS, one should identify important gene/QTLs, which are context- independent and whose expression is not affected by change in genetic background. We identified 56 important MTAs involving 38 SSRs (12 SSRs associated with more than one trait) for 11 agronomic traits excluding PL, SKS and FLL; several of these MTAs were also reported in earlier studies see, , suggestIn summary, based on the present study, we conclude that the following classes of MTAs, which are often ignored, may be equally useful for MAS: (i) MTAs, which do not qualify FDR correction in SLST analysis but are reported in earlier studies; (ii) MTAs that are context-independent, so that an introgression of desirable traits into unrelated genetic backgrounds may be successfully achieved; (iii) MTAs involving pleiotropic QTL/genes that can improve more than one desirable traits simultaneously, and (iv) MTAs involved in epistatic interactions, so that additional desirable genetic variation due to epistatic interactions may be exploited. In view of this, following eight genotypes which carried superior alleles for one or more traits were identified for future wheat breeding programmes: WH542 (HI and PH), Sharbati Sonora (DTH and DTM), NI345 (SV), NI179 (TGW), A90 (HW), HW1085 (GS), HYB 11 (GPC), and DWR39 (Pragati)(AL). These wheat genotypes were released in India for commercial cultivation during a period of 79 years spread from 1919 to 1998 and thus constitute breeding material not in current use. Therefore, we propose that the genetic variability available in these eight genotypes may be exploited by involving these genotypes in crosses to derive one or more multi-parental populations (MPP), each segregating for majority of QTLs. Such MPP may be subjected to molecular marker-assisted recurrent selection (MARS). This should allow selection of genotypes with superior alleles for main effect as well as epistatic QTL. Alternatively, desirable alleles available in the above eight genotypes may be introgressed and rapidly pyramided into the currently grown wheat cultivars to develop superior wheat genotype following pseudo-backcrossing as done in rice recently . These iGS2 was identified to increase grain size and yield in rice [Another issue that needs attention is the problem of rare alleles and the corresponding rare variants, which need to be eliminated from the analysis involving GWAS due to statistical reasons. These rare variants may sometimes represent the most important variants, since desirable variants are expected to occur at a very low frequency. This is borne out by several studies including the recent study, where a rare allele of grain size gene  in rice . During Despite the above, we feel that the importance of rare alleles and rare variants has perhaps been overemphasized in recent literature. Although rare alleles for all markers taken together may explain sizable proportion of genetic variation, but majority of rare alleles may not belong to a QTL for the trait of interest. Also, in order to study the rare marker alleles, an appropriate experimental set up is necessary, which either increases relative frequency of rare alleles or modify the statistical model that can deal with rare alleles. Some of the solutions, which may be used in future research, include the following: (i) use of biparental mapping population ; (ii) combined linkage-association mapping; (iii) use of large population; (iv) conducting separate analysis for common variants (CWAS) and rare variants (RVAS) , (v) advIn majority of crops including wheat, the quantitative traits with continuous variation are often complex in nature and are controlled each by a large number of main effect and interacting loci. In the present study, we identified a number of MTAs involving each of the 14 different traits using SLST, MLMM and MTMM. Some of the associations simply confirmed the QTLs reported earlier. The role of epistatic interactions in the genetic control of all the traits was also deciphered. Desirable alleles and allele combinations (at the interacting loci) along with eight superior wheat genotypes were identified. The problem of rare alleles and rare variants has also been discussed utilizing the data on rare variants from the present study. We also conclude from the present study that perhaps a combination of linkage analysis and association mapping could be the best approach for detecting maximum number of MTAS that are more robust and can be profitably utilized in molecular breeding.S1 Table* and** indicate significance at 0.05 and 0.01 levels, respectively. Trait-pair showing correlation coefficient value ≥ 0.25 were used in multi-trait analysis and are highlighted in bold.(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.S4 Table(DOCX)Click here for additional data file.


