This pattern was replicated in independent data, reflecting robustness of the method. In addition to improving prediction of disease susceptibility and broadening our understanding of the pathogenesis underlying psoriasis, these results demonstrate BlocBuster's potential for discovering combinatorial genetic associations within heterogeneous genome-wide data, thereby transcending the limiting “small effects” produced by individual markers examined in isolation.Hundreds of genetic markers have shown associations with various complex diseases, yet the “missing heritability” remains alarmingly elusive. Combinatorial interactions may account for a substantial portion of this missing heritability, but their discoveries have been impeded by computational complexity and genetic heterogeneity. We present BlocBuster, a novel systems-level approach that efficiently constructs genome-wide, allele-specific networks that accurately segregate homogenous combinations of genetic factors, tests the associations of these combinations with the given phenotype, and rigorously validates the results using a series of unbiased validation methods. BlocBuster employs a correlation measure that is customized for single nucleotide polymorphisms and returns a multi-faceted collection of values that captures genetic heterogeneity. We applied BlocBuster to analyze psoriasis, discovering a combinatorial pattern with an odds ratio of 3.64 and Bonferroni-corrected p-value of 5.01×10 genetic heterogeneity, in which different subsets of individuals develop a given disease due to different sets of genetic factors. We present BlocBuster, a network-based method that addresses these challenges and extracts inter-correlated genetic markers that manifest significant associations with complex diseases. Our analysis of psoriasis GWAS data revealed a significant combinatorial genetic pattern, which was validated using stringent computational tests and replication in independent data. This pattern is more significant than other previously identified markers. We also compared Pearson's correlation coefficient and observed that it introduced more type I errors and produced a less structured network than BlocBuster; the former also broke the combinatorial pattern into pieces. In addition to improving prediction of disease susceptibility and broadening our understanding of the pathogenesis underlying psoriasis, these results demonstrate BlocBuster's effectiveness for discovering combinatorial genetic associations within heterogeneous backgrounds, thereby transcending the limiting “small effects” produced by individual markers examined in isolation.Most complex diseases arise due to combinations of genetic factors, yet current genome-wide association studies (GWAS) typically examine individual genetic markers in isolation because of the complexity of considering a prohibitively large number of marker combinations. Another complication for GWAS stems from  Psoriasis is an incurable complex disease that is characterized by hyperproliferation and aberrant differentiation of the epidermis, coupled with marked cutaneous inflammation. Environmental triggers for onset of symptoms have been observed, yet genetic predisposition is strong and heritability has been estimated at 80% PSORS1, is within the major histocompatibility complex (MHC) region on chromosome 6 HLA-C, PSORS1C1 (aka SEEK1), PSORS1C2 (aka SPR1), PSORS1C3, CDSN, and several additional genes and pseudogenes in a ∼300-kb region of 6p21.3. A number of genome-wide association studies (GWAS) focused on psoriasis have identified associated single nucleotide polymorphisms (SNPs) in this region, as well as other regions of the genome, e.g., those reported in The strongest known genetic risk factor for psoriasis, Overall, it is estimated that less than 20% of genetic heritability can be accounted for by previous discoveries 17 trios. Consequently, directly testing every trio or higher-ordered combination is computationally intractable using currently available resources and will likely remain infeasible for the foreseeable future Identifying genetic risk factors and understanding the genetic basis of complex diseases, such as psoriasis, are central goals of medicine and biology. While GWAS have identified hundreds of individual genetic markers associated with complex diseases, it is clear that a substantial portion of heritability remains unexplained for the vast majority of these enigmatic phenotypes HLA-C and ERAPIn order to examine pair-wise epistasis involving two SNPs, several methods have been introduced in which subsets of SNPs are selected using previously known biological information, and pair-wise interactions are computed over these subsets Alternatively, haplotypes have the potential to provide more power than single SNPs HLA-Cw6 haplotype family consisting of HLA-Cw0602—Cw0613 alleles within PSORS1 has shown strong association with psoriasis PSORS1 region for one psoriatic individual and four controls, genotyped risk alleles in 678 psoriatic families, and employed three computational haplotype reconstruction methods as well as a combinatorial analysis to implicate the HLA-Cw6 haplotype as the most probable source of susceptibility within the PSORS1 locus for early-onset psoriasis of individuals with European ancestry. It should be noted that their analysis focused on age of onset and it only included exons from known protein-coding genes. Non-coding regions were left unexamined.The HLA-Cw6. They tested risk predictions via simple allele counts of multiple markers as well as weighted combinations and observed that the contribution due to the HLA-Cw6 SNP was about equal to the contribution of the other nine SNPs combined. The authors noted the possibility of overfitting in their weighted approach due to the use of the same data for model construction and subsequent analysis It has been demonstrated that complex phenotypes, e.g. human height One approach to address this limitation is to consider all genome-wide SNP states together for each individual and apply a regression analysis or maximum likelihood estimate over the genomic similarities between individuals. Yang et al. used this approach to estimate variance in human height communities, of nodes such that there is a high density of edges within each community and few edges spanning between communities. Many approaches utilize clustering methods to partition the network, followed by the use of reference databases – e.g. Gene Ontology Several network construction approaches utilizing known information have been introduced to capture combinations of markers with phenotypic associations, such as nested clade analysis CFTRr2. Importantly, each of these popular correlation methods returns a single scalar that can be crippled by heterogeneity. In fact, all of the correlation measures that we have examined, including PCC and r2, as well as dot product and entropy, are global, in that individuals in the entire group are viewed as a whole, and thus subtle but critical subgroup structures, which manifest heterogeneity of the individuals in the group, are ignored. r2 have low values, due to penalization for the uncorrelated individuals. In short, current correlation measures treat the correlation for all of the individuals as a whole, and consequently, fail to accommodate genetic heterogeneity within the sample studied.In addition to the challenges of combinatorial interactions, another serious issue that is impeding identification of phenotypic associations in GWAS is that most complex diseases are subject to genetic heterogeneity, in which different groups of individuals develop the same disease due to different genetic factors or gene-by-environment interactions. Heterogeneity can manifest as different mutations within a single gene or as mutations within different genes. For example, cystic fibrosis can arise due to more than 1,000 different mutations within a single gene, in toto. In our current implementation, each bi-allelic SNP is represented by two nodes, one for each SNP allele, which can be readily extended to multi-allelic SNPs. CCC is computed for every pair of SNPs, thereby revealing correlations that arise regardless of genomic distances between the SNPs. Significant values within the CCC vectors are represented by edges between the nodes representing the correlated alleles. After the network is built, we retrieve clusters of inter-correlated nodes that arise naturally separated from each other and do not require partitioning. Each of the corresponding patterns of SNP alleles is then tested for variation between phenotypic groups. Consequently, BlocBuster extracts patterns of inter-correlated haploid markers, referred to as blocs. These blocs seamlessly capture genetic heterogeneity as they are built upon the multi-faceted CCC metric that treats each pair of SNP alleles independently, thereby avoiding reduction of the correlation value by subgroups of individuals that lack correlation for the pair of alleles. An allele-specific network is utilized to eliminate the merging of both SNP allele states into a single node, which can lead to false positive signals, as described below. Our approach is direct and efficient, and scales efficiently to millions of markers with reasonable computational resources.In order to address these pressing challenges, we present BlocBuster, a systems-level, allele oriented network strategy designed to generate viable biological hypotheses of epistatic and/or additive interactions of genetic variations with a holistic and unbiased approach that honors genetic heterogeneity. BlocBuster has two key distinctions from the previous approaches. First, we introduce a significant extension to the custom correlation coefficient  In order to ensure accuracy of results, BlocBuster employs a series of computational validation trials, including two types of permutation tests, bootstrapping trials, variations of network density, and visual inspection. These computations economically screen the results and can be utilized prior to investment in replication trials using independent data.Aiming at identification of combinatorial interactions of SNP alleles underlying pathogenesis of psoriasis, we applied BlocBuster to genome-wide data for psoriatic cases and normal controls. This analysis identified a bloc of SNP alleles that is significantly associated with psoriasis and improves upon previous results by supplying a precise allelic pattern within the major histocompatibility complex (MHC). This newly identified genetic pattern was rigorously validated using multiple computational screening tests and was subsequently replicated in independent data, thereby ensuring its accuracy and suitability for further research efforts. Finally, we compare and contrast our approach with Pearson's Correlation Coefficient (PCC) and observe that the PCC network had substantially weaker community structure, was more likely to introduce false-positive correlations, and required three times as much computation time.all individuals and the network construction is blind to phenotype status. Furthermore, CCC is computed for every pair of SNPs, providing a holistic systems-level network. After the network is constructed, groups of nodes that are connected by edges are easily identified as they are completely