In population association studies, standard methods of statistical inferenceassume that study subjects are independent samples. In genetic associationstudies, it is therefore of interest to diagnose undocumented close relationshipsin nominally unrelated study samples.R package CrypticIBDcheck to identify pairs ofclosely-related subjects based on genetic marker data from single-nucleotidepolymorphisms (SNPs). The package is able to accommodate SNPs in linkagedisequibrium (LD), without the need to thin the markers so that they areapproximately independent in the population. Sample pairs are identified bysuperposing their estimated identity-by-descent (IBD) coefficients on plots of IBDcoefficients for pairs of simulated subjects from one of several common closerelationships.We describe the CrypticIBDcheck are particularly relevant tocandidate-gene association studies, in which dependent SNPs cluster in arelatively small number of genes spread throughout the genome. The accommodationof LD allows the use of all available genetic data, a desirable property whenworking with a modest number of dependent SNPs within candidate genes.CrypticIBDcheck is available from the Comprehensive R Archive Network(CRAN).The methods implemented in  CrypticIBDcheck, an R)eck, an R package The relatedness between two individuals may be defined in terms of the proportion ofloci at which they share zero, one or two alleles that are identical-by-descent (IBD).We refer to these proportions as the actual IBD-sharing coefficients, or IBDcoefficients. The alleles from two individuals are IBD if they are descended from acommon ancestor in a given reference population . ThoughCrypticIBDcheck uses estimated IBD coefficients to summarize possiblerelationships among pairs of study subjects. The approach is exploratory andgraphically-based, similar to the GRR approach of [ibdPlot function of theGWASToolsBioconductor package.roach of  and the roach of implemenGRR calculates and displays the mean and variance of IBS allele sharing over polymorphicloci for each pair of individuals. Pairs of known relationships form reference clusterson the plot, allowing the user to identify errors in reported relationships. Inassociation studies of nominally unrelated individuals, however, there are no referenceclusters available. In principle, reference clusters could be obtained theoreticallyfrom the joint distribution of the IBS mean and variance estimators, but it is unclearhow to derive this distribution in the presence of LD.ibdPlot function in GWASTools may be applied to viewestimated IBD coefficients along with reference clusters for the unobserved, true IBDcoefficients based on theoretical moments of their distribution [The ribution . HoweverCrypticIBDcheck is to identify closely-related study pairs bydisplaying their estimated IBD coefficients together with those from simulatedpairs of known relationships. The simulated reference pairs provide an empiricaljoint distribution of the IBD estimators under selected relationships which, in turn,suggest possible relationships amongst study pairs. Working with simulated pairs fromknown relationships avoids having to derive the joint distribution of the IBD estimatorswhen the genetic markers are in LD. Simulated pairs are obtained by gene drop on arelationship-specific pedigree, with pedigree-founder haplotypes drawn from a fittedhaplotype model that accounts for LD [Examples section).The idea behind s for LD . We haveMethods section we describe the IBDestimators and methods for gene drop simulation in the presence of LD to obtainreference clusters. The Results and Discussion section describes implementationdetails provides two examples of how to use the package. The paper ends with aConclusions section that includes ideas for future work.The paper is structured as follows. In the There are two common approaches to estimating IBD coefficients: maximum likelihood-12 and tA and a, a pairof individuals that are, say, AA and aa, respectively, will bedenoted .In this section, we review a popular method of moments approach to estimating IBDcoefficients introduced by  andimplI and identity-by-descent by the random variable Z, withpossible states being 0, 1, and 2 for both random variables. The IBD coefficients tobe estimated are the proportions of genome shared IBD, denoted byP(Z = 0), P(Z = 1), and P(Z= 2). For a given SNP m, the procedure begins by expressing the priorprobability of IBS sharing asIdentity-by-state (IBS) for a pair of subjects is denoted by the random variableP(Z = z) and Pm(I =i) are specific to the pair of subjects being considered, while theconditional SNP-specific IBS probabilities Pm(I= i|Z = z) apply to all pairs. For a given pair ofindividuals at a given SNP, the above equation specifies three identities for the IBSstates 0, 1, and 2. These three identities are summed over SNPs and then rearrangedto express P(Z = 0), P(Z = 1), andP(Z = 2) for the pair in terms of marginal and conditional IBSprobabilities. For example, in the case of i = z = 0, we obtainPm(I = i|Z =z), pertaining to any pair and the pair’s marginal SNP-specific IBSprobabilities, Pm(I = i), into theidentities and then solving for P(Z = i).The method-of-moments estimators of IBD coefficients for a given pair are obtained bysubstituting estimators of the conditional SNP-specific IBS probabilities,Pm(I = i) for a pair of subjectsmay be estimated by the indicator function for whether the pair has I =i at the SNP. An unbiased estimator of i alleles IBS.Estimates of the SNP-specific conditional IBS probabilities,Pm(I = i|Z =z), are based on data from all subjects in the sample. Derivation ofunbiased estimators of Pm(I =i|Z = z) is more involved. To simplify notation, wetemporarily drop the SNP subscript m. If p and q =1−p denote the frequencies of A and a in the basepopulation, then P(I = i|Z = z) is afunction of p and q. For example, two individuals share 0 allelesIBS if they are either  or . Given that Z= 0, the probabilities of these genotypes arep2q2 andq2p2, respectively, leading toP(I = 0|Z = 0) =2p2q2. The plug-in estimators ofconditional IBS probabilities, such as P(I = 0|Z=0),obtained by inserting estimators The marginal SNP-specific IBS probabilities,X and Y be the counts of the alleles A and a,respectively, so that the allele frequency estimators are T is twice the number of observed genotypes in the population randomsample. The estimators of the conditional IBS probabilities P(I =i|Z = z) may be motivated by the following model. Thegenotype of each individual in the present population is obtained from twoindependent draws from an infinite base population of alleles. Consequently, theT alleles of a population random sample of study subjects can be viewedas a random sample from the base population. Moreover, conditional on IBD status, anypair of individuals in the present population can be viewed as independent allelicdraws from the base population, with the number of draws determined by their IBDstatus.Let Z = 0, a random pair of individuals results fromrandomly drawing two pairs of alleles from the base population. An indicator variableof whether this sampling process results in I = 0 is an unbiased estimatorof P(I = 0|Z = 0). An unbiased estimator is therefore theaverage of these indicator variables over all possible draws from the Talleles on which we have data; i.e., the proportion of pairs of allelic pairs withI = 0. The proportion can be computed as follows. The number of ways ofselecting four distinct alleles from a total of T is T(T− 1)(T − 2)(T − 3). Without loss of generality,suppose the first two alleles are assigned to the first individual in a pair and thelast two alleles to the second individual. Then the number of pairs that are  and  are X(X −1)Y(Y − 1) and Y(Y −1)X(X − 1), respectively. Hence,For example, in the case of P(I=0|Z=0) .The number of ways to select three distinct alleles from a total of T isT(T − 1)(T − 2). Among these, the genotypepairs that are I = 1 are the X(X − 1)Y,YX(X − 1), Y(Y −1)X, and XY(Y − 1) that are , , , and ,respectively. Thus,For The other conditional IBS probabilities are estimated in an analogous manner andtheir expressions are provided in Table one of .With estimates L is the total number of SNPs with genotype data on both individuals.For any pair of subjects, summing equation (1) over all the SNPs and using equation(3) gives the following method-of-moment estimators of the IBD coefficients:where Adjustments to bound these estimators to values consistent with their interpretationas IBD proportions were proposed in . WehaveThe package provides a graphical display that can be used to identify related samplepairs by plotting the estimated IBD coefficients s for LD . AstrenA graphical model is an approach to modeling the joint distribution of a set ofdependent random variables when many independences or conditional independences existbetween subsets of the variables. In the case of LD, it is expected that the jointdistribution of alleles allong haplotypes shows such a structure. A flexiblegraphical model of haplotype frequencies that captures LD between loci is describedin . The modOnce the LD model is fit, it is used to sample haplotypes for the founders of apedigree. Data on the remaining members of the pedigree are simulated by gene drop.Gene drop is a method for randomly generating the genotypes of related individuals ina pedigree. Alleles are “dropped” from the founders through the pedigreeaccording to Mendel’s laws. Multi-locus gene drop incorporates the process ofrecombination. To illustrate the simulation procedure, consider a parent-offspringrelationship. A pedigree that encompasses this relationship is one comprised of twoparents and the offspring. The founders are the parents. Parental haplotypes aresimulated from the fitted LD model and are then dropped to the offspring. To mimicreal data with missing genotypes, selected genotypes for a simulated individual areset to missing according to the missing genotype pattern of a randomly-sampled studysubject.http://balance.med.utah.edu/wiki/index.php/JPSGCS). We use theR package rJPSGCS[Programs for fitting LD models and performing gene drop simulations are available inthe Java Programs for Statistical Genetics and Computational Statistics (JPSGSC)library developed by Alun Thomas or not (FALSE) each subjectis to be used to estimate the conditional IBS probabilities and fit the LD model.Optionally, the SNP information may include genetic map positions, in centiMorgans.If genetic map positions are missing, they are inferred assuming the physicalpositions are from build 36 of the human genome. Users with SNP data on diploidnon-human organisms, such as mouse or drosophila, must supply their own genetic mappositions. The documentation for new.IBD and the examplesbelow provide further details. The function filter.controlsets options for quality control filtering of data by SNPs and by subjects, while thefunction sim.control sets options that control simulation ofsubjects by gene drop. The respective help files and the examples below providefurther details. As the fitting of LD models in IBDcheck canbe computationally demanding, users have the option of splitting computations acrossa snow cluster [IBDcheck is an object of classIBD, which includes the estimated IBD coefficients for pairsof study subjects and for simulated pairs with known relationship.The arguments of package , a data  cluster , as descIBD objects are graphically displayed by the plot method ofthe class; the documentation for this method is available throughhelp(‘‘plot.IBD''). Plots are ofIBDcheck is to omit simulated pairs from the object. Whensimulated pairs are omitted, plotting produces a single interactive display ofestimated IBD coefficients for pairs of study subjects, on which points may beidentified by clicking with the mouse. On the other hand, when theIBD object includes simulated pairs, the function returns aseries of plots, which the user is prompted to view and interact with successively.The first plot to appear is non-clickable and shows the estimated IBD coefficientsfor all pairs of study subjects, along with the prediction ellipse for unrelated,simulated pairs. Subsequent plots are clickable and correspond to each relationshiprequested in the call to IBDcheck. Theserelationship-specific plots are for identifying pairs of study subjects which couldhave the relationship. The plotting regions are restricted to the neighborhood of theprediction ellipse for the simulated pairs of that relationship, which is also drawn.If, however, the plotting region overlaps with the prediction ellipse for simulatedunrelated pairs, the