We also apply CLiP-Y to detect heterogeneity in neuroticism in over 10, 000 individuals from the UK Biobank and detect heterogeneity with a p-value of 1.68 × 10−9. Scores were not significantly reduced when partitioning by known subclusters (“Depression” and “Worry”), suggesting that these factors are not the primary source of observed heterogeneity.Evidence from both GWAS and clinical observation has suggested that certain psychiatric, metabolic, and autoimmune diseases are heterogeneous, comprising multiple subtypes with distinct genomic etiologies and Polygenic Risk Scores (PRS). However, the presence of subtypes within many phenotypes is frequently unknown. We present CLiP (Correlated Liability Predictors), a method to detect heterogeneity in single GWAS cohorts. CLiP calculates a weighted sum of correlations between SNPs contributing to a PRS on the case/control liability scale. We demonstrate mathematically and through simulation that among i.i.d. homogeneous cases generated by a liability threshold model, significant anti-correlations are expected between otherwise independent predictors due to ascertainment on the hidden liability score. In the presence of heterogeneity from distinct etiologies, confounding by covariates, or mislabeling, these correlation patterns are altered predictably. We further extend our method to two additional association study designs: CLiP-X for quantitative predictors in applications such as transcriptome-wide association, and CLiP-Y for quantitative phenotypes, where there is no clear distinction between cases and controls. Through simulations, we demonstrate that CLiP and its extensions reliably distinguish between homogeneous and heterogeneous cohorts when the PRS explains as low as 3% of variance on the liability scale and cohorts comprise 50, 000 − 100, 000 samples, an increasingly practical size for modern GWAS. We apply CLiP to heterogeneity detection in schizophrenia cohorts totaling > 50, 000 cases and controls collected by the Psychiatric Genomics Consortium. We observe significant heterogeneity in mega-analysis of the combined PGC data , a method that does not identify subtype-specific effects, but is very well-powered to detect heterogeneity of any kind within the very weak signals of GWAS. CLiP serves as a method to flag particular phenotypes for potential further study into the genomic factors driving heterogeneity, as well as a means to evaluate the transferability of polygenic risk scores. We also develop extensions of CLiP applicable to scoring heterogeneity in quantitative phenotypes and quantitative predictors such as gene expression. We apply CLiP to scoring heterogeneity in schizophrenia cohorts from the Psychiatric Genomics Consortium and neuroticism in individuals in the UK Biobank and find significant heterogeneity in both phenotypes, warranting further study. In recent years Genome-Wide Association Studies (GWAS) have identified thousands of genomic risk factors and generated insights into disease etiologies and potential treatments , 2, 3. MOne such avenue has concerned the apparent heterogeneity of diseases which has not been sufficiently recognized by GWAS: while individuals in cohorts for these studies are frequently classified simply as cases or controls, clinical evidence for several GWAS traits have suggested that there are multiple different subtypes consisting of distinct sets of symptoms and association with distinct rare risk alleles , 15. ForHeterogeneity in disease etiology has also become a concern for clinical applications, as the predictive accuracy of polygenic risk scores is known to vary across different demographics of patients. As most genomic studies to date have been conducted on primarily Northern European populations, accuracy of the discovered predictors, measured as R-squared, is lower in other populations, raising the possibility of inequities in care by the direct application of these PRSs . Even ifTo date there have been few strategies to identify subtypes in GWAS cohorts, largely due to two challenges: the very small signals typically found in polygenic traits, and the presence of confounding sources of heterogeneity such as batch effects. One method  purportsWithin-phenotype heterogeneity has also surfaced as a possible confounding factor in the discovery of pleiotropic associations between phenotypes . AssuminRecent work by Han et al.  has sougWe propose a generalized method called CLiP (Correlation of Liability Predictors) that leverages these correlations more broadly to detect heterogeneity in single-trait GWAS, rather than strictly in two labeled pleiotropic traits. In comparison to BUHMBOX, CLiP improves overall power to detect heterogeneity while remaining robust to false positive confounding factors such as ancestry. CLiP also detects heterogeneity arising from multiple subtypes with highly dissimilar PRSs, which produce specific correlation patterns that attenuate positive heterogeneity signals. These benefits, however, are contingent on the assumption that case/control GWAS behaves according to a liability threshold model rather than a logistic model. Although these models are commonly interpreted to be interchangeable , they prThe goals of this work are fourfold: First, we demonstrate that in a homogeneous (null) set of cases in a case/control cohort, predictors with effect sizes of the same sign are not uncorrelated as stated by Han et al.  but negaWhile the