isolated from each other. Then the entire pattern of SNP alleles represented by each bloc is tested as a whole for association with the phenotype. These patterns are comprised of specific SNP alleles and can be considered as a type of haplotype – with two noteworthy exceptions: (1) only SNP alleles that exhibit inter-correlations are included and (2) the SNPs are not necessarily contiguous and are included regardless of genomic position.In order to discover combinatorial interactions in heterogeneous samples of a given complex disease, we developed a novel computational approach, referred to as BlocBuster, which identifies clusters, or blocs, of correlated SNP alleles and subsequently tests these blocs for phenotypic associations. Briefly, an allele-specific network is constructed in which each SNP allele is represented by a node and edges are placed between pairs of nodes representing SNP alleles that exhibit significant pair-wise correlations. In order to address genetic heterogeneity, we utilize a multi-faceted correlation metric that is customized for SNP data, referred to as CCC. Note that the CCC computation is conducted for the entire sample of In this section, we present the results provided by BlocBuster for psoriasis GWAS data. These results were carefully validated using a series of computational trials and these outcomes are overviewed. The most significant result is a bloc of 17 SNP alleles that is strongly associated with psoriasis. We replicated this result by utilizing independent data and found that the bloc has a stronger association in the replication data than in the discovery data. Finally, we compare CCC with a standard correlation metric, Pearson's correlation coefficient (PCC), and observe the benefits of utilizing a metric that is customized specifically for SNP data and is designed to accommodate heterogeneity.doubletons, each of which was comprised of a single edge connecting two nodes; with every node connected to precisely one other node in the network.We used both psoriatic cases and normal controls in the GAIN General Research Use (GRU) genome-wide data to construct the BlocBuster network for this complex disease. These data consisted of 443,020 autosomal SNPs for 929 cases and 681 controls see . The corsingleton nodes with no incident edges, and many discrete blocs of densely connected nodes, with each bloc isolated from one another. Specifically, 631,462 (71.3%) of the nodes were singletons, and there were 54,425 discrete blocs, ranging from 2 to 313 nodes, with an average of 4.7 nodes per bloc.In sharp contrast to a network with uniform distribution, the observed network exhibited strong community structure. Instead of doubletons spread across the network, there were a large percentage of entire SNP allele pattern must be present to be counted in the bloc frequency. This policy assumes that the entire pattern is required for the phenotypic association for a given subset of individuals. However, it is possible that one or more of the SNP alleles in the bloc is not essential. The visual validation described below facilitates the observation of this situation, should it arise.Importantly, the blocs arose naturally separated in the network and there was no need to employ methods such as clustering strategies to partition the nodes. For each of the 54,425 blocs, the frequencies of the entire corresponding SNP allele pattern were tallied and the odds ratio with 95% confidence interval (CI) and Bonferroni-corrected p-value, based on the G-test of independence, were computed between cases and controls see . Any indps_1, which was comprised of 17 SNP alleles and had a significant odds ratio and CI  than the risk pattern (with a frequency of 0.157), which is likely the reason that the protective pattern appeared in the network that was constructed using all individuals without phenotypic labeling.This analysis revealed a single bloc, referred to as o and CI . Individps_1, along with alleles and their individual frequencies. The SNPs within ps_1 span ∼211 kb, from positions 31054511 to 31265057 in the MHC on chromosome 6. Two SNPs are located within known genes: rs3130573 in PSORS1C1 (aka SEEK1) and PSORS1C2 (aka SPR1), and rs1265078 in CCHCR1 . All three of these genes have been previously associated with psoriasis In order to evaluate the robustness of our results, we ran five computational validations: two types of permutation tests, trials in which we varied the network density, bootstrapping trials, plus visualization of results. The first series of permutation tests were conducted to determine a significant G-test score given multiple tests see . In thes10 pairs of SNPs with permuted genotypes was 0.6515. The lowest CCC value representing an edge in the original network was 0.6949. This result indicates that it is not likely that there were any edges representing false-positive correlations in the original network.The second series of permutation tests were used to remove inherent correlations among SNP alleles in the data in order to verify that it is unlikely that type I errors were introduced during computations of correlations. For each SNP, we randomly shuffled the genotypes across all individuals. This randomization breaks inherent correlations while each SNP retains the same allele frequencies and balance of genotype states as in the original data. Consequently, it is not expected that there would be significant correlations within the permuted data. These trials aim to estimate the highest CCC value that might arise by random chance for uncorrelated data drawn from these samples. The maximum CCC value for 9.8×10n, the highest n CCC values were determined and the corresponding SNP allele pairs were connected by edges in the network. We constructed networks with 50,000 to 500,000 edges, in increments of 50,000, and tracked ps_1 within these networks. The CCC thresholds for edge placement for these trials varied from 0.7501  to 0.6906 , which is substantially higher than the maximum CCC value of 0.6515 that was produced during the permutation trials, indicating that it is not likely that false positives arose during these trials.In the third validation trial, we varied the density of the network to test the sensitivity to this parameter. For a given number of edges ps_1. The 350,000 edge network possessed a bloc with 16 of the 17 nodes in ps_1; node 6 was not included in this bloc. The association of this bloc was similar to the original 17-node bloc as it had frequencies of 0.218 and 0.071 for cases and controls, respectively, with an odds ratio of 3.64 (CI: 2.83–4.67) and Bonferroni corrected p-value of 1.81×10−23. The 400,000 edge network possessed the entire 17-node bloc. The 450,000 edge network added another node to the bloc, rs2442736. This bloc had frequencies of 0.137 and 0.039 for the cases and controls, respectively, with an odds ratio of 3.91 (CI: 2.81–5.45) and Bonferroni-corrected p-value of 1.10×10−14. For the 500,000 edge network, the bloc grew to 30 nodes, had frequencies of 0.020 and 0.006, and an odds ratio of 3.32 (CI:1.54–7.19). The p-value was not significant after correcting for multiple testing. ps_1 was significant for a range of network densities. However, when the network grew to a half million edges, this bloc grew substantially, its frequency fell to less than two percent, and it exhibited a weaker association with the phenotype.The sparse networks with no more than 300,000 edges did not include ps_1. Over the 1,000 computations, the odds ratios had a mean of 3.66 with CI: 3.64–3.69. This result is slightly better than the results found for the entire dataset, and the confidence interval is tighter, as it was based on 1,000 trials. The average p-value was 2.91×10−11, which is larger than the original result, likely due to the fact that these trials each had half of the original sample size. Overall, these results indicate robustness to sample selection as randomly selected subsets of the individuals yield strong phenotypic associations.In our fourth validation, we tested the sensitivity of the selection of individuals with a series of bootstrapping trials. This resampling technique evaluates the stability of results computed over a sample drawn from a population and has been shown to be more accurate than methods that are based on asymptotic approximation or normality assumptions ps_1, and plotted them for visual inspection, as shown in Finally, we extracted the genotypes for the SNPs corresponding to ps_1 using the GAIN Autoimmune Disease Only (ADO) data. These data consisted of 443,020 genotype states for 439 psoriatic cases and 728 controls. For these data, the frequencies of the entire ps_1 bloc were 0.260 and 0.083, with an odds ratio of 3.86 (CI: 2.98–5.01) and p-value of 1.81×10−25. Note that only one bloc was tested, so there was no correction for multiple testing. These results are even stronger than those for the discovery data, demonstrating the validity of the association of this bloc with psoriasis.We tested the identified bloc r2, required many thousands times more computation time than CCC or PCC, and is not practical for studies involving large numbers of SNPs. Accordingly, in this section we disregard r2 and focus on comparisons between PCC with CCC. Due to computational demands, we used the 30,178 SNPs from chromosome 6 for the following trials. We first computed all pair-wise correlations using both metrics and compared the network structures that each produced. Second, we ran permutation trials and compared the numbers of false positives produced by each method, as well as average computation time. Third, we extracted the clusters in the PCC network that possessed the SNPs in ps_1 and compared differences in the results.In our analysis, we found that the linkage disequilibrium measure, First, we created two networks for the SNPs using each of the correlation metrics. BlocBuster networks possess two nodes for each SNP thereby capturing allele-specific correlations. In comparison, PCC does not return the alleles associated with a correlation, so only one node was used to specify each SNP. In order to compare the two methods, we built a CCC network with only one node per SNP and placed an edge between a SNP pair if any of the four allele-specific CCC facets exceeded the threshold. Setting the number of edges equal to the number of SNPs for chromosome 6 corresponded to thresholds of 0.6990 and 0.7350 for CCC and PCC, respectively.These two networks were compared for community structure. Strong community structure in a network opposes uniform edge distribution and is instead exemplified by clusters of tightly interconnected nodes such that few edges connect these clusters In our second comparison we ran ten permutation trials in which genotypes were randomly reordered over the individuals as previously described, computing CCC and PCC on each of the permuted datasets. The maximum PCC value for the entire networks ranged from 0.7068 to 1.0000 over the ten trials, with an average of 0.8534. Despite the fact that true correlations should have been eliminated from the data, there were a total of seven edges with PCC values of 1.0000. The maximum CCC values ranged from 0.6474 to 0.6492, with an average of 0.6483. These results suggest that CCC is less likely than PCC to produce