Background: The roles of genetic factors in human longevity would be better understood if one can use more efficient methods in genetic analyses and investigate pleiotropic effects of genetic variants on aging and health related traits.Data and methods: We used EMMAX software with modified correction for population stratification to perform genome wide association studies (GWAS) of female lifespan from the original FHS cohort. The male data from the original FHS cohort and male and female data combined from the offspring FHS cohort were used to confirm findings. We evaluated pleiotropic effects of selected genetic variants as well as gene-smoking interactions on health and aging related traits. Then we reviewed current knowledge on functional properties of genes related to detected variants.Results: The eight SNPs with genome-wide significant variants were negatively associated with lifespan in both males and females. After additional QC, two of these variants were selected for further analyses of their associations with major diseases (cancer and CHD) and physiological aging changes. Gene-smoking interactions contributed to these effects. Genes closest to detected variants appear to be involved in similar biological processes and health disorders, as those found in other studies of aging and longevity e.g., in cancer and neurodegeneration.Conclusions: The impact of genes on longevity may involve trade-off-like effects on different health traits. Genes that influence lifespan represent various molecular functions but may be involved in similar biological processes and health disorders, which could contribute to genetic heterogeneity of longevity and the lack of replication in genetic association studies. The literature review on the genetic influence on human aging and longevity indicates limited progress in identifying genetic mechanisms regulating human aging, health, and longevity using genome wide association studies (GWAS). Most associations detected in these studies tend to be weak and have not reached the genome-wide level of statistical significance. They also suffer from the lack of replication in studies of independent populations. What factors and conditions might be responsible for such a situation? What methods and approaches have to be used to properly address these issues?The literature on genetic studies of human longevity lacks an appropriate biologically-based conceptual framework that would allow one to efficiently address questions about the dynamic roles of genes in forming aging and longevity related traits. Such a framework would help specify necessary steps for efficient comprehensive analyses of corresponding genetic mechanisms using available data. The approaches based on the systems biology of aging, health, and longevity Kriete,  merged wThe literature review also revealed the underutilized research potential of available data that were used in genetic analyses of aging and longevity traits. The possibility of more efficient analyses of genetic associations with such traits was demonstrated in Yashin et al. , 2000 whIn genetic analyses performed in this paper we used a modified statistical procedure of testing genetic associations with longevity related traits. The populations whose data are used in GWAS often have genetic structures called “population stratification” (PS). Such structures are caused by non-random mating between groups of individuals followed by different patterns of genetic drift of allele frequencies in each group. Without proper controlling for PS in the statistical procedures used in GWAS of complex traits the analyses may result in erroneous  associations. To avoid such errors the genetic association studies of complex traits include control for potential PS. The method of principal components analyses (PCA) suggested in Price et al.  identifip-value > 1E-7. After applying the QC procedure, the data on 1111 individuals with information about lifespan and 429,783 SNPs were available for the analysis. Life spans for 204 study subjects  were censored. We used EMMAX software to perform GWAS of female lifespan data from the original FHS cohort with modified correction for population stratification. In the confirmation phase we used genetic and the life span data on males from the same FHS cohort and the life span data on males and females combined from the offspring FHS cohort. Using available data on cancer  and CVD as well as longitudinal data on physiological indices we estimated age trajectories of probabilities of staying free of the corresponding diseases for carriers and non-carriers of selected genetic variants as well as associations of these variants with age trajectories of physiological indices. We also investigated how smoking modulates estimated associations. More details about methods of data analyses used in this paper are given in Section In the discovery phase of the analyses we used the life span data on genotyped females collected in the original cohort of the Framingham Heart Study (FHS) Giroux,  as well p-values, genetic frequencies, and other important characteristics of these SNPs.The most significant genetic variants  resulted from GWAS on human life span using female data from the original FHS cohort are shown in Table p-values, genetic frequencies, and other important characteristics of these SNPs. This table shows that the eight genetic variants that had negative associations with lifespan in females also showed statistically significant negative associations with lifespan in males.To test whether the selected genetic variants also show significant associations with lifespan in males we performed genetic analysis of the ten selected SNPs using lifespan data on 432 males from the original FHS cohort. The same (additive) genetic model and the same observed covariates were used in these analyses. The results are summarized in Table Statistical