Introduction described previous methods to partition heterogeneous SNP effects or cohorts into distinct clusters, the highly polygenic nature of most phenotypes renders these methods largely under-powered for single trait GWAS even when data sizes are large. CLiP serves as a compromise on this task by providing a well-powered method to detect potentially disease-relevant heterogeneity, without further decomposing detected signals into clusters. In this regard CLiP can serve as an initial test to flag heterogeneous data sets for further study. CLiP increases power by aggregating pairwise correlations between disease-associated SNPs from summary statistics. Both the logistic and liability threshold models are generalized linear models that transform a linear predictor (the log-odds or the liability score) into a probability of assigning a binary label. The models share highly similar inverse link functions , and they are understood to produce regression coefficients that can be directly transformed from one model to another by an invertible function see . HoweverTo contrast the performance of the logistic model with the Risch model, in which SNPs are uncorrelated see , we simup = 0.2. Effect sizes were set to a fixed value to produce a desired variance explained of 0.034 in a standard normal PRS distribution. SNPs of control cohorts were sampled independently according to population allele frequencies. Homogeneous case sets were generated by repeatedly sampling controls and selecting individuals whose PRSs pass a threshold corresponding to a prevalence of 0.01. Heterogeneous cohorts were created by combining an equal number of homogeneous cases and controls. The scores of these cohorts were evaluated over a range of sample sizes keeping variance explained constant at 0.034  tends to produce highly positive scores, as all ascertained SNPs are ascertained among one subgroup, and not ascertained in the other, producing identical correlation patterns between all SNP pairs. In the subtyping scenario (β2 → β1), SNP pairs within either S1 or S2 are positively correlated, but SNP pairs with one S1 SNP and one S2 SNP are negatively correlated, significantly attenuating the score. This pattern is also observed in the logistic model in S1 and S2 are slightly ascertained over the entire case set, a negative correlation bias in the liability model is still observed in these SNPs, decreasing the score from zero.We find in Lastly, we tested the performance of CLiP in the subtyping scenario when associated SNPs are subdivided amongst an increasing number of hidden subtypes. We tested the performance of CLiP by fixing the number of cases and controls at 50,000 each, the total number of SNPs at 100, and the total variance explained at 0.05, while varying the number of sub-phenotypes and the fraction of SNPs that are shared across all sub-phenotypes. When this fraction is zero, the sub-phenotypes are completely independent, and the SNPs are divided into mutually exclusive subsets associated with each sub-phenotype. When the fraction is non-zero, that fraction of SNPs has the same effect size across all sub-phenotypes. Results of these simulations are shown in ϕ(Y) against a conventional unweighted correlation over the same individuals.To demonstrate heterogeneity detection in quantitative phenotypes, we simulated homogeneous cohorts by sampling phenotypes from the true PRS-dependent distribution ϕ over phenotypes converted to percentiles improved performance for all learned weight functions, possibly because percentiles limit the domain of the phenotype over which the weight function must be positive, reducing the contribution to the score calculation by extreme PRS values. In addition to testing pre-selected functions for ϕ, we performed a local search over polynomials of increasing degree , intended to assign large weights to the positive extreme of the phenotype distribution, both underperform. The three learned polynomial functions perform similarly and significantly outperform all manually selected functions.We evaluated the performance of our polynomial weight functions against the step function and other weight functions by the difference between the CLiP-Y score of simulated heterogeneous cohorts and the calculated expected homogeneous score. A derivation for the expected score is shown in The same relative performance of the weight functions is observed when tested against an increasing cohort size with a fixed variance explained of 0.1, shown in the left plot of G and gene expression Z, TWAS performs association tests to estimate SNP-gene effect sizes β. In a larger genotype cohort G′, gene expression is then imputed by Z′ = G′β and used to estimate gene-trait effect sizes α. The effect sizes α are interpreted as the fraction of SNP variance mediated by the involved genes. CLiP-X tests for heterogeneity among these quantitative gene-trait associations. In our simulations, we allow for correlations between genes due to shared SNP effects. To model this, we generate gene expression variables as linear functions over a common set of SNPs along with normally distributed error, with a specified SNP-gene variance explained.CLiP-X performs heterogeneity detection in case/control liability threshold models with quantitative predictors. While the identity of these predictors may be arbitrary, we consider in particular the application of CLiP-X to Transcriptome-Wide Association Studies (TWAS), in which imputed gene expression variables are tested for association with disease status , 39. In To demonstrate the performance of CLiP-X in case/control cohorts with continuous predictors instead of binomial SNPs, we simulated quantitative expression data by first sampling 100 SNPs, and then sampling 10 normally-distributed expression variables as linear functions of these SNPs with variance explained gene see . These 1We observe that for all sample sizes, the heterogeneity score is approximately distributed with mean 0 and standard deviation 1 in control cohorts. As predicted, the homogeneous case group exhibits highly negative correlations between associated SNPs, and the resulting CLiP-X score can be accurately estimated from expected correlations (blue) using knowledge of summary statistics only. Additionally, because the input predictors of CLiP-X are normally distributed, we can confirm by Fisher’s transformation that sample correlations between predictors exhibit the expected variance around the calculated null score, indicating the null score accurately estimates the true expected correlation . This es−4, though some heterogeneity may be contributed by batch effects. By summing scores across cohorts, we obtain a larger but still significant p-value of 0.011, suggesting that while batch effects contribute to detected heterogeneity, they do not completely account for all heterogeneity observed in the data. Lastly, by applying meta-analysis methods over individual cohort scores, we obtain a Fisher’s χ2 p-value of 0.030, and a Z-score of 2.03, also supporting the presence of a significant heterogeneity signal.To evaluate the performance of CLiP on real genomic data sets, we tested for the presence of heterogeneity in case/control cohorts collected by the Psychiatric Genomics Consortium (PGC) for schizophrenia, from which 108 associated loci were discovered by GWAS . After tTo investigate the potential contribution of demographics to observed heterogeneity, we inferred ancestry subgroups of the largest four case/control cohorts in the PGC data set  and scored cases and controls belonging to each subgroup individually. Ancestry inference was performed using fastStructure  with the−9 to 8.45 × 10−11. As expected, all polynomial functions performed similarly, so only the degree-6 polynomial was applied to further analyses. After partitioning by sex and neuroticism subcluster, we obtained scores which no longer passed a p-value threshold of 0.01 for heterogeneity: a value of.0165 in males, and.0249 in the “Worry” subcluster. However, from simulation results in We also applied CLiP-Y to test for heterogeneity in neuroticism in a sample of 10719 individuals from the UK Biobank , 42. ParWe present a general framework for identifying hidden heterogeneity among cases given only genotype and phenotype data for a single disease, while being robust to confounding heterogeneity from sources such as ancestry. We derive modified test statistics to account for non-genotype input variables such as expression data, which may be continuous and exhibit confounding correlations in controls due to shared eQTLs. Additionally, we allow for heterogeneity to be scored in quantitative phenotypes that lack a clear distinction between cases and controls which would facilitate a simple dichotomous contrast of correlation patterns.In addition to detecting heterogeneity, we describe an informal method to discern between heterogeneity arising from misclassification, in which a significant subset of cases do not exhibit elevated risk with respect to the PRS, and subtyping, in which the PRS comprises hidden sub-PRSs with distinct effect sizes and ascertained individuals. Prior to correction by the control score, misclassification produces highly positive scores, whereas subtyping produces negative scores in the liability threshold model and scores near zero in the logistic model (and are thus undetectable). However, the magnitude of the heterogeneity score itself is highly dependent on many variables including sample size, number of SNPs in the PRS, and the magnitude and distribution of effect sizes, and this precludes us from devising a more formal test for one or the other heterogeneity scenario.Our analysis of SNP correlations among cases also reveals a distinction between the logistic and liability threshold models which until now has been unreported. Wray and Goddard  report tWe caution against attributing detected heterogeneity directly to the underlying disease etiology. The source of heterogeneity may instead be due to issues such as batch effects arising from data collection or stratification of the PRS across demographic features such as age or sex. Depending on the degree to which these features are known, they can be ruled out as primary contributors to detected heterogeneity by separately scoring subsets of the data partitioned on these features, though this requires data sets large enough post-partition. Detecting heterogeneity due to demographic variables may be of interest itself in certain applications, such as evaluating the performance of PRSs for scoring disease risk when applied across diverse populations. While CLiP does not positively determine the source of heterogeneity within a data set, it serves as a lightweight method to screen for the presence of heterogeneity and a starting point for further investigation.Lastly, the real data results presented in