spurious edges. It also indicates that the original PCC network might have possessed false positive edges as the threshold was 0.7350, while it is unlikely that the original CCC network possessed false positive edges with its threshold of 0.6990.These trials also provided an opportunity to compare average computation time requirements. The CCC trials averaged 135 minutes and PCC averaged 402 minutes per trial; the former was three times faster than the latter.ps_1 were examined. Twelve of the 17 SNPs in ps_1 comprised one cluster in the PCC network, two additional SNPs were connected together as a doubleton, and the other three were singletons, as shown in Finally, the clusters in the PCC network possessing the SNPs in bloc ps_1, consisting of a combination of 17 SNP alleles that are highly inter-correlated and exhibit a psoriatic risk association as a whole with an odds ratio of 3.64 (CI: 2.75–4.80) and Bonferroni-corrected p-value of 5.01×10−16 in the discovery data. This bloc had an odds ratio of 3.86 (CI: 2.98–5.01) and p-value of 1.81×10−25 in the validation data. BlocBuster's success in replicating a 17-SNP allele pattern in independent data reflects the robustness of the approach. In the network, each edge within the bloc represents a strong allele-specific correlation that is not weakened by genetic heterogeneity. As shown in Psoriasis is a common complex disease that has been extensively studied and several GWAS have been previously conducted ps_1 corresponds to SNP rs3130573, which is in the overlapping region of the PSORS1C1 (aka SEEK1) and PSORS1C2 (aka SPR1) genes. Both of these genes have been previously indicted to be associated with psoriasis CCHCR1 . CCHCR1 has been observed to have differential expression in psoriatic lesions when compared with either normal skin or eczema lesions ps_1 lie in intergenic regions as shown in HLA-C, a gene that has been associated with psoriasis over decades of research efforts Node 1 of ps_1 span a 211 kb region of chromosome 6, as shown in The 17 SNPs in ps_1 is 2.41 (SNP rs12191877). In contrast, the entire bloc as one unit exhibited odds ratios of 3.64 and 3.86 for the discovery and validation data, respectively. These results illuminate the discriminative power of combinatorial patterns and the capability of this approach for transcending single-marker methods. While the cardinality of the actual causal mutations which are tagged by the SNPs in ps_1 may be less than 17 due to LD, recognition of multiple SNP alleles may reveal combinatorial interconnection among these SNPs underlying the etiology of psoriasis and tightens the fingerprint of the causal mutations, providing a fine-scaled pattern for future explorations of underlying genetic factors.Our network-based result is advantageous over the results from conventional GWAS. As shown in BlocBuster utilizes stringent validation procedures to efficiently weed out uninformative results to reduce resources that may have otherwise ensued in follow-up studies. These validation trials scrutinize blocs identified within the discovery data by examining their properties; specifically the robustness of the pattern and the improbability that it possesses type I errors or captures an incomplete and misleading portion of the data.The permutation tests in which genotypes were randomly reordered indicated that it is highly unlikely an edge in the BlocBuster network appeared by random chance. On the other hand, PCC produced spurious edges and was not as capable to discern true correlations from noise, presumably due to its inherent inability of capturing genetic heterogeneity. Consequently, seven edges with PCC values of 1.0000 were computed from the permuted data in which correlations should have been eliminated.In another validation, the genotype states of the identified blocs were plotted for visual inspection, as shown in BlocBuster compares the frequencies of each bloc between cases and controls, so it was necessary to correct for multiple testing. We employed two approaches for this task, Bonferroni correction and permutations of phenotypic labels, and observed that the theoretical and empirical approaches yielded similar thresholds for this study.LCT gene with human height. This association is believed to be false positive as it has not been validated. In general, testing on independent data is valuable for addressing the possibility of population stratification within GWAS. In this study, bootstrapping trials yield a tight confidence interval. Furthermore, replication in independent data provides an even stronger association than what was found using the original data. Taken together, it is not likely that population stratification inflated the association of ps_1 with psoriasis. These results indicate this is a bona fide genetic pattern that is strongly associated with psoriasis.Finally, the association of the bloc was confirmed in an independent dataset of 439 psoriatic cases and 728 controls with even higher significances than the original dataset. Replication in independent data addresses another concern in GWAS: population stratification. Population stratification arises when a subset of individuals in the sample share some common ancestry and are overrepresented in either the cases or controls. In these scenarios, alleles associated with their ancestry might appear to be associated with the phenotype. In order to avoid this issue, samples are commonly chosen with as much population homogeneity as possible. Note that bootstrapping trials may be useful to flag potential stratification as they empirically quantify the sensitivity of the results to the selections of the samples. High variability of the test statistic over bootstrapping trials might represent population stratification. More formally, various statistical methods that utilize reference panels have been applied to test for stratification. However, Campbell et al. BlocBuster is fundamentally different from standard network approaches in several ways. First, it introduces an extension of the CCC metric Second, the networks created by other methods typically are comprised of a single connected component that must be partitioned using some type of clustering strategy. It is not clear which clustering strategy is the most appropriate and selections of parameters, e.g. numbers of clusters, can introduce bias and/or error. In contrast, BlocBuster networks are comprised of discrete components that are not connected to one another, so there is no ambiguity about how to separate them. Third, traditional approaches do not provide specific information regarding the genetic patterns that have variations between populations, while BlocBuster explicitly defines these allelic patterns as well as the relevant statistics. Finally, many other methods rely upon matrices comprised of similarities between pairs of individuals while BlocBuster is based upon correlations between SNP alleles, not individuals. On a related note, BlocBuster supplies a different type of information than the LD structure captured by tools such as Haploview ps_1 and PCC split this bloc into pieces. More generally, PCC was more likely to introduce type I errors, and the PCC network had lower community structure than the corresponding CCC network, with the edges more dispersed throughout the network. As a practical consideration, PCC required three times as much computation time.When compared with Pearson's correlation coefficient (PCC), CCC identified more than twice as many correlations for the 17 SNPs in BlocBuster is a computationally efficient approach for GWAS. In general, direct identification of combinations of three or more inter-correlated markers is infeasible for GWAS due to the extremely large number of combinations. Given a pairwise correlation metric that can be quickly computed, network methods are efficient alternatives as they compute all pairwise correlations and build a network with potential to render higher-ordered inter-correlations. CCC is a straight-forward and simple metric and computations for the dataset of 1,610 individuals and 443,020 SNPs required a total of about 54 days. We ran the analysis on a cluster of 45 processors, which produced the results in less than a day and a half. At this rate, scaling up to 3,000,000 SNPs would require approximately 490 days of computation on a single CPU, which can be performed in parallel in a reasonable amount of time, given adequate resources (e.g. about five days on a cluster of 100 processors). Extraction of the blocs from the network using a breadth-first search and evaluating the associations of these blocs required only four minutes of computation time on a single processor.BlocBuster expands upon the previous CCC implementation Two caveats of our approach should be noted. First, BlocBuster is not designed to identify a marker that is independent in its association with a phenotype. There must be at least two correlated markers with a combination that exhibits association for recognition by this approach. For this reason, studies should employ standard single-marker association tests in addition to BlocBuster. Second, BlocBuster is diligent in removing false positives and consequently may miss true signals. However, this quality ensures the usefulness of the identified blocs for assessing risk and exploring pathogenesis.GWAS are prevalent for phenotypes of scientific interest and future advances hinge on embracing the complexities of combinatorial interactions. Previous approaches for identifying combinatorial patterns presented biases as they relied upon known information and previous correlation measures were weakened by heterogeneity. BlocBuster's multi-faceted approach and allele-specific network efficiently accommodate heterogeneity. The benefits of this accommodation are highlighted by the comparisons with Pearson's correlation coefficient, which clearly demonstrate higher accuracy and reduced type I errors for our approach. Looking forward, BlocBuster's efficient selection of correlated markers will further increase the value of this approach as genetic data become increasingly affordable and dense.http://view.ncbi.nlm.nih.gov/dbgap-controlled through dbGaP accession number phs000019.v1.p1.c1, General Research Use (GRU) and Autoimmune Disease Only (ADO). Perlegen 500K chips were utilized for both studies.The genotyping of samples was provided through the Genetic Association Information Network (GAIN). The datasets used for the analyses described in this manuscript were obtained from the GAIN Database at The GRU dataset included 451,724 SNPs for 1,683 individuals. The removal of mitochondrial DNA and the X and Y chromosome SNPs resulted with 443,020 autosomal SNPs. We removed the children as well as the individuals that did not pass quality control . We checked this extracted data for percentages of missing values and found that each of the 1,610 individuals and each of the 443,020 SNPs had no more than 10% missing data. In total, 929 and 681 of these individuals were labeled as psoriatic cases and normal controls, respectively.The ADO data consisted of 451,724 genotypes for each of 1,214 individuals. We removed the individuals that did not pass previously defined QC, leaving 1,167 individuals. We removed SNPs from the mitochondrial DNA and X and Y chromosomes, leaving 