estimates in Tables S1, S2 are obtained using mixed effect regression model with imputed life span data on 204 study subjects). It is unclear whether detected associations remain statistically significant when the methods free of life span imputation are used in the association analyses. To address this issue we evaluated genetic associations of selected genetic variants with mortality risk using Cox's regression model that does not require data imputation. The results of these analyses Table  showed hTo test whether detected variants are associated with life spans of the members of the offspring FHS cohort we performed genetic analyses of data for this cohort. Since the life span data for some members of this cohort are censored these analyses have been performed using the Cox's regression model using gender as an observed covariate. All selected variants showed significant associations with mortality risk using data from the offspring cohort Table .verify the research findings obtaned using regression models in GWAS by constructing and comparing empirical survival functions for carriers and non-carriers of selected variants. Note that the case-control analysis, typicaly used in genetic studies of centenarians, does not have data to make such a verification. Since associations of the variants with lifespan in our GWAS have the same direction of the effect in both genders, the Kaplan–Meier estimates of conditional survival functions for the genotyped members of the original FHS cohort were evaluated for males and females combined. In such evaluation we took into account that the life span data on the members of the original FHS cohort are right censored and left truncated. Note that for genetic analyses one should use age at blood collection (not the age at baseline) as the left truncation variable. We calculated these variables using data from the DNA Draw Date file available for FHS data from the dbGaP. Then we calculated ages at death/censoring of those 1111 individuals using age at the first exam and the number of days since the first exam until the death event or censoring which are provided in the Framingham data. Using these data and the R package “survival” we calculated Kaplan–Meier estimates of conditional survival functions for carriers and non-carriers of selected genetic variants who survived until specific ages .An important advantage of longitudinal data for genetic analyses of lifespan is the opportunity to Figure Figures Using data on the smoking habit (ever or never) as well as life span data on genotyped members of the original FHS cohort  we evaluated effects of interactions of detected genetic variants with the smoking habit on survival. The results are shown in Figure Figures Using available data on ages at disease onset, we evaluated conditional probabilities of staying free of cancer , for males and females combined who survived to 80 years of age. The results for the two SNPs, rs7894051 and rs4904670, are shown on Figure One can see from this figure that when males and females are combined, the rs7894051 does not influence cancer risk Figure , while cUsing longitudinal data on body mass index (BMI) for genotyped individuals from the original FHS cohort, we evaluated the average age trajectories of BMI for carriers and non-carriers of the minor allele for the same two SNPs, rs7894051 and rs4904670, in males and females. The results are shown in Figure One can see from Figures P-value), which could aid biological interpretation of the findings. We conducted review of current knowledge about biological and health effects of these SNPs and related genes using up-to-date publications and reliable online sources such as NCBI's PubMed, Entrez Gene, dbSNP, OMIM, Ensembl, GeneCards, GO, and MetaCore from Thomson Reuters. Genes related to SNPs identified in this study (or to SNPs that are in LD with them) are largely involved in mitochondrial oxidation, apoptosis, and protein degradation in cell. These processes are important part of cell/tissue responses to stress or damage. For example, the NRDE2 (C14orf102) gene is linked to PSMC1, a subunit of 26S proteasome involved in protein degradation, essential for cell damage response. PSMC1 may potentially interact with PSMD13, which is another subunit of the same 26S proteasome involved in protein degradation. ECHS1 is involved in mitochondrial oxidation and apoptosis, also essential for cell/tissue response to damage  allele of the two selected SNPs increased cancer risk in females. For males, however, the effect of these variants on cancer was the opposite, and carrying the vulnerability allele reduced the cancer risk in males.Since most centenarians avoid cancer  may sometimes do both, promote cancer and at the same time be potentially against certain phenotypes of physical senescence. This could happen because cancer  and senescent phenotypes such as physical frailty, and heart failure due to muscle atrophy, have peak manifestations at different ages: cancer risk reaches its maximum typically before oldest old age (<85), while senescence-related causes become major contributors to mortality risk later (at ages 85+)  in the same  cohort and in the offspring generation indicates that these findings are likely to be true-positive. It also indicates that GWAS of human longevity with inappropriate controls