this manuscript only consider PRS based on SNPs whose association signals are genome-wide significant. This removes concerns of false positive associations within the PRS. PRS constructions that do include lower-significance SNPs explain more heritability, and are an attractive next challenge for finding heterogeneity signals. Aside for the statistical challenge, this future work would require handling much larger sets of SNPs, and therefore larger matrices of correlations.We envision CLiP as a method to quickly screen many polygenic risk scores for heterogeneity and flag particular traits for further investigation, either as a way to further elucidate potential subtype-specific etiologies, or to detect unwanted transferability issues across different demographic groups. At the grander scheme of human genetics, generalized testing for heterogeneity paves the way for recovering additional layers of the network of effects that explain traits by interacting genetic and other factors. Going beyond the first-order, linear approximation of these effects holds the promise of better explaining mechanisms beyond identification of their contributing input factors.S comprises associated SNPs reported in GWAS summary statistics, with the counted allele selected so that the corresponding effect size is positive. As described in Results, associated SNPs participating in the same PRS are negatively correlated over a set of cases selected according to that PRS (panel B). When the cohort comprises both cases and misclassified controls, the pattern of ascertainment of risk-alleles is consistent for particular individuals across all SNPs, resulting in positive correlations between SNPs (panel D). Panel E depicts a mixture scenario with two hidden disjoint PRSs. Individuals labeled as cases of the observed phenotype may be in reality a case for sub-phenotype 1 only (blue), sub-phenotype 2 only (orange), or both, whereas controls are observed as such (grey). The presence of cases for multiple hidden sub-phenotypes produces a mixture of positively and negatively correlated SNPs depending on the membership of the compared SNPs (panel G).In a case-control GWAS, a heterogeneous cohort of cases can be interpreted as comprising a mixture of hidden case subtypes, each exhibiting an elevated risks of disease according to a unique polygenic risk score. These subtype-specific PRSs are unobserved and may confound discovery of case-control associations. We define two models for generating genotype matrices of heterogeneous cohorts: First, misclassification, where ideally a subset of individuals are not really cases, but have been rather labeled as such despite being controls. This may occur due to erroneous phenotyping, but it may also suggest distinct disease etiologies, some of which are not ascertained for the PRS of interest. Second, a mixture of multiple unobserved sub-phenotypes which are all captured to some degree by the PRS of interest. An idealized example would involve SNPs of a PRS divided between sub-types such that each SNP was truly associated with only one subtype, and no SNP shared associations with multiple subtypes. A case is observed if the individual passes the liability threshold of at least one of these sub-phenotype PRSs. The goal of CLiP is to distinguish a heterogeneous cohort from one that comprises only homogeneous cases and controls for a single PRS. In the following sections, we first describe a correction (CLiP) to current applications of heterogeneity scores , where wHere we describe three models characterizing risks of disease based on odds ratios or effects of SNPs. We will demonstrate in the Results section that only in the Risch method is independence of PRS SNPs preserved among cases, whereas both the logistic and liability threshold models introduce correlations between these SNPs after ascertaining for disease status.M SNPs in a PRS with relative risks RRm and constant A, an individual with genotypes x has the following disease risk:V = 0.01, we substitute odds ratios for relative risks. Additionally, we set the constant M SNPs have a constant odds ratio OR and allele frequency p, then A and appropriateness of substituting odds ratios for relative risks is shown in The Risch model describes disease risk as a prior disease prevalence multiplied by a product of relative risks corresponding to each risk factor. For M SNPs. Rearranging this function, the disease risk can be expressed as a sigmoid function over the log odds. The effects βm are interpreted as log ORm where ORm is the odds ratio of SNP m with respect to disease y. To ensure the fraction of cases in a random sample equals the desired prevalence V, the intercept term β0 is set to X are mean-centered to 0. For a particular individual x,The logistic regression model describes the log odds of disease risk as a linear function over βm no longer corresponds to an odds ratio, but rather an effect size on the standard normal liability scale. The fraction of variance explained by the PRS XTβ is subtracted from the total variance 1. Individuals are assigned to cases if their liability scores pass a threshold T on the standard normal distribution. If Φ denotes the standard normal cumulative distribution function, then T is placed such that 1 − Φ(T) equals the prevalence of the disease. Likewise, for any individual x, the disease risk is denoted by the probability of surpassing T given that only the value of