443,020 SNPs. Three of these SNPs possessed between 10% and 20% missing data and the rest had less than 10% missing values. None of the 1,167 individuals had more than 10% missing data. The final dataset included 439 cases and 728 controls.www.blocbuster.org or by contacting the first author. BlocBuster is a network model that employs a custom correlation coefficient (CCC) A and a represent the two alleles at the first SNP, and B and b represent the two alleles at the second SNP. There are four allelic combinations defined by these two SNPs: AB, Ab, aB, and ab. Each of these four combinations is evaluated independently of each other, providing a vector of four values that are utilized for network construction as described below.Our open-source code is available at Note that missing data should not be imputed prior to computing correlations as imputation errors are biased toward inflated LD. On the other hand, the retention of SNPs with missing data can yield unexpected consequences when combinations of SNPs are analyzed. For example, two SNPs with 20% missing data could results with up to 40% of the individuals missing one genotype value, and these individuals should not be included in an assessment of correlation between the two SNPs. Furthermore, when assessing associations for a combination of SNP alleles, the inclusion of individuals with excessive missing data for the combination can yield misleading results. BlocBuster employs several mechanisms to flag potential issues that might arise. BlocBuster omits individuals with missing genotypes for either of the SNPs in the given pair when computing CCC and warnings are printed out whenever a pair of SNPs possesses more than a user-defined percentage of individuals with missing data. Furthermore, each bloc identified as exhibiting a significant association  has the actual sample sizes utilized in the analysis printed out. Finally, all individuals are included in the visual inspection of the bloc (to be described shortly), with the missing genotypes represented by white cells. These mechanisms ensure that each pattern is correctly represented without imposing risks of imputation errors contributing to misleading associations.n nodes, where n is equal to the number of SNPs. Consequently, the allele states that exhibit correlations are lost in the network abstraction . This strategy supplies the actual alleles contributing to a pattern, not just the SNPs, and enables allele-specific testing of patterns. It may also reduce erroneous merging of distinct patterns into a single bloc, as shown in Standard SNP networks consist of traction . To overn highest CCC values are represented by edges in the network. Note that it is possible for one pair of SNPs to have more than one edge in the network and it is not uncommon to observe a high correlation between an allele pair as well as mirrored correlation between their alternate alleles. On the other hand, mirrored correlations may not exist, as demonstrated in n nodes and n edges, representing the n highest CCC values over all pairs of SNPs, resulting with an average node degree of one. If the edges were uniformly distributed, the network would consist of 443,020 doubletons, each of which was comprised of a single edge connecting two nodes; with every node connected to precisely one other node in the network. The choice of this number of edges is somewhat arbitrary, but any smaller number of edges would make it impossible for every node in the network to be connected to at least one other node, and a larger number of edges would result with a less stringent CCC threshold. The second set of permutation trials indicated that the network density could be substantially increased with low risk of introducing false-positive edges, so the number of edges could be increased. However, increasing the number of edges yields non-decreasing bloc size and non-increasing frequencies of the bloc pattern. In essence, the use of a stringent CCC threshold captures only the strongest of correlations, thereby facilitating the discovery of strong genetic patterns within the data.CCC is computed for each pair of SNPs, providing a vector of four values for each computation, with each value representing each of the possible SNP allele combinations, as described above. Then the We have observed that BlocBuster networks built from biological data consist of large numbers of singleton nodes (with no edges) and discrete blocs of nodes with relatively high densities of edges. Consequently, no clustering methods or other types of partitioning are required to separate the network. It is straight-forward to deterministically extract the blocs with a breadth-first search of the network. The SNP allele pattern that corresponds to each bloc is then tested for associations between two sets of individuals, with those that exhibit significant associations being reported to the user.www.blocbuster.org or by contacting the first author. The code was written in C++ and implemented and tested on a LINUX platform.Our open source software is freely available at A, B and C, in one cluster, if A is correlated with B and B is correlated with C, then A is implied to be correlated with C. However, this hidden assumption might not be valid, or even problematic, as different subsets of individuals may be contributing to each of the correlations. Consider the case where individuals bearing both A and B or bearing both B and C are at high risk for the disease, but individuals with only A and C are not at increased risk. Such a case would violate transitivity. For this reason, BlocBuster tests each of these patterns by tallying the frequencies of the bloc in its entirety. Furthermore, because we are interested in identifying associations with complex phenotypes, we compare the frequencies between phenotypic groups. Such tests are not straightforward for existing network approaches as current correlation metrics only indicate which pairs of SNPs are correlated and do not supply which alleles of the SNP pairs contribute to the correlations.An underlying entailment of most existing network approaches is that correlations are transitive. For example, when grouping markers into clusters, where for three markers, Since the networks were blindly built using a combination of the data for all of the individuals, it could be expected that most blocs are common at the population level, with no association to the phenotype. However, because CCC accommodates genetic heterogeneity, it might also be expected that some of these blocs exhibit significant association with the phenotype status, which is one type of heterogeneity. Three metrics were used to evaluate the significance of these patterns: odds ratio, Bonferroni-corrected p-value based on the G-test of independence, and corrected p-value based on permutation trials. These metrics were computed for all blocs that were possessed by at least ten individuals in the entire sample. Individuals that have more than 5% missing genotype values for the SNPs in a given bloc were not included in the computations. However, these individuals were included in the plots of genotype values for visual inspections, as described below.OR = ad/bc, where a and b equal the numbers of the bloc of interest possessed by the cases and controls, respectively. Each individual possesses two allelic combinations that include the SNPs in the bloc. The sum of the combinations that are not identical to the given bloc is represented by c for the cases and by d for the controls. /q(1-p), where p and q equal the frequencies of the bloc for cases and controls, respectively.) The 95% confidence interval is defined as e ∧ [ln(OR)+/−1.96 sqrt(1/a+1/b+1/c+1/d)], where ln(OR) equals the natural log of ad/bc and sqrt is the square root.The odds ratio was computed as iO and iE equal the observed and expected number of entire bloc patterns in subset i. The expected numbers of blocs were computed using the observed numbers of blocs as a 2×2 table, where the null hypothesis is that the relative proportions of each variable are independent of each other. The summation is over four subsets (corresponding to the four cells of the 2×2 table), and ‘ln’ denotes the natural logarithm.G-test is a maximum likelihood statistical significance test which converges to the chi-squared distribution more accurately than Pearson's chi-squared test In addition to using Bonferroni correction, an empirical approach via permutation trials was employed. We permuted the phenotype labels across the samples, tallied the numbers of carriers of each bloc for each of these randomized groups of individuals, and computed the G-test scores. There were 1,000 permutations and all 54,425 blocs in the original network were tested for each permutation. For each permutation, the individuals were randomly assigned into groups of 929 and 681 individuals and the bloc frequencies in these two groups were compared.In order to ensure the robustness of our results, we employed a series of validation trials, as follows.Permutation trials were utilized to test whether significant correlations might have arisen in the data by random chance. In these trials the genotypes of the individuals were randomly shuffled for each SNP. Consequently, each SNP had its original allele and genotype frequencies; the only change was that the inherent “correlations” between pairs of SNPs had been removed by randomly rearranging the genotypes across individuals. After each randomization, the CCC values for every pair of SNPs were computed. These trials indicated the likelihood that type I errors arose during computations of correlations; such errors would create false-positive edges in the network.n edges representing the n highest CCC values. We varied n from 50,000 to 500,000 edges, at 50,000 increments, and tracked the bloc of interest through these varying densities.To test the robustness of the blocs to variation of network density, we built a series of networks with Bootstrapping trials were employed in which we randomly selected half of the cases and half of the controls and computed the odds ratios and p-values for the bloc of interest. These randomized trials were repeated 1,000 times, with the odds ratio and p-value recorded for each trial. The means and the 95% confidence intervals over the 1,000 trials for each of these statistics were computed.kwww.tsp.gatech.edu/concorde.html). The individuals were reordered using this solution. Using this ordering of individuals, the genotypes were color-encoded with dark blue, light blue, red, and white representing homozygote for the protective allele, heterozygote, homozygote for the risk allele, and missing data, respectively. The matrices of genotypic values were plotted for the cases and controls, as shown in The genotype values for the significant bloc were plotted for the psoriatic cases and controls for visual inspection. We utilized our previously developed rearrangement clustering method, TSP+We tested the identified psoriasis bloc for phenotypic association in an independent data set, the Genetic Association Information Network (GAIN) Autoimmune Disease Only (ADO) data. These data are described at the beginning of this section.Table S1List of SNP alleles in 30-node bloc from 500,000 edge network.(DOC)Click here for additional data file.