for population stratification are likely to suffer from the low level of statistical significance  and from the lack of replication.The genetic data from the original FHS cohort were one of the first prepared for genetic analyses using GWAS, and a substantial portion of genotyped cohort members died before the quality of genotyping was substantially improved. Therefore, these data have higher chances of having genotyping error than more recently produced datasets. Taking this into account we performed testing of the quality of genotyping for eight genetic variants detected in this study  and CVD. One may argue that the health and longevity traits investigated in this study  are too heterogeneous: individual differences in life spans may depend on susceptibility to different chronic conditions and cause specific mortality risks; cancers of distinct sites are often associated with different genetic and non-genetic factors; the term CVD includes many diseases dealing with cardio-vascular problems, each having its own sets of risk factors; etc. Although these concerns are certainly correct, one often does not have much choice: the selection of a trait for analysis is determined by the available data which has to be enough to get reliable conclusions from the analyses. Studying factors affecting aggregated traits  may help us detect regularities and identify mechanisms that are common for many specific phenotypes  comprising such traits. An important question is how best to analyze heterogeneous traits when you must? How can an understanding that the trait is genetically heterogeneous affect methods and results of analyses?different genetic mechanisms may be responsible for the same manifestation of a given trait. The goal of the analyses thus becomes, not just finding the one or more longevity (or vulnerability) alleles/genotypes responsible for the genetic variation of life span in all individuals, but investigating possible alternative mechanisms responsible for developing this trait. These mechanisms may involve different sets of genes in different individuals or in different groups of individuals. The genetic heterogeneity of longevity could be partly responsible for the lack of replication of respective genetic association studies.Despite the fact that the presence of such heterogeneity is recognized by many researchers in the field, there is no agreement concerning the best strategies for dealing with this issue. The recommendation that follows from our experience would be to investigate genetic heterogeneity by using different statistical models of the connections between genetic factors and phenotypic traits, to consider how the results of analyses  differ for different quality control procedures, to perform careful studies of the non-replicating results, keeping in mind that Although exact replication, such as findings of identical SNPs or genes, is not common across genetic association studies of aging and longevity, biological and health effects of identified genes, especially their involvement in similar damage responses, and in similar pathology, often overlap between the different studies. In our case, the involvement of selected genes Table  in canceThe results of our review of current knowledge also suggest an intriguing possibility that the vulnerability SNPs in genes involved in neurological disorders might also contribute to accelerated brain aging, and through this negatively impact longevity, which idea deserves further investigation. Connections between lifespan related genes and cancer may involve complex trade-offs. More detail on potential biological mechanisms are provided in section on Biological Meaning above.In sum, our study demonstrated genetic connections among lifespan, physiological aging changes, and complex diseases. Comparison of functional properties of genes found in this and other genetic studies of aging/longevity indicates that human lifespan may be regulated by different sets of genes; however, these genes tend to be involved in similar biological processes and complex pathology. The fact that the same biological process or health outcome may be realized through the different genes suggests that genes may potentially be interchangeable in their influence on longevity. This could contribute to both genetic heterogeneity of longevity and to a lack of replication in genetic association studies of lifespan and related phenotypes. Additional studies with a higher quality genetic data are needed to support our conclusions.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Type 2 Diabetes (T2D) is a chronic disease arising from the development of insulin absence or resistance within the body, and a complex interplay of environmental and genetic factors. The incidence of T2D has increased throughout the last few decades, together with the occurrence of the obesity epidemic. The consideration of variants identified by Genome Wide Association Studies (GWAS) into risk assessment models for T2D could aid in the identification of at-risk patients who could benefit from preventive medicine. In this study, we build several risk assessment models, evaluated with two different classification approaches , to measure the effect of including genetic information in the prediction of T2D. We used data from to the Original and the Offspring cohorts of