the PRS xTβ is known.The liability threshold model assumes that case/control labels are assigned according to a hidden continuous liability score. Here A central assumption of the hypothesis test in Han et al.  is that X comprising N cases and M SNPs counting the number of risk-alleles, as well as a matrix of controls X0 with N0 individuals. The SNPs included in X are typically those reported in summary statistics at unique loci, and should be selected so that there is little LD between them and their correlation among controls is near 0. Pairwise SNP correlations are calculated over cases and controls separately and stored in R and R0 respectively. These correlations are then compared against their null expected values. If we interpret controls as population controls in that they are sampled from the full liability distribution, then the expected correlation among controls pj and γj are the allele frequency and odds ratio, respectively, for SNP j,SCLiP is a weighted sum of differences in correlation between cases and controls, to account for prior sources of SNP-SNP correlation such as ancestry. A high score resulting from a bias towards positive correlations would suggest the presence of subtypes with differing ascertainment for the included risk-alleles, and thus heterogeneity. The weights are intended to adjust the score’s sensitivity to certain SNPs based on their allele frequency p and odds ratio γ, with larger odds ratios and frequencies close to 0.5 producing greater weights. The BUHMBOX score is shown by Han et al. , assume Zij is sampled according to a mean and variance specific to the subtype of individual i, denoted by π. For a homogeneous group of cases, π = 0, and our simulations assume π = 0.5 for heterogeneous cases, but in practice this proportion is unknown. Incorporating this proportion allows the redefinition of expectations over the entire cohort as weighted sums of the expectations over the subgroups. The expected correlation evaluated over the entire group can then be calculated according to within-group expectations:Given wjk for each expected rjk.We would like to make use of these expectations over correlations by incorporating them as weights in the heterogeneity score. As predictors with high mean differences between subgroups and high effects are expected to contribute more signal to the score, weighting them higher than other predictors will increase power to detect heterogeneity. Therefore, we would like to define a set of weights π at the null value, π = 0.wjk.We derive the weights for continuous variables in an analogous manner to Han et al. , by takiZj⋅ and Zk⋅ can be expressed as the following. For further details on the derivation, please see Given the assumption of no correlation within subgroups, the correlation between two variables n et al.  for Bernμj. We can use this value as an approximation for Additionally, in practice we do not know the value of The basic CLiP test for heterogeneity relies on differential enrichment of SNP effect sizes or odds ratios across subtypes, and thus requires ascertainment for cases. But one can presume that heterogeneity exists in quantitative phenotypes as well; e.g., are there distinct genetic mechanisms predisposing individuals to being tall? But extending this method to quantitative phenotypes presents a challenge as there is no dichotomous delineation between cases and controls. A naive solution may be to pick an arbitrary z-score as a threshold and denote samples who score higher as “cases” and those lower as “controls.” This introduces a trade-off between sample size and signal specificity, as lowering this threshold provides more samples for the correlation analysis but also introduces more control-like samples which will attenuate SNP associations, and the correlations themselves. A more principled method would allow for the inclusion of all continuous samples, but give higher weight to those with large polygenic SNP scores. Thus we propose to score heterogeneity by a weighted correlation with phenotypes serving as a measure of the importance of a sample in the case set. These weights determine the degree to which individuals count as a “case”, and therefore their contribution to the total heterogeneity score of the genotype matrix. Artificially creating the two groups by applying a hard threshold over the quantitative phenotype values is a special case of this method with a step function as the weighting scheme, equally weighting all individuals above the threshold “step.”Y is calculated from the PRS score with normally distributed noise added according to the desired PRS variance explained. As in the CLiP-X simulation procedure, we generate heterogeneous cohorts by concatenating a subset of cases and controls together into a single putative set of cases. For quantitative phenotypes, the “control” subset is generated so that the quantitative phenotype value is simply sampled from the normal distribution with zero PRS variance explained. A more detailed description of the simulation procedure is provided in Here SNPs as input predictors are sampled directly from binomial distributions with fixed minor allele frequency of 0.5. The quantitative phenotype N individuals let Xij ∈ {0, 1, 2} be the number of risk alleles of SNP j in individual i, and let Y =  be values of the quantitative trait. We introduce a normalized weight vector across the N individuals defined as i, ϕi ≥ 0 and We