The CHARGE (Cohorts for Heart and Aging Research in Genomic Epidemiology) Sequencing Project is a national, collaborative effort from 3 studies: Framingham Heart Study (FHS), Cardiovascular Health Study (CHS), and Atherosclerosis Risk in Communities (ARIC). It uses a case-cohort design, whereby a random sample of study participants is enriched with participants in extremes of traits. Although statistical methods are available to investigate the role of rare variants, few have evaluated their performance in a case-cohort design.We evaluate several methods, including the sequence kernel association test (SKAT), Score-Seq, and weighted (Madsen and Browning) and unweighted burden tests. Using genotypes from the CHARGE targeted-sequencing project for FHS (n = 1096), we simulate phenotypes in a large population for 11 correlated traits and then sample individuals to mimic the CHARGE Sequencing study design. We evaluate type I error and power for 77 targeted regions.We provide some guidelines on the performance of these aggregate-based tests to detect associations with rare variants when applied to case-cohort study designs, using CHARGE targeted sequencing data. Type I error is conservative when we consider variants with minor allele frequency (MAF) < 1%. Power is generally low, although it is relatively larger for Score-Seq. Greater numbers of causal variants and a greater proportion of variance improve the power, but it tends to be lower in the presence of bi-directionality of effects of causal genotypes, especially for Score-Seq.The online version of this article (doi:10.1186/s12863-014-0104-9) contains supplementary material, which is available to authorized users. Genome-wide association studies (GWAS) have identified hundreds of disease susceptible loci that harbor common variants, but most are not causal and explain only a small portion of the genetic risk for most diseases. The role of rare variants with minor allele frequency (MAF) < 0.05 has not been comprehensively explored in GWAS, while rare variant associations are believed to play an important role in disease etiology -12. EmerThe Cohorts for Heart and Aging Research in Genomic Epidemiology (CHARGE) Sequencing Project is a national, collaborative effort from three studies: Framingham Heart Study (FHS), Cardiovascular Health Study (CHS) and Atherosclerosis Risk in Communities (ARIC). What makes the CHARGE sequencing study different from other studies is its case-cohort design, where a cohort random sample plus selected individuals with extreme values from one or more pre-specified traits are considered for analysis. Such a study design is advantageous when investigators wish to examine multiple traits. One component of the CHARGE targeted sequencing study involves 1096 individuals from FHS, consisting of a cohort random sample of 504 study participants from the Offspring Cohort and 592 participants selected from the extremes of 11 traits.In recent years, many statistical approaches have been developed to jointly analyze multiple rare variants in aggregate-based tests to gain power. But current statistical methods for rare variant association studies rarely consider a case-cohort design, and hence potential bias in estimation and type-I error might be observed in analyses of CHARGE targeted sequencing data. The methods developed to date are generally for studies in which participants are assumed to be independent and a random representation of the general population such as case–control design. Typically, all study participants are considered for analyses in a case-cohort design; for dichotomous traits, participants affected by a specific disease or trait are considered as cases and other participants carrying other diseases or from a random non-diseased sample are considered as controls; for quantitative traits, all participants are used in genetic association studies of a specific disease trait, but potential bias in effect estimates may arise when including selected extreme values. Some participants as “potential risk carriers” for multiple traits can also make the issue even more complex. The uniquely ascertained participants in a case-cohort design with correlated traits form a non-representative dataset and may generate biases.To address the concerns regarding the case-cohort study design and application of methods for rare variants, we evaluate type I error and power of statistical methods for aggregate-based association tests of rare variants in the case-cohort study design of the CHARGE targeted sequencing project. We examine the statistical performance of commonly used methods, the Sequence Kernel Association Test (SKAT) , Score-Shttp://stattech.wordpress.fos.auckland.ac.nz/files/2012/05/design-paper.pdf). The correlation between traits was induced by an iterative process. The initial trait was generated using a t distribution with 15 degrees of freedom. The number of traits was doubled after each iteration; half were generated by adding the previous traits to a randomly generated t value, and the second half were generated by adding the negative of the previous traits to a randomly generated t value. We generated 24 = 16 traits in this manner, and we selected the first 11 traits for analysis. The correlation among the traits is given in Table We used genotypes from our CHARGE targeted-sequencing project for the Framingham Heart Study n = 1096), and we simulated correlated phenotypes to mimic the potential relationship among phenotypes in real data. We generated 11 correlated traits similar to those found in FHS for a very large population of 12,000 people, using the method described by Lumley et al.  and y0 is generated under the null hypothesis. We randomly selected a portion of rare variants with MAF < 1% as causal variants, and the effect sizes for the causal variants were calculated by 0.4*|log10(MAF)|, following the approach of Wu et al. [where u et al. . Power wWhen the total number of variants for a region was low and less than 10, we selected all variants as causal regardless of whether they are high risk or not. We had 2 such regions.When the number of high risk variants in a region was low and less than 5 and the total number of variants was between 10 and 100, we randomly selected an additional 50% of the variants as causal. We had 22 such regions.When the number of high risk variants in a region was low and less than 5 but the total number was greater than 100, we selected an additional 5% of the non-high risk variants as causal.When the number of high risk variants in a region was greater than 5, we chose all of them as causal.We assigned causal variants to have the same direction of genetic effects for phenotypes using rules 1–4. We also assigned a second set of causal variants to have bi-directional effects on phenotypes using rules 1–4 by setting the first half to have positive effects and the second half to have negative effects on the phenotypes.We selected causal variants by including all potentially functional variants as annotated by , while aNote that rules 2–4 ensure that the number of causal variants in a region is 5 or more. However, removal of variants with a high missing rate (>10%) results in several regions having the number of causal variants < 5. These regions are 1, 9, 12, 18, 39 that have 4 causal variants and region 45 that has 3 causal variants.Gij denote the genotype of the jth variant for the ith person with values of 0, 1, or 2 according to the number of rare alleles for variant j, where i = 1, 2, …, n and j = 1, 2, … P. Let Yi denote the trait, and Zik the k th covariate for participant i, where k = 1, … M. We present methods for quantitative traits, but they can readily be extended to dichotomous traits.Unweighted burden test statistic (T1-Count) [1-Count) We chose several representative analysis methods for aggregate tests to compare, including an unweighted burden test , weighti2.Weighting of Variants by a function of MAF  with MAF < 1% in a targeted region where that person carries at least 1 rare allele. Association analysis with this new variable (T1-count) and a trait is carried out using linear (for a quantitative trait) or logistic (for a dichotomous trait) regression.For each person, a statistic is computed that is a weighted count of that person’s rare alleles within a targeted, using weights based on the MAF averaged over the three studies of the CHARGE targeted sequencing-project. The approach gives more weight to rarer variants. We restricted our tests to rare variants with MAF < 1%. For a targeted region, the weighted genotype score isj. Association with this genotype score and the trait of interest can be evaluated using linear or logistic regression.3.SKAT statistics [atistics where The Sequence Kernel Association Test (SKAT) assumes the modelα0, αk and βj are regression parameters. SKAT is a general approach and uses weights computed from the data. For our purposes in testing the null hypothesis H0: β = 0, SKAT takes a simple form, where β is the vector of all βjs. For a given set of weights, the score test can be expressed aswhere yi from the model when there are no genotypes in the model. We used the Beta distribution for the weights, wj ~ Beta, with the default parameters a1 = 1 d a2 = 25 as suggested by Wu et al. [4.Score-Seq statistics [atistics where u et al. . AssociaYi to Gi and Zi using the following linear regression model,We can relate i = τSi + γTZi + ϵi, where ϵi ~ N.YSi = ξTGi, a scalar from the product of a weighted linear combination of Gi1, …, GiP with weights of ξj. ξ = T is a P × 1 vector, ξ = β/τ and τ is a scalar constant, and β is a vector of coefficients for Gi as defined in Equation , for the 77 regions for trait 1 is presented in Figure 0,000, foFrom Figure Type I error is also mostly under control when the nominal level alpha is larger at 0.05 or smaller at 0.001 . The summary is in Additional file We explored different characteristics of regions to investigate the possible explanations for the difference in power over regions. The characteristics included the total number of causal variants, the total allele count, and the proportion of the variance explained by the rare variants , the significance level and directionality. Power for Score-Seq tended to be higher, when the total number of causal variants and the total allele count were larger. Score-Seq tended to have higher power when R2 is larger. Bi-directionality does not seem to influence power much for SKAT, but lowers the power for Score-Seq. Other characteristics were also investigated in prior reports to determine the influence on power of characteristics such as the ratio of causal variants to total number of variants, effect sizes and sample sizes [We examined different characteristics of targeted regions to explore possible explanations for the difference in power across regions in the case-cohort design based on CHARGE targeted sequencing data. The characteristics that we examined included the total number of causal variants, the total allele count, the proportion of variance explained by the causal variants (Rle sizes ,14,17. Tle sizes . Our stule sizes  to generhttp://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?study_id=phs000651.v3.p8.The data set supporting the results of this article is available in the dbGAP repository,