ellipse for simulated unrelated pairs is drawn as well. Pointsfalling within the prediction ellipse for the relationship and outside the predictionellipse for unrelated pairs are automatically flagged. In addition, users may clickon points of study pairs that appear to be related but are not automatically flagged.The plot method produces a data frame of information on pairs that have been flaggedon the different plots, either automatically or interactively by the user throughclicking the mouse.CrypticIBDcheck packageusing the genetic data Nhlsim that comes with the package.These data were simulated to mimic the characteristics of SNP genotypes in subjectsof European ancestry from a candidate-gene, case-control study of non-HodgkinLymphoma [snp.matrix object calledsnp.data with genotypes for 108 controls and 100 cases;(ii) a vector chromosome of chromosome numbers for each SNP;(iii) a vector physmap of physical map positions of each SNP,from build 36 of the human genome; and (iv) a binary vectorcsct with value one for cases and zero for populationcontrols. The binary vector csct is used to select controlsfor fitting LD models and estimating conditional IBS probabilities. All of theinformation in Nhlsim is required to runIBDcheck.We illustrate the features of the Lymphoma . The datDefault analysis with LD model fitting andgene drops), we illustrate basic use of IBDcheck tofit LD models and do gene drop simulations. Once the user requests simulations, thereare a number of parameters, such as the types of relationships to simulate, thatcontrol the simulations. Each simulation parameter has a default value, as describedin the help file for sim.control. In the first example weuse these default settings. In the second example , we illustrate re-use of fitted LD models to performadditional gene drop simulations, this time for a user-specified relationship. Forexamples of how to use IBDcheck to explore genome-wide data,we refer readers to the package vignette IBDcheck‐hapmapthat illustrates an analysis of genome-wide data from HapMap, using thinning ofmarkers to reduce the computational burden.We present two examples. In the first  for estimating conditional IBS probabilities andfitting LD models.Next we create an object of class filter.control) at their default values. We usesim.control to modify the default value ofsimulate=FALSE to simulate=TRUE,so that reference clusters are simulated.In this illustration, we leave all QC filtering options  versus P(Z=0), for allpairs of study subjects, with the prediction ellipse for unrelated pairssuperposed. The level of the prediction ellipse is left at its default value ofellipse.coverage=0.95 and, for unrelated pairs, isadjusted to account for the majority of study pairs being unrelated. Specifically,a Bonferroni-type adjustment,1−(1−ellipse.coverage)/np,is applied, where np is the number of pairs of studysubjects. One purpose of the prediction ellipse is to avoid confusing the displayby adding points for simulated pairs. Another purpose is to avoid having tomanually click points for study pairs that appear within a cloud of points fromsimulated pairs. We adopted a bivariate normal approximation to the predictionellipse because it correctly identified the majority of points in experiments withsimulated data  for the given relationship andoutside the prediction ellipse for unrelated pairs are automatically flagged. Inaddition, these plots are clickable, and points flagged manually are added to theoutput dataframe. For example, on the plot for half-siblings, the pointcorresponding to the pair sub35 andsub95 has been manually flagged , we obtain16 false-positive half sibling pairs. These observations highlight thatnaïvely ignoring the dependence among SNPs produces reference clusters thatare too tight relative to the true variability.The unrelated pair flagged as a potential half-sibling pair is a false-positiveresult. We observed (results not shown) that the number of false-positive relatedpairs is greatly increased if we fail to take the LD between SNPs into account.Specifically, if we repeat the simulation of unrelated and half-sibling pairs ofsubjects assuming independent SNPs  the predictionellipse for simulated mother-daughter pairs where the daughter is inbred is verysimilar to that from simulated pairs where the daughter is not inbred . Inour experiments with the example data set Nhlsim, containing 1249SNPs from 209 genes, between 325-350 SNPs from about 60 of the candidate genes appearsto be adequate for identifying the parent-offspring and full sibling pairs that arepresent. There is no upper limit on the number of SNPs that may be used. However, thecomputational time for fitting LD models scales approximately linearly with the numberof SNPs [IBDcheck‐HapMap.To provide guidance on the numbers of SNPs for which of SNPs . For theIBDcheck, or specify their ownrelationships, as illustrated in the section Additional gene drops usingpreviously-fit LD models.We offer the user complete flexibility with respect to the type of relationships andnumber of pairs of each relationship to be simulated. Users can choose from a number ofclose relationships built-in to A reviewer has pointed out that it would be useful to allow the reference distributionsof IBD coefficients, represented as ellipses on the graphical displays, to beconditional on the patterns of missing genotypes in a particular pair of subjects. Theintent is to allow for a two-stage analysis. In the first stage, potentially relatedsubjects are identified using the current implementation of reference distributions,which are mixtures over the patterns of missing genotypes in all pairs of subjects. Inthe second stage, the reference distributions can be customized to be conditional on themissing data patterns of a pair of subjects identified in the first stage. For anassessment of whether the pair of interest has a particular relationship, distributionsconditional on that pair’s missing data patterns are the most appropriate. We planto implement an option to use a specific missing data pattern to generate the referencedistributions in a future release of the package.IBD: Identity by descent; IBD: Identity by state; LD: Linkage disequilibrium; MLE:Maximum likelihood estimator; MME: Method of moments estimator.The authors declare that they have no competing interests.R package. JGconceived of the R package, contributed to writing of the manuscript andcontributed to development of the R package. BM contributed to writing of themanuscript and lead the development of the R package. All authors read andapproved the final manuscript.ANS drafted the manuscript and contributed to development of the Bias of conditional IBS estimators. This is a PDF file that includes acalculation of the bias of the plug-in and unbiased estimators ofP(I=0|Z=0). Bias calculations for estimators ofother conditional IBS probabilities are similar.Click here for fileSplitting computations over a snow cluster. This is a PDF file thatprovides details of how to split CrypticIBDcheck computations across acompute cluster.Click here for file


We present a statistical framework for estimation and application of sample allele frequency spectra from New-Generation Sequencing (NGS) data. In this method, we first estimate the allele frequency spectrum using maximum likelihood. In contrast to previous methods, the likelihood function is calculated using a dynamic programming algorithm and numerically optimized using analytical derivatives. We then use a Bayesian method for estimating the sample allele frequency in a single site, and show how the method can be used for genotype calling and SNP calling. We also show how the method can be extended to various other cases including cases with deviations from Hardy-Weinberg equilibrium. We evaluate the statistical properties of the methods using simulations and by application to a real data set. These tng e.g., , in humang e.g., , in geneng e.g., , in popung e.g., , and in STF  downloadable from i/2k in a sample of k diploid individuals, be ip. The SFS is then given by the vector . We here consider an expanded version of the SFS: the vector P =  , i.e. we also consider sites in the alignment that are fixed. The zero category then represent sites in which all individuals are homozygous for the ancestral allele, and the 2k category represents sites that are fixed for the derived allele. The SFS also exists in a so-called folded version, P* = i<k and i = k. The folded version of the SFS is often used when no reliable information can be used to determine which allele is ancestral and which is derived.The SFS describes the distribution of allele frequencies. Let the proportion of SNPs, with a derived allele frequency of p, as in the preceding section, and the latter by f. Most of the methods discussed in this paper concerns sample allele frequencies, but we also occasionally discuss the use of population allele frequencies. A number of previous papers have focused on population allele frequencies, including As a note of notation, we distinguish between population allele frequencies and sample allele frequencies by denoting the former by 10 likelihood ratio relative to the most common base. Standard next-generation sequencing methods provide such quality scores associated with each base call. However, the raw quality scores are often not very accurate and must be re-calibrated taking observed error rates in the data into account. The objective of this paper is not to explore different methods for calculating and calibrating quality scores. The methods presented here can be used based on any method for calculating quality scores. However, in our data analyses we use a method similar to the method currently implemented in SOAPsnp i of a particular site as a likelihood of a particular allele, b ∈ B, B = {A, C, T, G}. The genotype likelihood, in a site covered by r reads, can then be obtained as the product of individual allelic likelihood values . However, this is not the same as assuming Hardy-Weinberg Equilibrium (HWE) as the probability is calculated conditional on the genotype. Posterior probabilities will, in contrast, depend either on HWE assumptions or on an explicit modeling of deviations from HWE. It is also important to notice that the modeling of the error structure in the data is done through the calculation of the genotype likelihood.For low coverage data, estimation of allele frequency for a particular site can be associated with great uncertainty. Likewise, SNP calling for rare SNPs can be difficult. However, as shown in the Results section based on methods developed here, the joint estimation for multiple sites in the genome of the distribution of allele frequencies, and the number of SNPs can be carried out with quite high accuracy.k individuals there are 2k+1 possible sample allele frequencies including 0 and 1. The vector of parameters is then P =  defined on the unit simplex ip ≥ 0 for all i}. These sample allele frequencies define the SFS with fixed ancestral and derived alleles included. The ith sample allele frequency, ip, is the proportion of sites in the sample in which the derived allele has a frequency of i/2k in the sample, i = 0,1,..,2k. As the sample allele frequencies must sum to one, there are 2k parameters to estimate. Estimation of these 2k parameters assumes that the ancestral state of each SNP can be identified using outgroups (e.g. other primates for humans). However, if the identification of ancestral state is uncertain, the frequency spectrum can be folded, i.e. the number of observations in category i and category 2k-i can be added together as described in the results section. For next-generation sequencing data P is not known, but must be estimated from the data. An estimate of P also provides an estimate of the fraction of variable sites (SNPs) in the sample as 1 – p0 – pk2. Notice that there is here an implicit assumption that at most two nucleotides are present in the locus. We will later describe how to take into account the presence of more than two nucleotides, but will for now assume that there are at most two alleles, an ancestral allele (a) and a derived allele (A), and that they can be unambiguously identified in each site, except for sites with only one allele.Consider a statistical model in which the sample allele frequencies are free parameters, i.e. for P can be defined as a function of the genotype likelihood values. Letd in site v. The genotype counts the number of derived alleles, i.e. d in site v can then, with this expanded notation, be written as P, in site v would be found by taking the product of the probability of the data given the