the Framingham Heart Study, which provides phenotypic and genetic information for 5245 subjects (4306 controls and 939 cases). Models were built by using several covariates: gender, exposure time, cohort, body mass index (BMI), and 65 SNPs associated to T2D. We fitted Logistic Regressions and Bayesian Regularized Neural Networks and then assessed their predictive ability by using a ten-fold cross validation. We found that the inclusion of genetic information into the risk assessment models increased the predictive ability by 2%, when compared to the baseline model. Furthermore, the models that included BMI at the onset of diabetes as a possible effector, gave an improvement of 6% in the area under the curve derived from the ROC analysis. The highest AUC achieved (0.75) belonged to the model that included BMI, and a genetic score based on the 65 established T2D-associated SNPs. Finally, the inclusion of SNPs and BMI raised predictive ability in all models as expected; however, results from the AUC in Neural Networks and Logistic Regression did not differ significantly in their prediction accuracy. Type 2 Diabetes (T2D) is one of the fastest growing diseases in the United States and other developed nations Nugent, . In the Previous studies that have included genetic profiling and scores in T2D preventive models, have shown only a slight increase in predictive ability. Generally, the use of genetic variants provides a small contribution in terms of prediction accuracy due to their small effects, especially if compared to the use of age and clinically measured variables, such as BMI, and triglyceride levels and known risk factors for this disease  to data from the Framingham Heart Study, and incorporated 65 SNPs that are confirmed to be associated with T2D  came from the Framingham Heart Study which followed participants over seven decades and collected information from bi-yearly physical and blood examinations. Our sample was composed of 2378 females and 2861 males from the Original and Offspring cohorts; where 4300 are controls and 939 subjects are cases. Diagnosis of T2D for subjects varied by cohort. In the Original cohort, the presence of T2D was diagnosed with a blood glucose level greater than or equal to 200 mg/dL; however, for the offspring cohort, diabetes was diagnosed if fasting glucose levels were equal or greater to 125 mg/dL  and Neural Network (NN), respectively, will be introduced and finally, we will detail a series of nested models that incorporate BMI and genetic components consisting of the 65 SNPs . A group of covariates was selected based on the association with T2D (P < 0.01) and these were: cohort (ci), a dummy variable indicating whether the subject i belongs to the Original or Offspring cohort; age at last contact (li) 73.91 ± 11.74 (mean ± s.d.), was included to control for different exposure time or observational period; the first two principal components  derived from a set of 1000 European ethnicity-informative SNPs , also coded with an indicator variable, with this set of co-variables we generated a baseline model that is not influenced by genetic effects. Each one of the risk assessment models was extended by incorporating the body mass index  at diabetes onset in the case of diabetics and the last observed BMI for non-diabetics, which served as a measure of obesity [bi (mean ± s.d.) = 27.75 ± 5.38]. In some models, the SNPs were incorporated either by directly including the 65 SNPs or indirectly by a genetic score (GS) calculated as the count of risk alleles presents on each subject per SNP xij are the count of risk alleles in the thj SNP for the thi subject. Risk alleles for the inputted SNPs were given by the expected allele count xij being this a continuous number ranging from .Disease status of the participants was coded with a binary response variable thi was given by a linear predictor with a logit link  is the expected value for the diabetes status (yi); i isp the subject-specific probability of developing T2D given a set of covariates for subject i and exp(·) is the exponential function. The linear predictor (ηi) for a model built with only the non-genetic predictor variables is described in equation (2) and obtained as follows:0 is an intercept common to all observations, plus a regression on the “fixed effects”; and α1 to α4 are the corresponding regression coefficients or effects, for each one of the included variables.The probability of diabetes peculiar to subject  Dobson,  in the fxij  the hidden layer that contains s neurons; and the output layer. Each input connects to each one of the neurons creating an unknown weight iw for each input. This inner product between the weights and the input vector in each neuron of the hidden layer is given by equation:uki in the hidden layer is transformed by applying an activation function. We used the tangent hyperbolic function: yi = h(zi). Since the activation function can be a nonlinear function, it allows the classifier to capture non-linear effects.Bayesian Regularized Neural Network is a machine learning algorithm that is suited for classification problems  consisting of the sum of all variants that increase diabetes risk. To test whether there are genetic effects on T2D after accounting for BMI, models GENSBMI and GENBMI are extensions of the model of GENS and GEN65, respectively, including