Cluster analysis based on 22 traits grouped the 43 rice genotypes into five clusters. Cluster II was the largest and consisted of 20 genotypes mostly originating from the Philippines. The first four principle components of 22 traits accounted for about 72% of the total variation and indicated a wide variation among the genotypes. The selected best trait of the number of filled grains/panicle and yields/plant (g), which showed high heritability and high genetic advance, could be used as a selection criterion for hybridisation programmes in the future.Upland rice is important for sustainable crop production to meet future food demands. The expansion in area of irrigated rice faces limitations due to water scarcity resulting from climate change. Therefore, this research aimed to identify potential genotypes and suitable traits of upland rice germplasm for breeding programmes. Forty-three genotypes were evaluated in a randomised complete block design with three replications. All genotypes exhibited a wide and significant variation for 22 traits. The highest phenotypic and genotypic coefficient of variation was recorded for the number of filled grains/panicle and yields/plant (g). The highest heritability was found for photosynthetic rate, transpiration rate, stomatal conductance, intercellular CO Upland rice has been gaining popularity, because current high-yielding varieties have led to an increase in genetic vulnerability, a scarcity of water for irrigation, and a breakdown of resistance genes against emerging races of pathogen due to intensive cultivation. In recent decades, the increases in world rice production that have resulted from successes in research and the transfer of modern technology have mainly concerned irrigated high-yielding varieties. Research into upland rice has been very limited and most of the research findings have not been published; therefore, these successes have had virtually no effect on upland rice production. Upland rice comprises 11% of the total global rice production and is cultivated on about 14 million hectares .In Brazil, the mean yield of upland rice is about 2 t/ha, compared to about 5 t/ha for lowland or irrigated rice . In NigeTo boost the yield potential of upland rice, it is necessary to identify cultivars with improved yield and other desirable agronomic characters, to overcome the global problem of hunger and starvation, especially in African countries . GeneticThe experiment was conducted at the net house of the experimental field #10, at the Universiti Putra Malaysia (UPM) from August to December 2013. The experimental site is located between 3°02′N and 101°42′E at an altitude of 31 m above sea level. The study was laid out as a randomised complete block design (RCBD) with three replications. Metal tanks were used for planting the rice genotypes. The size of the tank was 1.85 m × 1.24 m × 0.45 m. The tank was filled with well-pulverised soil.Forty-three upland rice genotypes  obtainedPN, μmol/m/s), transpiration rate , stomatal conductance , intercellular CO2 , total number of tillers/plant , number of effective tillers/plant , panicle length , number of filled grains/panicle , number of unfilled grains/panicle , grain length , grain breadth , grain length/breadth ratio (L/B), straw yield/plant , harvest index , 100-grain weight , and yield/plant . The data were recorded based on a standard evaluation system (SES) introduced by the International Rice Research Institute [The following parameters were considered for data collection: days to flowering , days to maturity , plant height , flag leaf length , leaf chlorophyll content at 67 and 97 days after transplanting (CC67 and CC97), photosynthetic rate  and Minitab software (version 15). The genetic parameters, including the genotypic and phenotypic variance, genotypic and phenotypic coefficient of variance, heritability (broad sense), and the expected genetic advance (GA), were calculated using the formula given by Burton and DeVane (1953) and Johnson et al. (1955) , 14.σ2P) of all traits was higher than the genotypic variance (σ2G); similarly, the phenotypic coefficient of variation (PCV) was also higher than genotypic coefficient of variation (GCV). The highest PCV was recorded for the traits FG and Y, which were 72.62 and 84.36%, respectively. In contrast, the lowest PCV belonged to the characters CC67 (7.00%) and CC97 (8.25%). The GCV ranged from 4.62 (CC67) to 80.07% (Y). The next highest GCV contained the characters FG (69.73%), HI (61.60%), TT (47.17%), and SY (41.31%). Similarly, CC97 (5.78%), GL (7.87%), DM (8.14%), and DF (11.14%) were the traits observed for the next-lowest GCV. Most of the traits in the present study exhibited a high heritability. A heritability of 100% was recorded for the characters PN, E, gs, and Ci. Furthermore, a higher heritability was also recorded for FG (92.21%), Y (90.09%), and GB (85.71%). In this study, genetic advance (GA) was also calculated and ranged from 6.28% for CC67 to 156.56% for Y.The results revealed a wide range of variability among 43 upland rice genotypes for 22 quantitative traits . The pheThe Euclidean distance was calculated using standardised morphological data and a UPGMA dendrogram was constructed using these values for 43 upland rice genotypes. Five major groups were observed among 43 upland rice genotypes based on multivariate analysis at a 1.08 dissimilarity coefficient value . The valPN (0.43), E (0.40), gs (0.39), and GB (0.40) were the important parameters of the second PC.The results of PCA partly confirmed the findings of cluster analysis: in PCA, the genotypes also clustered into five groups , with onPN, E, gs, Ci, and GL, represented some degree of environmental influence on the phenotypic expression of these characters. It also suggests that selection based on these characters would be effective for future crossing programmes. The other traits, which showed a higher difference between PCV and GCV, indicated that the environmental effect on the expression of those traits is higher and that selection based on these characters is not effective for further yield improvement. The highest PCV was recorded for FG and Y. High GCV and PCV for FG and Y were also recorded by the following researchers [PN, E, gs, and Ci revealed 100% heritability, which indicated the presence of additive gene action. This also showed that selection based on these characters would be more effective and efficient than the use of other traits for segregating generations in future breeding programmes, which indicated an exploitable amount of variation. A study conducted by Jahn et al. [PN, E, and gs capacity of rice varieties under drought stress and control conditions and showed that all these parameters decrease under water stress in rice [Y showed a very high heritability coupled with the highest genetic advance, suggesting that these traits were mainly under genetic control and that they can be scored by their phenotypic performance. In a separate study of 19 upland rice accessions, Vange [The genetic analysis of quantitative traits is a prerequisite for plant breeding programmes, which can lead to a systemic method of design and to the appropriate planning of plant breeding strategies. The current study suggests that the PCV was higher than the GCV for all traits. This was also the case for all the traits observed in another study , which rearchers –18. The n et al.  reported in rice , 21. Thes, Vange  estimates, Vange .The 43 upland rice genotypes clustered into five groups based on the dendrograms of cluster analysis and PCA. The groupings of hierarchical cluster analysis exhibited a similar dendrogram topology and cluster membership to that produced using PCA analysis, thereby confirming the accuracy of the constructed dendrogram. Likewise, Worede et al.  calculatThe present study showed the existence of a considerable level of diversity among the 43 upland rice genotypes. The highest heritability recorded for the parameters photosynthetic rate, transpiration rate, and number of filled grains/panicle and yields/plant demonstrates that these traits could be successfully transferred to offspring, if selection for these characters is performed in the hybridisation programme. The aforementioned traits of number of filled grains/panicle and yields/plant showed a very high genetic advance, which implies that these characters could be used to select upland accession genotypes for a notable improvement in cultivation in changing environments, particularly under conditions of water scarcity in the tropics. Furthermore, crossing the genotypes IR 5533-13-1-1 × Beu E-Soo and IR 5533-14-1-1 × Beu E-Soo could result in heterotic expression and a large variability in the segregating generation.