sample allele frequency multiplied by the probability of the sample allele frequency, given P, and then summing over all possible values of the sample allele frequency:Assuming that genotype likelihoods can be calculated as discussed above, a likelihood function for where the functionAS alleles of the derived type. This expression assumes Hardy-Weinberg equilibrium.is the combinatorial probability that a sample contains the labeled genotype vector P must, therefore, be obtained by summing over all the unknown genotypes:However, the true genotypes are not known. The likelihood function for Assuming independence among sites, we then multiply the likelihood among allsites and obtain:k and v directly, a simple dynamic programming algorithm can be devised that greatly simplifies these calculations.This likelihood function is the one underlying the EM algorithm applied in v in the notation to enhance readability:The first step in the algorithm is to calculate the likelihood function for each site, Initialization:jh = 0 for j = 3,4,…,2k.Set Recursiond = 2, 3,…, k:For j = 2d, 2d-1,…,2:For Seth1 = p(dX | dG = 0)h1 + p(dX | dG = 1)h0Set h0 = p(dX | dG = 0)h0Set Terminationj = 0,1,2,…,2k.Set The likelihood function can then be expressed asjh calculated for the vth site (k+1)×S, where S is the total number of sites, the likelihood function can be re-calculated very fast for different values of P. Notice that the computational speed is O(k2S). Similar algorithms have been used for single site inferences in where k+1 dimensional parameter space instead of a 2k+1 dimensional parameter space.We have here assumed an unfolded (polarized) frequency spectrum. However, the algorithm can also be applied directly to folded data, but with a P using the BFGS algorithm k+1 to 2k parameters. The transformation used isAfter tabulation of values of θ = (θ1… θk2) using analytical derivatives. Application of standard calculus techniques lead to the following derivatives of the log likelihood function for the transformed parameters:We then optimize the log likelihood function with respect to the transformed parameters θ, and the estimates of the natural parameters, P, can be found by using the transformation in eq. (6).The BFGS algorithm can then be applied to The representation given above assumes that the ancestral and derived (if it exists) alleles always can be unambiguously identified. However, for most next-generation sequencing data, there might be considerable difficulties in separating errors from true low frequency alleles. If the ancestral allele is the common allele, identification of the derived allele will then be ambiguous. The frequency spectrum is only properly defined for di-allelic loci. The approach we will take to this problem is to assume that all loci are truly di-allelic, and errors are responsible when more than two alleles are observed. For most human data, mutation rates are so low that this should be a reasonable approximation. The likelihood function can then be modified by calculating the likelihood for each locus assuming any of the three possible derived alleles, and then adding these likelihood values together, weighted by the probability that each possible derived allele is truly the derived allele. This probability has been set to 1/3 in all analyses presented in this paper. But we note that the inference method could potentially be improved by instead using empirical substitution matrices for this weighting.We also note that a situation might arise where the inferred ancestral allele is not observed in the data, but two other alleles are segregating, both at high frequency. In these cases the unfolded frequency spectrum is not well-defined. Such loci are typically ignored in population genetic analyses, and will also be ignored here.To estimate the sample allele frequency in a single site, we could in theory sum the posterior expectation of the marginal allele frequency calculated for each individual together for all individuals. However, in most applications it will be desirable to obtain the joint posterior distribution for the allele frequency, as downstream inferences then can be performed by integrating over this distribution.The ML estimates can be used directly in inferences in individual sites for SNP calling, genotype calling, and estimation of allele frequencies. In particular, an Empirical Bayes (EB) method in which the ML estimates are used to make inferences for each individual site might have desirable properties. The posterior probability of the allele frequency in a particular site is given byas in jarg max{p(mS = j | X)}. As we often will be interested in SNP calling and genotype calling in all sites, and not only in sites in which the ancestral base is among the segregating nucleotides, inferences can be done using the folded, rather than the unfolded, frequency spectrum. To calculate the posterior probability, we then need to sum over foldings, and over assignments of derived and ancestral alleles:A point estimate of the sample allele frequency can then be obtained as Finally, if we wish to take into account uncertainty in the assignments of ancestral and derived alleles, we need to sum over all possible pairs of segregating alleles:jh calculated assuming a is derived and b is ancestral, and the sum is over all ordered pairs  ∈ B2. There is here an implicit assumption of equal weighting of all possible alleles as ancestral and derived. The method could possibly be improved by using a more careful weighting using empirically derived proportions of segregating nucleotide pairs.where The expression given above can be used directly for SNP calling using a fixed cut-off forIf SNP calling has already been performed based on the same data, so that only sites expected to be variable are included in the analysis, estimation of allele frequencies should proceed by conditioning on the site being variable in the sample, by modifying the denominator in the expression above to reflex that zero probability is assigned to the event h and g.The framework derived above for allele frequency estimation and SNP calling can also be used for estimating individual genotype probabilities, leveraging information from all other individuals in the genotype call for a single individual. We will assume that the site has already been called to be variable with a SNP of a specific type with nucleotides d, then becomesThe posterior probability for a genotype for an individual, andd has genotype j ∈ {0, 1, 2}, j indicating the number of derived allele, with g as the derived and h as the ancestral allele. d-1, d+1,.., k). This algorithm for estimation of genotype probabilities, therefore requires recalculation of the jh functions for all k possible subsets found by excluding one individual from the data.Here, the event We notice thatLikewise, the numerator becomesIn cases where SNP calling precedes genotype calling, the summations in the numerator and denominator should be modified to appropriately condition on variability.a, b) could possibly be used to improve the estimates. Finally, we note that these expressions assume Hardy-Weinberg equilibrium.Again, specific weighting schemes for the pairs  procedure in that a parameter of the prior for each individual is estimated jointly based on all individuals . We will use the maximum likelihood estimator of population allele frequency  described by f. In such cases, it might work better to obtain joint ML estimates of genotypes from all individuals using an EM algorithm with f as the latent variable, to use a full Bayesian approach integrating the joint likelihood function all individuals over f, or to revert to the previously discussed methods which does not rely on estimation of f. When k is relatively large , the EB procedure should provide marginal posteriors for the genotypes from each individual close to the ones that would have been obtained using a full Bayesian approach.f obtained for each site independently, but jointly for all individuals: the maximum likelihood estimator described by mS <2k.Similarly, we will use an estimator of We are then interested in obtainingX =  now is the vector of read data for all individuals. The variable ‘var’ indicates the event that the site is a variant, i.e. 0 < mS <2k. Termination stepand Terminationj,h =  j = 1,2,…,2k-1.Set The posterior probabilities are then given byp(mS > k | X) >0.5. Alternatively, the results can be polarized with respect to ancestral and derived allele or be folded. The allele frequency can then be estimated as the value of j that maximizes mS.After completion of the algorithm, status of major and minor allele might then appropriately be re-assigned if this is used in the downstream inferences and if dF, has been estimated for individual d, d = 1, 2, …, k. dF can take on both positive and negative values. Let The EB estimator of allele frequency can also be modified to incorporate deviations from HWE. Assume that an inbreeding coefficient, Initialization:jh = 0 for j = 3,4,…,2k.Set Recursiond = 2, 3,…, k:For j = 2d, 2d-1,…,2:For Seth1dm0p(dX | dG = 0)h1 + dm1p(dX | dG = 1)h0Set h0 = dm0p(dX | dG = 0)h0Set Terminationjhj = 1,2,…,2k-1.Set The posterior probabilities can then be evaluated as before.x) was assumed to be proportional to 1/x in the population. Each site is assumed to be variable with probability varp. Errors are introduced randomly an symmetrically among all bases. Genotype probabilities are calculated according to the model assuming known error rates. We also compared methods by examining their performance on real data. This was done using HapMap data with known genotypes (the reported genotype error rate is <0.1%).To compare methods we conducted simulations under simplified assumptions. In all simulations, except if otherwise stated, we simulated data by allowing a Poisson distributed number of reads for each individual in each site independently of each other. The distribution of allele frequency , where X is all the sequencing data from multiple individuals and multiple sites. This is the likelihood function underlying the EM algorithm for estimating the SFS presented in In the Methods section, we described a likelihood function for To evaluate the method, we simulate data with known error rates , mimickiθ ( = 4Nµ where N is the population size and μ is the mutation rate) when using low or moderate coverage shotgun sequencing data. The same effect is observed for estimation of the SFS. Using filters in which only high confidence genotypes are called leads to new biases because it is easier to call homozygous than heterozygous individuals. This bias will affect different allele frequency categories differentially and lead to biases in the estimate of the SFS. θ should instead take the inherent uncertainty in the data into account. The method developed here is a conceptual extension of this concept to the SFS.To illustrate the difference between the new method and methods based directly on genotype calling, we compared with the case where the most likely genotype is chosen, with and without filtering of genotypes with low confidence . ClearlyThe method used for inferences of the SFS for a whole genome or for a large set of sites, can also be modified to make inferences for a single site X high quality reads of the minor allele, and (2) a likelihood ratio test based on testing the null hypothesis that the minor allele frequency is zero . The SFS method is the main method described in the text. The GC method is based on genotype calling using the genotype with the highest posterior probability. The LR method is based on a likelihood ratio test of the hypothesis that the allele frequency is zero. larger panels of individuals.(DOC)Click here for additional data file.Figure S2The error rate of different genotype callers for different call rates. The SFS-method is the method described in the main text. The MAF method is based on first obtaining a maximum likelihood estimate of the allele frequency, and then use the estimated allele frequency to define priors for genotype calling. The GC-max method is based on calling genotypes with highest posterior probability. The GC-ratio method is based on calling genotypes depending on the ratio of the likelihood for the most likely to second most likely genotype. The jagged behavior of some of the curves is a consequence of the discrete nature of the data, i.e. an individual contains a discrete number of copies of the minor allele. 10 individuals are simulated for 50,000 variable sites with a distribution of allele frequencies (p), proportional to 1/p and with a varying error rate.(DOC)Click here for additional data file.