BMI. Finally, GENBMI was also extended accommodating SNPs by BMI interactions, into a model called GENBSNPs × BMI. Table Six models were built, with the aim of evaluating the genetic effects of the 65 variants associated to T2D as risk factors. Our starting point was a Baseline model (BASE), which is composed of only the non-genetic covariates or fixed effects: cohort, age at last contact, gender and principal components. BASEP-values were used to discriminate SNPs association to T2D and a 95% Confidence Interval of the OR was built to determine the statistical significance of the association between the response and the predictors.The estimated effects of gene markers and other covariates for the risk of T2D were calculated and displayed in terms of Odds Ratio (OR). The BASE model was used to estimate the effects for all the non-genetic covariates. In addition To evaluate the risk assessment models, a 10-fold cross-validation was used to compare the accuracy of their respective predictions. Each of the subjects within the data was assigned randomly to the 10 folds. The testing sample consisted of a subset of 1/10th of the data, and training would take the rest of the sample in order to achieve an optimal predictive model. Predictive ability of the models was assessed with the Receiver Operating Characteristic Curve Fawcett, , using tn = 2864), and only 18% of the overall subjects were diabetic. Within the data set, BMI (mean ± standard deviation) for diabetics was 29.9 ± 6.0, and healthy subjects 27.3 ± 5.1. According to the subjects BMI indexes, 28.2% of the observed subjects demonstrated to be obese (n = 1482) and 67.4% of the sample were overweight, while the rest were classified as normal. The mean observed age at which sample subjects acquired T2D was 63 years old. A reduction in the proportion of incidences of T2D can be seen in the Offspring cohort since the subjects of the Original cohort were observed during a longer time when compared to the Offspring cohort.The characteristics of the 5245 subjects are described and summarized in Table GS is a subject specific count of all the risk alleles in each one of the SNPs reported to be associated with risk of T2D. Table NN is a classifier that yields multiple estimated effects (depending on the number of neurons), which complicates the interpretation of the results. For that reason, estimates shown in this section are results from the Logistic Regression model.P < 0.01). Fixed effects estimates across the models were consistent for each of the covariates . Therefore, describing one model (GENSBMI) suffices to understand the effect of the covariates in the prediction of diabetes. For GENSBMI, gender had an OR = 0.60 which implies a much lower risk of developing T2D in women when compared to men. The Cohort's odds ratio (OR = 0.45), implies a lower risk of T2D in Offspring members in comparison to the Original Cohort. Exposure time had an OR of 1.03, resulting in a 3% increase in risk of development for every year of exposure. The OR for the Genetic Score is approximated to 1.1, which implies an increase in risk of developing T2D, with the increase in value of the genetic score. The OR for BMI was 1.13 in the models that included BMI. This value demonstrates there is a 13% increment in risk of T2D when increasing 1 kg/m2 in BMI.Table P-value of the 21 SNPs that gave a statistical association with T2D in our study; we also present the P-value of those SNPs, in association to BMI and WHR as reported in the Giant Consortium , IGF2BP2 (Insulin-Like Growth Factor 2 MRNA Binding Protein 2), and PTPRD (protein tyrosine phosphatase receptor D). In addition, two SNPs strongly associated to BMI, were located in the genes IRS1 (Insulin Receptor Substrate 1) and TCF7L2 (Transcription Factor 7-Like 2).Table P < 0.05, and 8 genes SNPs with P < 0.1. These results along with the estimated OR are provided in Table TCFL2), Gastric Inhibitory Polypeptide Receptor (GIPR), Growth Factor Receptor-Bound Protein (GRB14), G1/S-Specific Cyclin D2 (CCND2), Transducin-Like Enhancer of Split 1 (TLE1), Cartilage Intermediate Layer Protein 2 (CILP2) and HNF1 homeobox B (HNF1B). Genes CILP2, HNF1B, and HMGA2, were confirmed to have an association with BMI (P < 0.001). We did not detect any significant interaction in the model where genetic effects were incorporated as a Genetic Score .Our results suggest SNP by BMI interaction with five SNPs at a Predictive ability of the models was evaluated with a ten-fold cross validation and measured in terms of AUC. Values of the AUC in cross validation, for all risk assessment models in the Logistic Regression and Neural Networks, are reported in Table BMI), increased the AUC to 0.739 and 0.735 for LR and NN, respectively. Also, accounting for genetic markers in GEN65, increased the predictive ability of the models by approximately 2%, when compared to the baseline factors alone. We further analyzed the extent to which the predictive accuracy could be improved by adding BMI to the GEN65 model and achieved a discriminative value of 0.745 and 0.741 , resulting in an increase of approximately 7%. Previous studies have shown a correlation between the increases in weight and body mass with an increase in probabilities of developing T2D. The incorporation of the genetic score after accounting for BMI further