Identifying genetic variants associated with complex diseases is an important task in genetic research. Although association studies based on unrelated individuals  have successfully identified common single-nucleotide polymorphisms for many complex diseases, these studies are not so likely to identify rare genetic variants. In contrast, family-based association studies are particularly useful for identifying rare-variant associations. Recently, there has been some interest in employing multilevel models in family-based genetic association studies. However, the performance of such models in these studies, especially for longitudinal family-based sequence data, has not been fully investigated. Therefore, in this study, we investigated the performance of the multilevel model in the family-based genetic association analysis and compared it with the conventional family-based association test, by examining the powers and type I error rates of the 2 approaches using 3 data sets from the Genetic Analysis Workshop 18 simulated data: genome-wide association single-nucleotide polymorphism data, sequence data, and rare-variants-only data. Compared with the univariate family-based association test, the multilevel model had slightly higher power to identify most of the causal genetic variants using the genome-wide association single-nucleotide polymorphism data and sequence data. However, both approaches had low power to identify most of the causal single-nucleotide polymorphisms, especially those among the relatively rare genetic variants. Therefore, we suggest a unified method that combines both approaches and incorporates collapsing strategy, which may be more powerful than either approach alone for studying genetic associations using family-based data. Identifying genetic variants associated with complex diseases is an important task in genetic studies, including genome-wide association (GWA) studies and whole-genome sequencing studies. Although association studies based on unrelated individuals  have successfully identified common single-nucleotide polymorphisms (SNPs) in many complex diseases, these studies are not so likely to identify rare genetic variants. In contrast, family-based association studies have the ability to identify rare variants. Moreover, a family-based study design can avoid the problem of population stratification, tend to be more homogeneous regarding early exposure to environmental factors, and test both linkage and association ,2.Multilevel models are statistical models with parameters that vary at more than 1 level  and haveFor GAW18, 200 replicates of simulated longitudinal phenotype data were available that had been generated utilizing the real pedigree structures, the imputed sequence data, and distributions of phenotypes . The ava2 r<0.02 for sequence data and 2 r<0.01 and MAF >0.05 for GWA data) to ensure no indirect associations. To assess rare variants using sequence data, we selected noncausal variants with a MAF of <0.05. We assumed an additive genetic model for all variants in our analyses. We performed the multilevel model and FBAT analyses on a single variant at a time.To investigate the powers and type I error rates of both the multilevel model and the FBAT approach, we selected causal and noncausal genetic variants, respectively, using data from GWA and sequence studies. Based on the provided answers, we found that there were 1457 causal genetic variants across all available chromosomes, of which 1020 variants were causal for SBP and 1215 variants were causal for DBP on the basis of the sequence data. Among these causal genetic variants, 149 were available in the GWA SNP data set, of which 105 SNPs were causal for SBP and 117 SNPs were causal for DBP. We also analyzed the relatively rare variants  separately. We found that among all 1457 causal genetic variants, 1019 variants were relatively rare; of those, 722 were causal for SBP and 844 were causal for DBP. To assess type I error rates, we selected the noncausal SNPs that were not in linkage disequilibrium (LD) with any causal variants (2 r<0.02). We included the top 10 largest principal components (PCs) as covariates in our analyses. The final, 3-level model we obtained was ijk = β0 + β1 × SNPij + β2 × SEXij + β3 × AGEijk + α1 × PC1ij +...+ α10 × PC10ij + µi + τij + eijkY, where ijk Yis the SBP or DBP value at time point k = 1, 2, or 3 for individual j = 1, ..., 741 within sibship i = 1, ..., 310. u, u β= 0,..., 3, and v, v α= 1,..., 10, are the coefficients (fixed effects) of the intercept and slopes of different covariates, and i, τijµ, and ijk eare the error terms (random effects) between sibships, between individuals within sibships, and between time points within individuals, respectively. The multilevel model analyses were conducted using R package lme4 [Intraclass correlation refers to correlation among observations within a higher-level unit . In general, the statistical significance of the intraclass correlation coefficient (ICC) is tested to evaluate the degree of this correlation and, therefore, is used to assess whether a multilevel model is necessary in the study of a hierarchical data set . In our age lme4 .The FBATs for all the causal and noncausal genetic variants were conducted using software package FBAT 2.0.4 ,6. The FWe investigated powers and type I error rates for the multilevel model and FBAT approach using 3 data sets: (a) GWA SNP data, in which most of the SNPs are relatively common (MAF >0.05); (b) sequence data, which include rare and common genetic variants; and (c) rare sequence data, which include only rare genetic variants (MAF <0.05). All the results were based on the 200 simulated replicates.2 r<0.01) with any of the 149 causal SNPs. When using SBP as the phenotype of interest, we found that of the 246 noncausal SNPs, 76 SNPs in the multilevel model analysis, and 77 SNPs in the FBAT approach had inflated type I error rates . The average type I error rates across all noncausal SNPs were 0.05 (SE = 0.05) for the multilevel model and 0.047 (SE = 0.035) for the FBAT approach. Therefore, the type I error rates for both approaches are comparable for the GWA SNP data . For the sequence data (rare and common variants), we employed 13,440 noncausal genetic variants that were not in LD (2 r<0.02) with any of the 1457 causal variants. Using SBP as the phenotype of interest, of the 13,440 noncausal variants, we observed 4357 variants with inflated type I error rates using multilevel model analysis and 3958 variants with inflated type I error rates using the FBAT approach. The average type I error rates across all noncausal variants were 0.06 (SE = 0.074) for the multilevel model and 0.046 (SE = 0.041) for the FBAT approach. From the noncausal genetic variants in the sequence data set, we selected 218 variants with MAF <0.05 . Using SBP as the phenotype of interest, of these 218 variants, we observed 68 variants with inflated type I error rates using multilevel model analysis, with an average type I error rate of 0.058 (SE = 0.075). The proportion of variants with inflated type I error rates and the average type I error rate was very similar to that in the studies of the first 2 data sets. However, for the FBAT approach, only 2 variants had inflated type I error rates; the average type I error rate using the FBAT approach to analyze rare variants was 0.007 (SE = 0.013). Because the type I error rates of the 2 approaches for the study of rare-variants-only data are not comparable, we conducted the power calculations for both approaches by adjusting for their type I errors. Specifically, using p values from the 200 replicates for noncausal variants , we identified thresholds for the multilevel model and FBAT approach that correspond to the controlled type I error rates and then computed powers based on these thresholds. We also investigated type I error rates using DBP as the phenotype of interest and obtained similar results (data not shown).All the results were based on a nominal significance level of 0.05. We did not perform multiple testing corrections owing to the small number of replicates (200). For the GWA SNP data, we employed 246 noncausal SNPs with MAF >0.05 that were not in LD . Most of the causal genetic variants were removed from this set because the powers using either approach were less than 20%. However, interestingly, for the rest of the causal variants, multilevel model analysis had higher power than the FBAT approach for almost all of them.We further investigated the relationships between power, effect size (unit = mm Hg), and MAF using the GWA SNP data set with SBP as the phenotype of interest. We found that variants with very high effect sizes could be identified with high power for both approaches; for example, rs11711953 had an effect size of −9.9107, and both approaches had powers of almost 100% to identify this variant at a 0.05 significance level; however, when the Bonferroni correction was applied, the FBAT's power decreased dramatically (85.5%), while the multilevel model's power remained at 100%. We also observed that both approaches had relatively low power to identify causal variants with high effect sizes but low MAFs and relatively high power to identify causal variants with low effect sizes but high MAFs, as has been shown in our previous study [It is natural to consider the use of multilevel modeling for family studies because children are nested within families -14. ReceWe considered using 3 different data sets, including GWA SNP data, sequence genome data, and rare-variants-only data. We observed that the multilevel model had consistent type I error results for all 3 data sets; in all the scenarios, approximately 30% of the noncausal genetic variants had inflated type I error rates, and the average type I error rates across all noncausal genetic variants were controlled at a 0.05 significance level. However, the FBAT approach had different patterns of type I error rates for the different data sets. The type I error rates of the FBAT for GWA SNP data and sequence data were very similar and comparable to those of the multilevel model (~30% were inflated), but the type I error rates of FBAT for rare variants only were quite conservative. Therefore, for the purpose of power comparisons, we calculated the powers of the multilevel model and the FBAT approach by adjusting for their type I error rates when studying the rare variants only. The multilevel model had relatively higher power than FBAT for most of the causal genetic variants in the GWA SNP data and sequence data. However, both approaches had poor power to identify most of the causal variants, even those with large effect sizes, especially the relatively rare variants.For future studies, we recommend a unified method combining both the multilevel and FBAT approaches, which may be more powerful than either approach alone for genetic association studies using family-based data. For the rare variants analysis, we can also employ the most commonly used strategy of collapsing methods, which combines the effects of multiple rare variants using a weighted linear combination and treats the combined variable as one variant in the analysis. This strategy has been used in family-based association studies, for instance, in the FBAT-Rare method, which linearly combines rare variants in a single gene . We woulThe authors declare that they have no competing interests.JW and SS conceived and designed the overall study, JW conducted statistical analyses and drafted the manuscript, and RY conducted data preparation and management. All authors read and approved the final manuscript.