Here we present two new computer tools, PREMIM and EMIM, for the estimation of parental and child genetic effects, based on genotype data from a variety of different child-parent configurations. PREMIM allows the extraction of child-parent genotype data from standard-format pedigree data files, while EMIM uses the extracted genotype data to perform subsequent statistical analysis. The use of genotype data from the parents as well as from the child in question allows the estimation of complex genetic effects such as maternal genotype effects, maternal-foetal interactions and parent-of-origin (imprinting) effects. These effects are estimated by EMIM, incorporating chosen assumptions such as Hardy-Weinberg equilibrium or exchangeability of parental matings as required.In application to simulated data, we show that the inference provided by EMIM is essentially equivalent to that provided by alternative (competing) software packages such as MENDEL and LEM. However, PREMIM and EMIM (used in combination) considerably outperform MENDEL and LEM in terms of speed and ease of execution.Together, EMIM and PREMIM provide easy-to-use command-line tools for the analysis of pedigree data, giving unbiased estimates of parental and child genotype relative risks. Genomewide association studies have popularized the use of the case/control design to detect effects associated with an individual’s own genotype, however many diseases  may in fact be due to more complex effects such as maternal genotype effects, maternal-fetal genotype interactions or parent-of-origin (imprinting) effects. To detect such effects it is necessary to collect genotype data from one or both parents of cases, in addition to genotyping the cases themselves. Two existing popular approaches analyse either genetic data from affected offspring and their mothers (case/mother duos), along with an appropriate control sample -3, or elFull details and evaluation of the multinomial modelling approach used by EMIM have been described previously . The earFor each SNP in turn, PREMIM performs a simple algorithm to select from each pedigree the most informative sub-unit of child-parent genotype data. Different pedigree sub-units are chosen in order of preference as listed in Table There are a number of options that may be given to PREMIM. In particular, it is possible to override the default choice of individuals by stating a proband subject for certain pedigrees. These proband subjects are then chosen as cases (with parents where available). This may be useful to avoid possible bias when larger pedigrees have been ascertained on the basis of a specific affected individual. For larger pedigrees, it is also possible to select multiple case/parent trios or multiple control matings from each pedigree, potentially increasing the power to detect genetic effects. This option does have the potential to generate bias , andR1(R2) the factor by which an individual’s disease risk is multiplied if they possess one (two) risk alleles at a given locus. We denote by S1(S2) the factor by which an individual’s disease risk is multiplied if their mother possesses one (two) risk alleles at that locus. We denote by Im(Ip) the factor by which an individual’s disease risk is multiplied if they inherit a risk allele from their mother (father). Lastly, to test for mother-child interactions, we denote by γij the factor by which an individual’s disease risk is multiplied if the mother carries i risk alleles and the child carries j risk alleles. A summary of these relative risk parameters is shown in Table The basic principle behind EMIM is simple: to test for the existence of (and estimate) genotype relative risk parameters that increase (or decrease) the probability that a child is affected. By default, PREMIM chooses the minor allele to be considered as the ‘risk’ allele, although this option can be overridden if required. We denote by R1R the fact effects ,5 . A maximum of 7 parameters are estimable, meaning that not all of these parameters can be estimated simultaneously. Cordell et al. [EMIM uses a multinomial model to estimate the relative risk parameters on the basis of observed counts of genotype combinations in case/parent trios as shown in Table i. The probabilities μ1−μ6 for the following types of unit: case/parent trios (15 possible genotype combinations); parents of cases (9 possible genotype combinations); case/mother duos (7 possible combinations); case/father duos (7 possible combinations); mothers of cases (3 possible combinations); fathers of cases (3 possible combinations); cases (3 possible combinations). The data for each unit creates a table corresponding to a (possibly collapsed) version of Table gm=igf=j) are as likely as matings (gm=jgf=i). This results in the estimation of six mating type stratification parameters [μ1−μ61. A model that assumes parental allelic exchangeability (PAE)  (which c2. A model that assumes Hardy-Weinberg equilibrium (HWE) and random mating, estimating a single allele frequency parameter in place of the six mating type stratification parameters.μ1−μ9, see Table In addition to these more restricted models, a less restricted ‘conditional on parental genotypes’ (CPG) ,9,12 modEMIM reads in genotype data from input files created by PREMIM. In addition, there are two other files required by EMIM. Firstly, a file ‘emimmarkers.dat’, which provides the minor allele frequencies for each SNP . These can optionally be estimated by PREMIM using the pedigree data, although other (e.g. population-based) sources for this information may be preferred where available.  at SNP 76 and maternal genotype effects (S1=2 and S2=3) at SNP 6004. We then used EMIM to test for maternal effects, with and without allowing for child genotype effects  is available on the PREMIM and EMIM website: R2=2), a maternal genotype effect (S2=2), or a maternal imprinting effect (Im=1.8). PREMIM and EMIM were used to estimate the parameters R1, R2, S1, S2 and Im for each different likelihood assumption and for each set of simulated data. Figure The power to detect genetic effects can vary depending on the assumptions made. As a demonstration, we simulated 1000 replicates of data at a single SNP for a sample consisting of 50 of each of the following units: case/parent trios, case/mother duos, case/father duos, control matings, control/mother duos and control/father duos. We assumed either a child genotype effect R=2, a matS1=1.5, S2=2.25). The expected proportion of pedigree units of different types remaining in the analysis are shown in Figure As a demonstration of the effect that missing data has on the power, we performed analyses at a single SNP using simulated data  and assuming a range of probabilities of missing genotype data. We assumed a maternal genotype effect  to compare the performance of MENDEL and EMIM under three different comparable models: Model 1. This model has been used to test for RhD incompatibility [γ01 was Model 2. This model has been used to test for non-inherited maternal antigens (NIMA) on rheumatoid arthritis (RA) [γ10) for MFG when the mother has one risk allele and the child has no risk alleles, and two parameters for child effects when the child has one or two risk alleles. In order to compare EMIM with MENDEL under this model, we used PREMIM to reassign which allele should be considered as the risk allele by EMIM. A model equivalent to MENDEL’s NIMA model can then be fit in EMIM by estimating parameters  R1R2and γ12. Data were simulated assuming an MFG effect γ10=2. The power to detect the the MFG effect in either MENDEL or EMIM was calculated by considering twice the difference between the negative log likelihood from a model that includes all three parameters (R1R2and the MFG parameter) and that from a model where the MFG parameter has been removed.2. tis (RA)  and consModel 3. This MENDEL model is a general MFG test consisting of one relative risk parameter for each of the 7 mother/child genotype combinations. The relative risk parameter denoted U_00 in the MENDEL documentation  was set to 1 and not estimated to avoid over-parametrization. The other 6 parameters, U_22, U_21, U_12, U_11, U_10, U_01, were estimated. The 6 parameters estimated by EMIM were R1, R2, S1, S2, γ11and γ22. These parameters are not indvidually equivalent to the 6 MENDEL parameters, but the models as a whole can be shown to be equivalent. Data for this comparison were simulated assuming R1=S1=γ11=γ22=1.5 and R2=S2=2.25.3. Figures One difference between EMIM and MENDEL was the time taken to perform the analysis, with EMIM performing considerably quicker than MENDEL. For example, the time to run model 3 (with 200 case/parent trios) showed that PREMIM and EMIM combined took 0.0257 seconds and MENDEL took 6.45 seconds (averaged over 300 runs). This shows that PREMIM and EMIM combined were approximately 250 times faster than MENDEL in this example. The same analysis with 400 case/parent trios gave times of 0.0302 seconds for PREMIM and EMIM combined and 14.3 seconds for MENDEL (averaged over 300 runs), showing PREMIM and EMIM to be approximately 472 times faster then MENDEL. A possible reason for the difference in running times is the fact that the extended MFG model  implemenAnother program with the capability to analyse complex genetic effects (most notably mother/child/imprinting effects) is LEM . LEM is Case/parent trios. SimPed [R1=1.5, R2=2.25) were simulated at SNP number 1004 and maternal effects  were simulated at SNP number 6004. In both EMIM and LEM we tested for maternal effects while allowing for child and maternal imprinting effects  with a null 3-parameter model (R1R2Im)). We calculated the p-value for LEM on the basis of the reported log likelihoods by using the Wald statistic as a χ2value with 2 degrees of freedom. .1. . SimPed  was usedCase/mother duos and control/mother duos. Again, data were simulated at 8000 SNPs but this time for 2000 case/mother duos and 2000 control/mother duos. Child effects  were simulated at SNP number 1000 and maternal effects  were simulated at SNP number 6004. In both EMIM and LEM we tested for maternal and child effects i.e. we compared a null model with no fitted parameters to an alternative model with parameters .2. R1 and S1 are approximately equal and Figures R2and S2 are also approximately equal, but with more variability.A comparison of EMIM versus LEM for the case/mother and control/mother duos is shown in Figure Im. We see that the p-values and parameter estimates provided by the two