increased AUC to 0.750 . A difference of approximately 8% in predictive ability was observed in the GEN65BMI model, when compared with the baseline model . The effect of including genetic information was examined by adding 65 candidate SNPs for T2D and computing a genetic score based on these SNPs.GLIS3, TCF7L2, LGR5, and PTPRD), showed a strong association with Type 2 Diabetes. In addition, IGF2BP2 and GCKR have been identified by several meta-analyses  provides a component needed to trigger the reactions for the linkage of the insulin receptor to tissue. However, it was excluded as a risk gene for Type 2 Diabetes by Bektas et al.  was included in the model, no further increase was seen. The consistency of AUC throughout the models, with the use of both Neural Network and Logistic Regression, suggests that the use of different statistical approaches neither aided nor reduced the predictive ability of the models. The limitation in predictive accuracy seems to be associated to factors other than the statistical model, such as: the size of the training sample, the number of SNPs included in the model, missing heritability issues and low heritability of the trait. A few concerns about SNPs information, were observed. The first pertains to the imputation uncertainty of the SNPs, since it was not fully taken into account in our analyses. Nevertheless, an alternative methods that consider imputation uncertainty are proposed by Marchini and Howie . SecondlBMI. A limitation of our study is that we did not take into account other clinical variables that have shown some degree of association with diabetes, such as triglyceride levels, high blood pressure, LDL or HDL, which could have enhanced our results. The Framingham Heart Study provides these variables, but there are missing values in many exams and subjects. To avoid reducing sample size, we only included BMI longitudinally , and we found that genetic signal from the SNPs is captured beyond what could be explained by the BMI. BMI estimated effect on diabetes may result biased since we incorporated BMI as the BMI at first diabetes diagnosis for diabetic subjects and last BMI on record for healthy subjects. However, preliminary analysis (not included in the paper) show us that the effect and their significance, for BMI and other covariables in the models, are insensitive to alternative ways to account for BMI, such as, BMI at the first exam, or maximum BMI of the subjects observed period. Despite our limitations, our study can provide important remarks. The effect of genetic information in the improvement of the prediction accuracy, was evaluated in our models by incorporating 65 SNPs both directly and into a genetic score. In addition, we looked at the inclusion of gene-environment (BMI) and gene-gene interaction into risk prediction. Also, a classical logistic regression and a Neural Network  were explored.The most commonly identified covariates used in assessment analyses that provide a high AUC (0.60–0.80) as a clinical baseline model have been: age, high blood pressure, and glucose levels between other covariates  of approximately 2%. However, modeling strategies such as Neural Network or Logistic Regression did not yield differences in terms of prediction. We also showed that the inclusion of BMI into the risk assessment models, improved the predictive accuracy by approximately 8%. Furthermore, the risk assessment model yielded a modest increment in prediction accuracy when including genetic risk score, even after accounting for BMI. This small improvement suggests that there is still genetic signal involved in the development of T2D, yet to be captured, that could produce effects beyond the increase in BMI. In summary, marker information in addition to commonly used baseline covariates such as BMI, could lead to an overall modest improvement of predictive performance.In summary, this study confirmed the association of 21 genetic variants with T2D. It was observed that individuals who have a high genetic score may have increased probabilities of developing Type 2 Diabetes. Also, accounting for genetic information, either by including SNPs or a Genetic Score in the regression, led to an improvement in prediction accuracy (All individuals that helped in the writing process of this manuscript are listed as authors and co-authors, and were part of: the formation of the research, recompilation and management of the data, data analysis and interpretation as well as the redaction and edition of this manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Grandiosity and Paranoia showed modest SNP heritability estimates , and zero estimates were found for Hallucinations and Negative Symptoms. The estimates for Anhedonia, Cognitive Disorganization and Grandiosity accounted for approximately half the previously reported twin heritability. SNP heritability estimates from the MAF-stratified approach were mostly consistent with the standard estimates and offered additional information about the distribution of heritability across the MAF range of the SNPs. In contrast, the estimates derived from the pruned data were for the most part not consistent with the other two approaches. It is likely that the difference seen in the pruned estimates was driven by the loss of tagged causal variants, an issue fundamental to this approach. The