Anorexia nervosa (AN) is a complex psychiatric disease with a moderate to strong genetic contribution. In addition to conventional genome wide association (GWA) studies, researchers have been using machine learning methods in conjunction with genomic data to predict risk of diseases in which genetics play an important role.In this study, we collected whole genome genotyping data on 3940 AN cases and 9266 controls from the Genetic Consortium for Anorexia Nervosa (GCAN), the Wellcome Trust Case Control Consortium 3 (WTCCC3), Price Foundation Collaborative Group and the Children’s Hospital of Philadelphia (CHOP), and applied machine learning methods for predicting AN disease risk. The prediction performance is measured by area under the receiver operating characteristic curve (AUC), indicating how well the model distinguishes cases from unaffected control subjects.Logistic regression model with the lasso penalty technique generated an AUC of 0.693, while Support Vector Machines and Gradient Boosted Trees reached AUC’s of 0.691 and 0.623, respectively. Using different sample sizes, our results suggest that larger datasets are required to optimize the machine learning models and achieve higher AUC values.To our knowledge, this is the first attempt to assess AN risk based on genome wide genotype level data. Future integration of genomic, environmental and family-based information is likely to improve the AN risk evaluation process, eventually benefitting AN patients and families in the clinical setting.The online version of this article (doi:10.1186/s12920-016-0165-x) contains supplementary material, which is available to authorized users. Anorexia nervosa (AN) is a complex eating disorder with psychiatric manifestations, including strong obsessive concern about gaining weight, twisted self-depiction towards body shape and eating, and extremely low food intake resulting in below-average body mass index –3. The eP value < 5E-8. Nevertheless, several genome wide marginal results have been reported, suggesting larger sample size and/or denser genotyping or high throughput parallel sequencing may be required to unveil the genetic underpinnings of AN.Recent efforts have shown that genetics plays an important role in AN susceptibility with heritability estimates from twin studies are as high as 84 % –26. The Recently, machine learning based risk prediction methods using genotyping data have gained momentum in relation with GWA studies in complex disease –46, makiLocal ethical approvals were granted for each participating study. For participants under the age of 16, written informed consent from their parents were obtained; for participants over the age of 16, written informed consent from themselves were obtained. Full names and locations of the ethic committees can be found in the end of the Additional file th Edition) diagnostic criteria (amenorrhea criterion not required). Genotyping was done using Illumina microarrays, followed by quality control and imputation /Wellcome Trust Case Control Consortium 3 (WTCCC3), The Price Foundation Collaborative Group –55 and C in ref. ). We als in ref. –59.TableThe entire dataset was randomly partitioned into three equal parts using Fisher-Yates permutation , withoutP value of 1E-6. Then we retained SNPs with genome-wide case-control association test P value < 1E-3 to the next stage. Next we employed lasso regularized LR model with ten-fold cross validation in R package ‘glmnet’ [http://cran.r-project.org/web/packages/glmnet/index.html) in fold2 data. A grid of lambda values (the regularization parameter in the model to reduce overfitting) are computed for the lasso penalty and AUC was measured to assess the performance. At the third stage, the model trained on fold2 data was then tested on fold3 data, and we calculated its AUC.In the pre-selection stage, a GWA study was conducted in fold1 using PLINK  with con‘glmnet’   and Gradient Boosted Trees with default parameters  approaches were also used thereafter to train models within fold2 and assess the performance within fold3.In order to compare different machine learning techniques, Support Vector Machines (SVM) with RBF kernels and default parameters  and Gradient Boosted Trees (GBT), and implemented them on our dataset following ten randomized repeats. While SVM provided similar performance in terms of AUC  have been identified for both T1D and IBD, allowing for high performance machine learning models to discriminate cases from unaffected controls based on genotypic information. With regard to T1D [P values < 4E-136. For IBD [IL23R region have P values < 1E-160. For both T1D and IBD, large sample sizes with approximately 10,000 patients in each case and significant contribution from the MHC region, are responsible for these successes and consequent superior disease risk prediction. Therefore with data from more AN samples in addition to the current 3940, it is highly likely that we will see better results for both the GWA effort and machine learning based risk prediction. Research into schizophrenia genetics provides a similar example in which large datasets led to the breakthrough of 128 independent genome-wide association signals [Our previous disease risk prediction efforts for type 1 diabetes (T1D)  and IBD d to T1D , more th For IBD , more th signals  followin signals .In this report, we compared multiple machine learning methods LR, SVM and GBM. Results suggested that LR and SVM are similar in terms of AUC values, while GBM showed lower performance. From a practical perspective, the LR results are promising and LR models are easier to interpret and construct than SVM, although the current result requires improvement if genotype based AN risk prediction is to be used clinically. GBT is good at capturing interacting effects and may not be optimal when true models are linear. We have many SNPs typed thus it is likely interacting SNPs, if any, may already be interrogated well by a single SNP. In addition, here the number of SNPs is much larger than the sample size; a simple linear model may be more robust to over-fitting than assuming complex tree structures. We also tried to use random forests (RF) as well, but due to high time complexity and slow convergence this methods was excluded from the analysis. Further investigation is required to assess the performance of RF. Moreover, we can compare these methods with different parameter combinations and settings when a larger cohort of AN samples are available.We shuffled LR model 10 times and got variable number of SNPs as predictors, with the observation that three SNPs are always in the shuffles , and two SNPs (rs10250561 and rs16835204) are in 9 of the 10 shuffles. Those SNPs have the highest p values (from 4.39E-6 to 3.05E-4) in the fold1 GWA study. In light of AN’s high heritability  and currUsing machine learning techniques, here we present the first AN risk prediction study based on genome wide genotype data. Our results indicated higher performances of LR and SVM as opposed to GBT, with the greatest discriminative value AUC being 0.693 for the linear model. In addition, we showed that larger sample sizes can improve the machine learning risk prediction outcome, urging expanded AN case collection through international collaboration. With more genomic and other data in a greater sample pool, our study and the motheds we used will serve as the first step toward genomic screening of AN risk in a clinical setting.https://www.med.unc.edu/pgc/downloads).Anorexia nervosa case summary statistics can be found at the PGC website , after rerunning 10 times. Table S3. AUCs of different size for training dataset , after rerunning 10 times. Member lists of the Genetic Consortium for Anorexia Nervosa (GCAN)/the Wellcome Trust Case Control Consortium 3 (WTCCC 3)/the Price Foundation Collaborative Group. Supplementary acknowledgements. Ethic committee information. (DOCX 45 kb)Additional file 2: Figure S1.ROC curve for linear regression model in shuffle 1. (PDF 17 kb)