programs are virtually indistinguishable.Figure TM Processor with 2.6 GHz CPUs) or 2 minutes 4 seconds on Windows (using a 2-core IntelTM Processor with 2.93 GHz CPUs), whereas the same analysis in LEM took 16 hours, 52 minutes and 8 seconds on Windows (via the DOS command line). The difference in speed between the two programs for the case/parent trios analysis was not as extreme, with PREMIM/EMIM taking 3 minutes 7 seconds on Linux or 4 minutes 49 seconds on Windows, versus LEM’s time of 63 minutes 58 seconds on Windows. The improved speed for the LEM trios analysis was most likely due to the fact that it took fewer steps than the duos analysis during the likelihood maximization process . It is possible that differences between maximization algorithms and convergence criteria could account for some of the differences in speed between PREMIM/EMIM and LEM; we found it difficult to determine how to obtain precise control over such factors in LEM and were forced to use input files that very closely matched the examples provided by [These results indicate that the inference provided by LEM and EMIM is essentially identical. This is as expected given the mathematical equivalence ,22 betwevided by ,21. AnotHere we have presented two new computer tools, PREMIM and EMIM, for the estimation of parental and child genetic effects, based on genotype data from a variety of different child-parent configurations. The current version of EMIM improves upon the early beta version described in  by allowIn application to simulated data, we have shown that the inference provided by EMIM is essentially equivalent to that provided by alternative (competing) software packages such as MENDEL and LEM. EMIM does have the advantage of allowing easy implementation of a wider class of models than are most easily implemented in MENDEL and LEM, although the expert MENDEL/LEM user could probably achieve the same model flexibility through judicious choice of parameter restrictions. However, PREMIM and EMIM (used in combination) considerably outperform MENDEL and LEM in terms of speed of execution, an advantage that is likely to be all the more important when applying these approaches to large-scale data sets such as those generated in genome-wide association studies. To allow further increases in speed, PREMIM and EMIM also have the advantage of allowing easy parallel processing (e.g. on a computer cluster) by dividing the SNPs to analyse into different batches.Limitations of PREMIM and EMIM include the fact that larger pedigrees are divided into case/parent or control/parent trios  prior to analysis, and the fact that SNPs are analysed one at a time, without borrowing information from neighbouring markers . Methods for dealing with larger pedigrees, valid under the assumptions of random mating and/or Hardy-Weinberg equilibrium (HWE), have been described by ,11, whilProject name: EMIM and PREMIM Project home page:http://www.staﬀ.ncl.ac.uk/richard.howey/emim/Operating systems: Windows and Linux executables; FORTRAN and C++ source code Programming language: FORTRAN and C++ Other requirements: None Licence: GNU General Public License Any restrictions to use by non-academics: NoneThe authors declare that they have no competing interests.RH developed the PREMIM software, performed computer simulations and drafted the manuscript. HJC conceived the experiment, developed the EMIM software and revised the manuscript. Both authors read and approved the final manuscript.HJC is Professor of Statistical Genetics and a Wellcome Senior Fellow at the Institute of Genetic Medicine, Newcastle University, UK. RH is a Research Associate at the Institute of Genetic Medicine, Newcastle University, UK.


Vata, Pitta and Kapha, based on their physical and mental constitution, referred to as Prakriti. We hypothesised that conditioning association studies on prior risk, predictable in Ayurveda, will uncover much more variance and potentially open up more predictive health.Inconsistent results across association studies including Genome-wide association, have posed a major challenge in complex disease genetics. Of the several factors which contribute to this, phenotypic heterogeneity is a serious limitation encountered in modern medicine. On the other hand, Ayurveda, a holistic Indian traditional system of medicine, enables subgrouping of individuals into three major categories namely prakriti based subgrouping of individuals with genetic analysis tools was attempted in a Rheumatoid arthritis (RA) cohort. Association of 21 markers from commonly implicated inflammatory and oxidative stress pathways was tested using a case-control approach in a total cohort comprising 325 cases and 356 controls and in the three subgroups separately. We also tested few postulates of Ayurveda on the disease characteristics in different prakriti groups using clinico-genetic data.Identification of genetic susceptibility markers by combining the IL1β  and CD40  seem to be the determinants in Vata subgroup whereas oxidative stress pathway genes are observed in Pitta  and Kapha  subgroups. Fixed effect analysis of the associated markers from CD40, SOD3 and TNFα with genotype X prakriti interaction terms suggests heterogeneity of effects within the subgroups. Further, disease characteristics such as severity was most pronounced in Vata group.Inflammatory genes like prakriti based subgroups, thereby, validating concepts of prakriti and personalized medicine in Ayurveda. Ayurgenomics approach holds promise for biomarker discovery in complex diseases.This exploratory study suggests discrete causal pathways for RA etiology in  Vata predominant, Pitta predominant and Kapha predominant. This classification is based on the body constitution termed as prakriti in Ayurveda lexicon prakriti. Prakriti is determined by proportions of the five basic elements namely Space, Air, Fire, Water and Earth which constitutes the Tridoshas  which are present in each and every cell of the body. Together these three doshas determine the physiological balance and constitution of the individual. The equilibrium of doshas is called health and imbalance is called disease prakriti of an individual. Therefore, in the practice of Ayurveda, determination of prakriti is necessary not only for examination of the person/patient for understanding the physical and mental nature but also for recommendation of a suitable diet and life style regime for maintenance of health, prevention and cure of diseases. Prakriti also plays an important role in the pathogenesis, treatment and prognosis of various diseases .Challenges in identifying clinically relevant genetic determinants underlying complex diseases include phenotypic and genetic heterogeneity; gene-gene interactions and allelic spectrum which include both common and rare genetic variants. Of these, clinical heterogeneity is the primary limitation and necessitates deployment of alternate or combinatorial approaches. Variation, in particular, clinical phenotypic covariates may reflect differences in the underlying genetic etiology of disease. Therefore, stratifying the cohort and conducting genetic analysis or functional studies within strata may facilitate the biomedical researchers to search for “the needle” in a haystack. It is at this juncture that the insights from Ayurveda, the traditional holistic Indian system of medicine, seem promising Prakriti can be used as a tool to sub-group both healthy and diseased individuals and hence overcome the contemporary limitation of clinical heterogeneity in molecular genetic analysis of complex traits. Such an attempt has been made and a correlation between different prakritis and their biochemical and transcriptomic profiles has been previously reported prakriti groups in RA cohort and a significant difference has been reported prakriti groups was used to establish association of high-altitude pulmonary edema with EGLN1 polymorphism prakriti based subgrouping may help overcome the limitation of phenotypic heterogeneity commonly encountered in case-control based genetic association studies and thus delineate a possible involvement of different pathways underlining the disease in different subgroups. RA is referred to as Amavata in Ayurveda and according to Ayurveda text, its etiology may be briefly described as follows: With excessive intake of heavy, incompatible, unwholesome and untimely food, Agni (digestive mechanism) gets impaired and results in indigestion and produces Ama . If this Ama combines with vitiated Vata dosha and while circulating all over the body, it gets lodged in joints and results in pain, swelling, feverishness and stiffness in joints, loss of appetite, indigestion and body ache. If the disease progresses, severity of pain, stiffness and other symptoms increase leading to deformities and disabilities Vata prakriti people are more prone to get joint diseases with severe pain Vata prakriti. This suggests that Ayurvedic categories may be a suitable platform for assessing prior risk of illness. Further, conditioning association studies on this prior risk may uncover much more variance and potentially open up more predictive health.In the present exploratory study, we revisited the Ayurveda system of medicine and attempted to subgroup both Rheumatoid Arthritis (RA) patients and healthy controls to test the hypothesis that prakriti and prakriti based subgrouping of individuals as an alternate strategy to sort the issue of clinical heterogeneity in genetic association studies of complex traits. For this we selected reported markers/genes from inflammatory pathway and a few oxidative stress pathway genes involved in inflammation. Inflammatory pathway genes were selected as most of the candidate gene studies SOD3, PON1 and PON2 with joint diseases/RA Nrf2, a transcription factor, that maintains the cellular defense against oxidative stress , Department of AYUSH, Ministry of health and family welfare, Government of India, New Delhi. The questionnaire consists of 47 questions related to physiological, physical and psychological characteristics of the person . Intensity of prakriti assessment signs and symptoms as well as the objective questionnaire together were considered for determining the prakriti of the study subjects. An excess of at least five prakriti features (∼11%) were considered for estimating the predominant prakriti of an individual. Objective parameters like height, weight, BMI, blood pressure, swelling, blood/serum examination, X-rays and MRI were used in the clinical