current results suggest that common genetic variants play a role in the etiology of some adolescent psychotic experiences, however further research on larger samples is desired and the use of MAF-stratified approach recommended.Occurrence of psychotic experiences is common amongst adolescents in the general population. Twin studies suggest that a third to a half of variance in adolescent psychotic experiences is explained by genetic influences. Here we test the extent to which common genetic variants account for some of the twin-based heritability. Psychotic experiences were assessed with the Specific Psychotic Experiences Questionnaire in a community sample of 2152 16-year-olds. Self-reported measures of Paranoia, Hallucinations, Cognitive Disorganization, Grandiosity, Anhedonia, and Parent-rated Negative Symptoms were obtained. Estimates of SNP heritability were derived and compared to the twin heritability estimates from the same sample. Three approaches to genome-wide restricted maximum likelihood (GREML) analyses were compared: (1) standard GREML performed on full genome-wide data; (2) GREML stratified by minor allele frequency (MAF); and (3) GREML performed on pruned data. The standard GREML revealed a significant SNP heritability of 20 % for Anhedonia (SE = 0.12;  These experiences are common but vary in severity of expression across the population  study on psychotic experiences, which was performed on a single measure of adolescent positive psychotic experiences and no SNPs reached significance post correction for multiple testing . In total, 3665 samples were successfully hybridized to AffymetrixGeneChip 6.0 SNP genotyping arrays. Of those, 513 were excluded based on low call rate or heterozygosity outliers, atypical population ancestry, sample duplication or relatedness to other sample members, unusual hybridization intensity, and gender mismatches , a longitudinal general population sample of twins born in England and Wales between 1994 and 1996    .Due to a moderate skew of some of the SPEQ subscales , the data on these subscales were normalised using van der Waerden’s transformation Lehman , which cGenome-wide restricted maximum likelihood (GREML) analysis performed in the genome-wide complex trait analysis (GCTA) software allows to estimate the heritability of a trait captured by common single nucleotide polymorphisms (SNPs), referred to as SNP heritability. It is achieved by comparing matrices of pairwise genetic and phenotypic similarity across unrelated individuals ; and (2) a MAF-stratified approach was applied to the full genome-wide data  was first calculated to ensure that the individuals were truly unrelated, and those with a pairwise relatedness of ≥0.025 were removed (this corresponds approximately to a cousin three times removed). Then univariate heritability estimates were obtained using a standard GREML approach  and in Cognitive Disorganization 0.19 . This is in comparison to the twin-based heritability estimates which were 0.47 and 0.43, respectively . The standard GREML analysis revealed that 14 % of phenotypic variation in Paranoia was captured by common variants but the standard error was large and the estimate dropped to almost zero when the other two approaches were applied. Point estimates for Hallucinations and Parent-rated Negative Symptoms were particularly low, which was consistent across all three approaches. If replicated, these results suggest that detection of common SNPs associated with hallucinations and parent-rated negative symptoms may prove to be more difficult than identifying common SNPs associated with adolescent anhedonia, cognitive disorganization, grandiosity or paranoia because the former appear to have less net variance explained by common SNPs than the latter.As expected, most of the SNP heritability estimates of psychotic experiences reported here were lower than the previously reported twin-based estimates. These findings are in line with results of other studies from a number of phenotypes such as schizophrenia  deserve discussion. Our results suggested that common genetic variants play a role in the etiology of self-rated Anhedonia but not in Parent-rated Negative Symptoms. These two measures capture different aspects of negative psychotic experiences, and, importantly, rely on different raters (self and parent) which is reflected by the modest correlation of 0.14  of the twin sample (4743 twin pairs) (Zavos et al. This is the first study to show that common genetic variants play a role in the etiology of some individual psychotic experiences in adolescence. Common SNPs accounted for approximately half of the twin-based heritability estimates in anhedonia and cognitive disorganization. There is some evidence that common genetic variants may be important for the genetic architecture of grandiosity and paranoia but further research in larger samples is required. No common genetic effects were found for hallucinations and parent-rated negative symptoms in the current sample. It is hoped that further exploration of the role of common genetic variants in the etiology of adolescent psychotic experiences will help with early intervention and prevention of transitions into clinical diagnosis. Replication of the current findings in a larger sample is desired and the use of the MAF-stratified approach recommended.