assessment. Height, weight, colour and texture of skin and hair etc., are assessed in comparison to normal healthy individuals from matched geographical region/race. Visual analogue scale was used for most of the subjective features like pain, burning sensation, heaviness etc. Blood was drawn and used for analysis of Hb%, ESR, RA factor (quantitative), Anti CCP (quantitative) and for DNA extraction according to routine protocol. Age, gender and ethnicity matched individuals not having RA were recruited as controls. These individuals were then subjected to prakriti analysis using the same prakriti determination questionnaire that was used for RA patients. Peripheral blood sample from 350 cases and 376 matched controls was collected using standard phlebotomy procedures following ethical guidelines of Indian Council of Medical Research, Government of India. Control individuals were also subjected to genetic analysis similar to the cases.Patients of both sexes, aged between 18 to 50 years diagnosed with IL10, IL6, TNFα, IL1β, PTPN22, TRAF1, CD40 and a gene PADI102, and a locus (6q23) from Inflammatory pathways previously reported to be associated with RA, were selected. In addition, six SNPs from four genes namely PON1, PON2, CYP1A2 and SOD3 from oxidative stress pathways were also selected. Thus, a total of 21 SNPs from 12 genes and a locus (6q23) were analyzed in this study. Genotyping of these SNPs were done using the PCR-RFLP method .These parameters were compared across different 2) test. Allelic and genotypic associations of markers found significant (p<0.05) by Pearson’s X2 test were evaluated by computing odds ratio (OR) and 95% confidence intervals (CI). Haplotypes were reconstructed using PHASE ver 2.0.2 (http://stephenslab.uchicago.edu/software.html) prakriti was carried out to see heterogeneity of effects between the prakritis for the associated markers (p<0.1) This was done using General Linear Model with sex and disease status as dependent variables, prakriti as fixed factor, genotype as covariate and with genotype and prakriti as interaction terms (GxP). P value <0.05 was considered to be significantly different in GxP interaction.Hardy–Weinberg equilibrium was tested for each marker using Chi square . Power estimates were calculated for small (w = 0.10) and medium effect sizes (w = 0.25). Analysis was done for a total case-control cohort as well as for three individual prakriti groups separately.All the statistical analyses were performed using Statistical Package for Social Sciences  version 15.0 software for windows. Power calculations were carried out using the Power and Precision Software  as dependent variables. P-values <0.05 were considered as significant. Statistical analyses were done using Statistical Package for Social Sciences ver.15.0 .To identify the independent contribution of clinico-genetic variables, data was adjusted for confounding factors like age, gender, BMI, ESR and Hb. A regression model was fitted for the total case-control cohort as well as for each of the three Amavata (RA) patients and 376 control subjects were recruited for this study. A comparative presentation of demographic details and all quantitative clinical parameters among the patient and control groups are provided in A total of 350 prakriti analysis, 13 cases and 14 controls did not fit into the classification criteria of the three predominant subgroups, and were therefore, eliminated from the study. DNA from 12 cases and 6 controls could not be obtained and therefore could not be included in genetic analysis. A total of 325 cases and 356 controls were taken further for the genetic analysis. Over 95% genotyping success was observed in this study. Allelic, genotypic and haplotypic tests of association was carried out for all markers analyzed in this study for the total cohort and for each of the three prakriti based subgroups of cases and controls separately. Results of all these tests are presented in detail in Following SOD3 (rs699473 and rs2536512) and IL1β (rs1143627) was observed in total RA cohort and a trend of association was observed with PON1 (rs662)  . Test of markers .PON2  was associated with Vata cohort and an association trend was observed at CD40 (rs4810485)  in IL1β was found to be over-represented in RA patients in this sub-group (4810485) . Of the ub-group .SOD3 (rs699473 and rs2536512) markers and a trend of PON1 (rs662) were seen in this subgroup similar to that observed in the total cohort  as well as haplotypic (in order of rs13306703-rs699473-rs2536512) association (No significant association was observed in ociation .prakriti showed a significant difference in interaction among the prakriti groups. CD40 and PON2 interaction with Vata was different from that with Kapha (p = 0.03 and p = 0.02 respectively) and Pitta (p = 0.04 and p = 0.02 respectively). On the other hand, TNFα (rs1800630) genotype suggested significant interaction difference between Vata and Kapha (p = 0.02); and SOD3 (rs2536512) genotype between Kapha and Pitta  when compared for gender  were considered as independent variables. Only age, gender and ESR but none of the genotypes emerged as significant variables in the total cohort. On the other hand, ESR along with TNFα SNP (rs1800629) and CD40 (rs4810485) were seen to be significant in Vata category. Notably, PON2 association was lost on adjusting for gender. In Pitta group, BMI, ESR, & SOD3 (rs2536512) emerged significant. Age, Hb and TNFα (rs1800630) were identified in the Kapha category (PTPN22 (rs2476601) was not used in the regression analysis due to its low MAF (<0.05) and absence of one of the genotypes  as dependent variable and all associated clinical variables and genotypes with p<0.2 from association analysis as independent variables. In the Vata-Pitta comparison, BMI, TNFα (rs1800630) & SOD3 (rs2536512) SNPs were significant and the non-overlapping contribution of these markers seems to best explain the differences in disease susceptibility between these two groups. Similarly, BMI, ESR and TNFα (rs1800630) SNP emerged in the Vata-Kapha comparison; and only BMI and none of the SNPs was seen to contribute to differences in the Kapha-Pitta comparison . It was also observed that even with a small sample size of Vata subgroup, proportion of rarer genotype of CD40  and of TNFα  was found to be significantly higher in Vata cases compared to other subgroups (It is clear from the results that a higher number of RA patients recruited in the study were with the prakriti . Howeverubgroups . In addiubgroups .prakriti as described in Ayurveda Amavata (RA) patients and 300 healthy controls, with a 100 each of Vata, Pitta and Kapha predominant prakriti in this exploratory study on Ayurgenomics. However, it was observed by the clinical team and supported by demographic data , reasonable association of SNPs in IL1β, PON1 and SOD3 markers was observed  and TNFα (rs1800630) rare genotype is significantly interacting with Vata subgroup than with other subgroups . These observations are in line with Ayurveda documentation which states that Vata prakriti patients are more severely affected by Amavata than the other prakriti groups.A plethora of candidate gene association studies and more recently GWAS have been carried out in the last decade to identify genes associated with susceptibility to RA. In the first GWAS which was carried out in Caucasian population with 1860 RA cases and 2938 controls, a strong association of analysis ; this waanalysis ; and alsprakriti . Other dprakriti with the susceptibility genes/markers also provides promising leads in this study. As there were significant differences in clinical features among Vata, Pitta and Kapha groups (Vata subgroup patients is unique in its association with CD40 and RA in Pitta subgroup with PON1 and SOD3 (rs699473) (data not shown). These observations reiterate that subgrouping of individuals, based on prakriti, may be useful in underpinning some of the masked associations , by overcoming the major limitation of sample heterogeneity.Results from regression analysis with total cases and the subgroups showed distinct genetic associations in the different subgroups which were not seen in the total cohort . This sua groups , we checPrakriti groups demonstrated by fixed effect analysis clearly shows that there exists prakriti specific disease susceptibility pathways. It also rules out the possibility that finding evidence for an association in one subset but not in another in this study is due to the suboptimal power of the sample set. As expected the genotype term remained significant and remarkably also GxP  RA cases and controls; b) the three Prakriti subgroups of RA cases.(DOC)Click here for additional data file.Figure S2Histogram depicting BMI comparision across Prakriti subgroups of a) RA cases; b) control group.(DOC)Click here for additional data file.Figure S3Histogram depicting comparison of clinical characteristics a) pain across Prakriti subgroups in RA cases b) swelling across Prakriti subgroups in RA cases c) stiffness across Prakriti subgroups in RA cases d) Hemoglobin across Prakriti subgroups in i) RA cases ii) controls; e) ESR across Prakriti subgroups in i) RA cases ii) controls; f) RA-factor i) between RA cases and controls, ii) across Prakriti subgroups in RA cases; g) anti-CCP antibodies in RA cases across Prakriti subgroups.(DOC)Click here for additional data file.Figure S4Histogram depicting genotypic distribution of CD40 (rs4810485) and TNF-α (rs1800630) among Prakriti subgroups of RA cases and controls.(DOC)Click here for additional data file.Table S1Showing Primers and conditions used for PCR-RFLP.(DOC)Click here for additional data file.Table S2Showing genotypic  and alle(DOC)Click here for additional data file.Table S3Showing genotypic  and alleVata RA cohort.(DOC)Click here for additional data file.Table S4Showing genotypic  and allePitta RA cohort.(DOC)Click here for additional data file.Table S5Showing genotypic  and alleKapha RA cohort.(DOC)Click here for additional data file.Table S6Showing significant Genotype x Prakriti interaction differences.(DOC)Click here for additional data file.Table S7Showing regression analysis of clinico-genetic variables across prakriti groups.(DOC)Click here for additional data file.Material S1An overview of principles of Ayurveda and concepts of Prakriti.(DOC)Click here for additional data file.Material S2Questionnaire used for assessment of Prakriti subgroups in RA cases and controls.(DOC)Click here for additional data file.


FLT1 and KDR are 100% and 68% for Q1, respectively. The powers to detect VNN3 and BCHE are 34% and 30% for Q2, respectively.We develop statistical methods for detecting rare variants that are associated with quantitative traits. We propose two strategies and their combination for this purpose: the iterative regression strategy and the extreme values strategy. In the iterative regression strategy, we use iterative regression on residuals and a multimarker association test to identify a group of significant variants. In the extreme values strategy, we use individuals with extreme trait values to select candidate genes and then test only these candidate genes. These two strategies are integrated into a hybrid approach through a weighting technology. We apply the proposed methods to analyze the Genetic Analysis Workshop 17 data set. The results show that the hybrid approach is the most powerful approach. Using the hybrid approach, the average power to detect causal genes for Q1 is about 40% and the powers to detect  Evidence is increasingly showing that complex diseases are caused by both common and rare variants -3. StatiIn this paper, we develop two strategies to search for both common and rare variants in multiple genes: iterative regression and extreme values. A hybrid approach of these two strategies is also explored to improve power. In the iterative regression strategy, common single-nucleotide polymorphisms (SNPs) and rare variant combinations are tested first. Then a best variant is selected. The regression is repeated against the residual to discover potential variants. A score test  is used ith individual as 1 if the ith individual has at least one rare mutation within the RVC; otherwise the genotype is coded as 0. For a common SNP with two alleles a and A, we define the numerical code of genotype for the ith individual as ix = 0, 1, or 2 for genotype aa, aA, or AA, respectively. The GAW17 data set contains genotypes at 24,487 SNPs in 3,205 genes on chromosomes 1–22 with 209 case subjects and 488 control subjects. In this study, the genes are removed from the data set if they do not have nonsynonymous SNPs. After the removal of 1,009 genes from the data set, 2,196 genes are used for the analysis in the following step. Then, synonymous SNPs in the remaining 2,196 genes are deleted. The original GAW17 data set is transformed into a new data set G, which includes 4,711 common SNPs or RVCs.The variants of the GAW17 data set are divided into common and rare. We define a variant as rare if its minor allele frequency (MAF) is less than 0.01. Within each gene, we collapse all rare variants to obtain a rare variant combination (RVC) . For an ix = T, and let iy denote the numerical code of the multimarker genotype and the trait value of the ith individual, where i = 1, …, N and N is the sample size. To test the null hypothesis of no association between the k markers and the trait, we use the score test statistic given by:We propose the iterative regression strategy to identify a group of significant common SNPs or RVCs. For this method, we need a multimarker test. We propose to use the score test given by Chapman et al. . Let xi where:and:S asymptotically follows a chi-square distribution with k degrees of freedom.The score test statistic L and a significance level α, the algorithm includes the following steps:For a given marker cutoff value Step 1. Use an L step procedure  to select L candidate SNPs or RVCs, denoted v1, …, Lv. In step 1j, a SNP or RVC that has the highest correlation with trait values is selected and denoted jv. Then, we update the trait value by residual:β0 and β1 in the linear model:where Step 2. Let A1, …, LA denote the L candidate SNP sets, where iA = {v1, …, iv}. The score test is used to test association of each iA. The raw p-value ip is calculated by using a chi-square distribution and the adjusted p-value iq is computed by using a permutation test. The SNP set with the smallest adjusted p-value is the final candidate SNP set. The final candidate SNP set is denoted fA.Step 3. Use a permutation test to evaluate the overall p-value of fA. Denote the overall p-value as poverall. If poverall <α, the final significant SNP set is the final candidate SNP set fA. Otherwise, the final significant SNP set is empty.poverall through another layer of permutation. We use a permutation procedure recently proposed by Ge et al. [p-values and the overall p-value at the same time using one layer of permutation. The permutation procedure includes the following steps:Using a standard permutation procedure, we obtain e et al.  to evaluStep 1. Generate S  permuted data sets. In each permutation, we randomly shuffle trait values. For each permuted data set, search for the L candidate SNP sets by using the same procedure. For the sth permuted data set , denote the L candidate SNP sets by sA1, …, sLA and the associated raw p-values by sP1, …, sLP. Then, the adjusted p-value corresponding to the candidate SNP set lA is estimated by:I(·) is the indicator function. We choose the SNP set with the smallest adjusted p-value,where as the final candidate SNP set.Step 2. To evaluate the overall p-value of the final candidate SNP set, we first adjust the raw p-values sP1, …, sLP for the sth permuted data, s = 1, …, S. The adjusted value of slP is given by:Let:p-value of the final candidate SNP set is given by:Then, the overall Intuitively, for a quantitative trait that has a positive relation with a disease, an individual with more causal mutations will have a higher trait value. Therefore we propose to use an extreme values strategy to select candidate genes for testing association with rare variants.The extreme values strategy includes two steps.Step 1. We select candidate genes using individuals with extreme trait values (top 5% in this study). In detail, we first select a group of individuals with extreme trait values and denote this group of individuals by EX = {i: iy >C}. For a gene with an RVC, let ix denote the numerical code of genotype of the ith individual. Then, we define this gene as candidate gene if EX has at least one rare mutation within the RVC of this gene.Step 2. We apply the score test to each of the candidate genes. For a given significance level α, a candidate gene is declared significant if the p-value is less than α/n, where n is the number of candidate genes.α, let αA denote the group of significant SNPs provided by the iterative regression strategy and αB denote the group of significant genes provided by the extreme values strategy. Then, the hybrid approach ends with the union of Aα/2 and Bα/2.The iterative regression and extreme values strategies are different. One is a gene-based method and the other is a SNP-based method. The integration of the two methods may improve the power to detect association. Thus we propose a hybrid approach. The hybrid approach ends with a group of significant genes and SNPs or RVCs. For a given significance level We use the three proposed methods and the CMC method to analyze the GAW17 data set. Before the data analysis, we already knew the answers. The first step of data analysis is to adjust trait values for covariates by assuming the linear model:y is the trait value and x1, …, kx are the covariates. In this application, we consider Age, Sex, and Smoking history as covariates. In the following discussion, we use residuals as trait values.where 1/2 ≈ 0.015, and the 95% confidence interval (CI) is  for the nominal level of 0.05. From Figure For evaluating the performance of the four methods, we first consider type I error rates. To evaluate type I error rates, we permute trait values in each of the 200 replications. The estimated type I error rates of the four methods based on permuted trait values are given in Figure Quantitative trait Q1 is influenced by 9 genes, and Q2 is affected by 13 genes. For the purpose of power comparisons, we calculate the average power to detect the 9 causal genes of Q1  and the average power to detect the 13 causal genes of Q2 . The power for Q1 and the power for Q2 of the four methods are summarized in Figure L (number of candidate SNPs in step 1). If L is too small, the iterative regression method may lose power because it cannot include all causal genes. If L is too large, the iterative method may also lose power because noise terms are included. Further investigation is needed for choosing the optimal value of L.New sequencing technologies that allow researchers to sequence parts of the genome—or, in the future, the whole genome—of large groups of individuals have made rare variant association studies feasible. However, statistical methods to test association between rare variants and phenotypes are still underdeveloped. Existing methods that essentially test one gene at a time may lose power to detect complex disease genes because complex diseases are presumed to be caused by many genes. In this paper, we have developed three novel methods: the iterative regression strategy, the extreme values strategy, and the hybrid approach. The iterative regression strategy can test multiple genes simultaneously, whereas the extreme values strategy can delete less important genes and thus makes the problem of multiple testing less severe. The hybrid approach is the combination of the two strategies. Analysis using the GAW17 data set shows that all three proposed methods are more powerful than the CMC method, one typical existing method used to test rare variant association. In this study, we collapse all rare variants within one gene into a single variant and analyze this variant together with common variants. We can also use other collapsing methods, such as the weighted-sum method [We propose three methods for detecting both rare and common variants. Application to the GAW17 data set shows that all three proposed methods are more powerful than the CMC method, one typical existing method used to test rare variant association.The authors declare that there are no competing interests.ZZ performed all computing, proposed part of the methods, and drafted the manuscript. QS participated in the methodology development and drafted the manuscript. XW helped to draft the manuscript and helped for the methodology development. SZ conceived the study, participated in the methodology development, and helped to draft the manuscript. All authors read and approved the final manuscript.


With the recent decreasing cost of genome sequence data, there has been increasing interest in rare variants and methods to detect their association to disease. We developed BioBin, a flexible collapsing method inspired by biological knowledge that can be used to automate the binning of low frequency variants for association testing. We also built the Library of Knowledge Integration (LOKI), a repository of data assembled from public databases, which contains resources such as: dbSNP and gene Entrez database information from the National Center for Biotechnology (NCBI), pathway information from Gene Ontology (GO), Protein families database (Pfam), Kyoto Encyclopedia of Genes and Genomes (KEGG), Reactome, NetPath - signal transduction pathways, Open Regulatory Annotation Database (ORegAnno), Biological General Repository for Interaction Datasets (BioGrid), Pharmacogenomics Knowledge Base (PharmGKB), Molecular INTeraction database (MINT), and evolutionary conserved regions (ECRs) from UCSC Genome Browser. The novelty of BioBin is access to comprehensive knowledge-guided multi-level binning. For example, bin boundaries can be formed using genomic locations from: functional regions, evolutionary conserved regions, genes, and/or pathways.We tested BioBin using simulated data and 1000 Genomes Project low coverage data to test our method with simulated causative variants and a pairwise comparison of rare variant (MAF < 0.03) burden differences between Yoruba individuals (YRI) and individuals of European descent (CEU). Lastly, we analyzed the NHLBI GO Exome Sequencing Project Kabuki dataset, a congenital disorder affecting multiple organs and often intellectual disability, contrasted with Complete Genomics data as controls.The results from our simulation studies indicate type I error rate is controlled, however, power falls quickly for small sample sizes using variants with modest effect sizes. Using BioBin, we were able to find simulated variants in genes with less than 20 loci, but found the sensitivity to be much less in large bins. We also highlighted the scale of population stratification between two 1000 Genomes Project data, CEU and YRI populations. Lastly, we were able to apply BioBin to natural biological data from dbGaP and identify an interesting candidate gene for further study.We have established that BioBin will be a very practical and flexible tool to analyze sequence data and potentially uncover novel associations between low frequency variants and complex disease. This gene has between 262 and 602 variant loci indicating a very polymorphic gene in the CEU genome (including the simulated variant). The addition of one simulated variant loci added a total of 43 variants (each case is heterozygous and only contributes one variant to bin). In a second test, we randomized the case/control status again and added a simulated variant to the gene CAV2 , with between 9-20 variant loci (including the simulated variant). BioBin was then used for a rare variant burden test across the chromosome 7 genomic region to see if either the GLI3 or CAV2 signal could be identified as significantly associated using a Wilcoxon Rank Sum test.We added our simulated variant to the gene ftp://ftp-trace.ncbi.nih.gov/1000genomes/ftp/release/20110521/). This analysis included 87 CEU samples and 88 YRI samples. We used BioBin to conduct a pairwise comparison of rare variant burden differences (MAF < 0.03) based on known gene regions (start and stop positions form bin boundaries), intergenic regions (intergenic variants caught by 50kb bins) and known pathways (gene bins in the same pathway are collapsed into one pathway bin).Second, we compared two populations, YRI and CEU, from 1000 Genomes Project to highlight rare variant burden differences. Rare variants found at different frequencies among ethnic-specific populations and sequence data is available through 1000 Genomes Project for a large number of individuals (October 2011 release http://www.ncbi.nlm.nih.gov/gap/) April 2012. According to the authors of the original study, ten unrelated individuals with Kabuki syndrome were sequenced: 7 of European ancestry, 2 of Hispanic ancestry, and one of mixed European and Haitian ancestry. Shotgun fragment libraries were hybridized to custom microarrays, and then enriched using massively parallel sequencing [We utilized the NHLBI Kabuki dataset available on dbGaP . Case/control status was evenly and randomly assigned in each of the 4000 replicates. The type I error rate was calculated as the number of replicates with p-value <= 0.05 divided by the total number of replicates. Shown in Table GLI3 bins. GLI3 has a large number of variants in addition to the simulated variant. While the statistical test did not identify GLI3, there were also no false positives. There were no significant bins in any of the three GLI3 analyses. The CAV2 bin was statistically significant after Bonferroni correction when the minor allele frequency threshold was less than or equal to 0.05, a gene with a very low number of additional non-simulated variants.Statistical analysis using bin output can be complicated considering dependent bin and variant architecture, variance in bin size, and complex genetic models. We used 1000 Genomes CEU data to evaluate if a) BioBin could detect bins containing a 100% penetrant simulated variant b) determine if bin size (number of variants in a bin) could affect the strength of a simulated association signal by seeding the variant into two genes with very different numbers of non-simulated variants, testing different minor allele frequency binning thresholds to see how the p-value changes with respect to small changes in the number of variants collapsed in the bin. BioBin can detect bins containing the penetrant simulated variant, but this is affected greatly by the number of other variants in a given bin. The results are shown in Table These two simulated variants scenarios were tested separately in BioBin. As a result, the phenotypes were randomly assigned, thus allowing for different bins to be generated based on which and how many variants met the MAF binning threshold criteria.We also tested BioBin using whole-genome population data from 1000 Genomes Project. Because of known population stratification between CEU and YRI, this is a reasonable rare variant burden test. using whole-genome data. For 87 CEU and 88 YRI individuals, there are approximately 11 million variants (rare and common) in the CEU sample and approximately 18 million variants in the YRI sample, an indication of similarity/dissimilarity to the reference genome In addition to having more variants, it is also clear that of these variants, there is a larger proportion of low frequency variants in the YRI sample. Figure Using a MAF binning threshold of 0.03, we binned genes, pathways, and intergenic regions. The results of this test are shown in Table MLL2 as a possible causative gene for Kabuki syndrome. In this analysis, in order to compare the cases and controls, we filtered both datasets by exome boundaries (available from UCSC) and filtered out variants present in the 1000 Genomes Project Phase I data. BioBin produced the MLL2 gene bin with 125 total variant loci  at a minor allele frequency threshold of 0.05, but was not significant .We used BioBin to collapse the whole-exome data for 10 Kabuki individuals with 54 individuals from Complete Genomics whole-genome data. The 10 Kabuki cases were sequenced using an exome-capture kit for an average coverage of 40x on the mappable, targeted exome . The 54 Shown in Table GLI3 had 431 variant loci with 1099 total variants in the CEU group. At the same binning threshold, CAV2 had 11 variant loci with 57 variants in the CEU group. We expect causative rare variants to be highly penetrant, but clearly the power of BioBin to detect a signal with a large main effect is greatly affected by the number of other variants in the bin. Using GLI3 as an example, when there were greater than 300 variants in the bin, the true signal was mitigated by the noise. However, when there were less than 20 variants in the bin, a single variant with a large main effect was easily detected. Optimistically, in natural data each case has one or more rare-variants in addition to the natural background variation . The number of variants in the background variation is deterministic of detecting a signal; this exemplifies the importance of maintaining bins of a reasonable size. However, if there are more causative variants acting in concert with a relatively high penetrance, this signal will be more robust. It also emphasizes the impact of flexible binning. The ideal bin will have as many rare variants with the same direction of effect and very few neutral variants. This has been shown to improve power in other methods [1000 Genomes Project has provided a unique opportunity to evaluate bins on natural data. In the first test, BioBin was used to identify bin containing simulated variants with known association to a simulated phenotype. These steps were taken for two genes with very different rare variant backgrounds. For example, using a minor allele frequency-binning threshold of 0.05, In the subsequent test using 1000 Genomes Project whole-genome data, we used BioBin to identify features with significant differences in rare variant burden. A similar method was used by Madsen and Browning and Moore et. al ,12. A poIt is also interesting that the rate of variation between CEU and YRI is not consistent across each feature tested. Gene bins had fewer significant rare variant differences than intergenic and pathway bins. Perhaps we see overall less variability in these regions because mutations are less tolerated. It has been suggested that genes undergo adaptive evolution, thus regions with potential for highly deleterious mutations such as genes, evolve lower mutation rates ,40. ThisNg et al. filtered out 1000 Genome variants and other non-causative variants from previous Kabuki studies. They also considered only nonsynonymous variants with predicted function. However, ten individuals with whole-exome data is not a large enough case sample size for sufficient power in a Wilcoxon 2-sample rank sum test. The uneven sample size and different sequencing approach for cases and controls is major limitation. To compare the cases and controls, we filtered both datasets by exome boundaries (available from UCSC). Because of the sample size limitation, reducing potentially neutral variants that contribute noise was advantageous. We removed any variants that were present in the 1000 Genomes Project Phase 1 release  . Then weMLL2 was not more significant in this analysis. In addition, population stratification exists in the cases and controls and was not accounted for in this analysis. Lastly, MLL2 has 54 exons and quite a bit of neutral variation. As shown in Table MLL2 was absent, one of the top pathways included EMG1, previously associated with Bowen- Conradi syndrome . Bowen-Conradi syndrome has a much more severe phenotype, but shares two disease characterizations with Kabuki: impaired growth and mental retardation [EMG1 association. To improve this analysis, one could potentially use a principle components analysis to adjust for the variant confounding between the two groups in a regression analysis or perform a permutation test to help adjust for unknown confounding. A better test data set would include at least 150-200 individuals that were sequenced on the same platform. Overall, BioBin can be used as a filtering mechanism to group data and evaluate rare variant burdens between two groups, but requires a more substantial sample size to gain power to detect significance.We have not used the same exact filters and have very low power for a case-control study, which together, likely explain why ardation . Given tTo explain more phenotypic variation in common complex disease, it is imperative to consider genetic variation beyond common single nucleotide polymorphisms. Rare variant analyses are appealing since effect sizes are likely larger . However1. Capability for whole-genome and whole-exome analyses2. Practical method for data reduction in sequence data analysis3. Utilizes domain knowledge to prioritize results for association testing4. Accurate binning increases the statistical power to detect associations5. Gene based output can formatted to identify GxG, GxE, and gene-drug interactions6. Can be combined with common variant methods7. Provides framework to integrate numerous types of complex data setsBioBin is unique because it relies on LOKI and does not include any statistical method. The user can easily test complicated and interesting hypotheses on many features. LOKI provides access to integrated biological knowledge , which is valuable to researchers that do not want to spend considerable effort to combine this knowledge manually. Additionally, the output of BioBin can be subsequently analyzed using the association tests most appropriate for their data analysis. For any given bin, many statistical tests from other published collapsing methods can be applied to BioBin output.Using a Wilcoxon 2-sample rank sum test, we have shown that the type I error rate is controlled, but that substantial (>500) sample sizes are needed to have greater than 80% power to detect rare variants with modest effect sizes. With BioBin, we were able to find simulated variants in genes with less than 20 loci, but found the sensitivity to be much less in large bins. This will be investigated further so that we can better control bin size for gene regions or groups, such as pathways. From the population comparison analysis, we learned more about the large degree of population stratification between CEU and YRI populations from 1000 Genomes data. Lastly, we were able to apply BioBin to natural biological data from dbGaP.https://ritchielab.psu.edu/ritchielab/software.With the rapid increase in available sequence data and available biological knowledge, we believe that BioBin will continue to be a useful analysis tool. The ability to quickly form and test unique, interesting, and biologically relevant hypotheses using aggregated low frequency variation will aide scientists in revealing hidden heritability for common complex disease. Software for BioBin is publicly available for download at The authors declare that they have no competing interests.CBM carried out the analyses, performed the sequence alignment and drafted the manuscript. JRW wrote and maintains BioBin code. ATF wrote and maintains LOKI. SAP participates in the design of LOKI and helped with manuscript revisions. MDR participated in the design of the study and manuscript revisions. All authors read and approved the final manuscript.