define a weight over individuals based on phenotype such that those with higher weight contribute more to the heterogeneity score. For a cohort of j, a random variable Xj⋅ with probability equal to the weight ϕi assigned to each individual i. Rather than calculate the correlations directly over SNPs in X, we now calculate correlations over these random variables. We omit the superscript ϕ in uϕ when it is clear from context. For a single SNP j, we define the weighted mean value across N individuals as:j and k, we define the weighted covariance as:Rϕ for any weighting ϕ as:ϕi. These changes produce the following preliminary heterogeneity score for quantitative phenotypes:Q a weighting scheme over SNPs as described in Han et al. , and determines the contribution of individuals to the weighted correlation substitution in CLiP-Y. Optimization is performed over a small set of discovery simulated cohorts, and validated in a larger set of simulated cohorts. A set of candidate functions which pass a fixed threshold are stored, and of these the function which performs best on the larger validation set is selected.(PDF)Click here for additional data file.S1 FigEach sample comprises 100,000 individuals with randomly sampled genotypes, and case/control status was assigned according to either a logistic or liability threshold model with a desired prevalence of 0.01. The resulting fraction of individuals assigned to cases by each model is plotted. Colors indicate a fixed odds ratio assigned to 10 SNPs, with each value simulated over 10 trials.(PDF)Click here for additional data file.S2 Fig(A) Case/control cohorts generated from logistic or Risch models with 100 diploid SNPs with allele frequency of 0.2 and odds ratio of 1.2. A prior prevalence of 0.01 is assumed for both models. Scores of logistic cohorts exhibit a negative bias resulting from correlations between SNPs not seen in the Risch model. (B) Case/control cohorts generated from logistic or Risch models with 100 diploid SNPs with allele frequency of 0.2 and odds ratios of 1.06, and prior prevalence of 0.01. With smaller effect sizes, the negative bias in the logistic model disappears.(PDF)Click here for additional data file.S3 FigHeterogeneity scores (y-axis) evaluated on heterogeneous cohorts comprising a mixture of true cases and controls at different proportions (x-axis). Colors indicate the total cohort size. The X-axis indicates the fraction of individuals that are true cases. When the fraction is 0, the cohort contains only controls, and all expected correlations are 0, producing a heterogeneity score of 0. When the fraction is 1, the cohort contains only cases, and produces a highly negative score due to negative correlations between all pairs of SNPs. As expected, a mixture of cases and controls produces positive scores, with the peak score occurring when the cohort is split evenly. More detailed results of this set of simulations are shown in (PDF)Click here for additional data file.S4 Fig(A) Simulated homogeneous and heterogeneous cohorts in which both cases and controls are sampled from two sub-populations with an Fst specified by color. (B) Power (dotted) and specificity (solid) over 20 trials. At high Fst values, both homogeneous and heterogeneous case scores are attenuated towards zero, and while power remains high, specificity begins to decline with values of Fst greater than 0.05.CLiP corrects for confounding heterogeneity such as ancestry by calculating the difference in SNP-SNP correlations between cases and controls. Any confounding patterns that are present in controls as well as cases are then canceled from the score. (PDF)Click here for additional data file.S5 FigPerformance is shown a function of the fraction of SNP effects unique to a particular sub-phenotype (x-axis). Colors indicate the number of sub-phenotypes. Simulations were performed with 50,000 simulated cases and 50,000 controls, and a total SNP variance explained over all sub-phenotype PRSs set to 0.05. More detailed results of this set of simulations are shown in (PDF)Click here for additional data file.S6 Figx, 1] (x-axis) and a decreasing one for  (y-axis) are combined so that their sum is the tested weight function. Each bin on the axes represents a transition point for the two step functions. The heterogeneity score is tested against a single homogeneous cohort, so optimal scores should be those that are most negative. (A) The best scores are those where x is low on the PRS percentile scale but not 0, while y is high on the PRS percentile scale but not 1. This coincides with the optimal polynomial functions obtained by a local search. (B) A zoomed view of the top left in A, showing that the optimal scores are not obtained by step functions at the periphery of the PRS distribution.To demonstrate that optimal quantitative weight functions for heterogeneity are concave functions, two interval indicator functions in , an increasing one for We are sorry that we cannot be more positive about your manuscript at this stage. Please do not hesitate to contact us if you have any concerns or questions.Yours sincerely,Samuli RipattiAssociate EditorPLOS GeneticsScott WilliamsSection Editor: Natural VariationPLOS GeneticsWhile the reviewers appreciate the potential novelty in the method, they also raise serious concerns about the modeling approach, clarity in the presentation of the method, its usefulness in the presence of population stratification and genotyping batch effects, the presented simulations and the applicability to the real world genetic data that need to be thoroughly addressed before reconsidering the publication of the manuscript.Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: The authors present a method to detect heterogeneity within a single GWAS sample. The main method (CLiP) is designed for case-control GWAS with SNP data, using only those SNPs that reach genome-wide significance in the GWAS to form a PRS. The authors explore two main scenarios: (1) misclassification in which the cases are comprised of true cases and controls, and (2) the cases are made up of subtypes of the diseases and controls are true controls for both subtypes. The simulations are well thought out and demonstrate the behavior of this method in a variety of scenarios. However, the authors do not spend adequate space discussing the benefit of CLiP versus prior methods with no direct comparisons of other metrics. Additionally, they do not demonstrate the distinction between multiple sources of heterogeneity, such as batch effects, population stratification, case misclassification, or clinical subtypes. This is a noted limitation of prior methods, therefore should be addressed in the main text.Major comments:• The Results section is currently written similarly to a Method section, with much of it detailing the simulation framework. While this is helpful, the section would also benefit from more context given to the results, with specific numbers given within the text. It is currently up to the reader to interpret the Results from the figures, which can be confusing.• The major criticisms of prior methods in the Introduction cite the inability to distinguish the hidden factors as due to population stratification or batch effects. However, it is not clear that this method is able to distinguish from these reasons either, as the example from PGC shows that it can detect batch effects between cohorts  that is not present in the summed stratified analyses.• As CLiP is an extension of BUHMBOX, but correcting for the negative correlation bias, it would be helpful for a direct and explicit comparison, both in the simulations and the applied PGC example. For example, a figure showing the power to detect heterogeneity with and without this correction should be included in the main results.• It is not clear from the manuscript if it is possible to distinguish between batch effects and heterogeneity by subtype/misclassification within a single sample. In the applied example given in PGC, multiple cohorts are required to distinguish between heterogeneity overall (pooled cases/controls) and heterogeneity without batch effects from the different cohorts (summed across cohort-level heterogeneity scores). Therefore, it may be misleading to conclude that this method is superior from other previous methods due to this ability.• The majority of simulations center around a misclassification framework, in which the “cases” are comprised of both true cases and controls. The framing of the method around subtypes, with examples given for bipolar disorder and schizophrenia, is not fully justified by the results and simulations. The manuscript may be better served by expanding upon results presented in Figure 2B to support this utility.• The application of CLiP to a schizophrenia case-control GWAS could also be expanded. While subtypes of schizophrenia are less well defined, an exploration for possible sources of heterogeneity within these cohorts would be useful for interpretation. As subtypes of bipolar disorder are better defined, if this data is available it may be a better suited example to pick apart the potential contributions of batch effects, population stratification, and heterogeneity due to subtypes.• A discussion of the limitations for this method should be included in the Discussion. For example, what are the assumptions made for the negative correlation bias correction that may not be appropriate for some scenarios?• As low power is cited as a prior limitation to detect heterogeneity, an analysis evaluating power should also be included in the results section to weigh the merits of this new method.• In general, it would be helpful to expand upon the schizophrenia analysis to fully demonstrate the underlying factors of heterogeneity. This would provide more context for the usefulness of this method and what underlying issues or future directions it can uncover. A discussion of these aspects would make this manuscript more relevant for a general genetics audience and increase the likelihood of adoption.Minor comments:• Page 11, lines 203-204 refer to Figure 3, but it is unclear which panels they refer to. Figure 3B and Figure 3C are not referenced directly in the text.• Page 8, line 150 has “heterogeneity” misspelled.• There are currently no methods detailing the studies in PGC. For example, were all participants of European ancestry and similar ages? Similar diagnostic criteria? This would help in the interpretation of results.• The word “cohort” is used for both the “cases”  and the overall sample size of “cases” and “controls” This can be confusing at times and alternative language should be used to distinguish between the samples.Reviewer #2: This study presents a method called CLiP which uses the correlations between SNPs (or predicted expression levels) in case patients to dissect heterogeneous subsets in cases. This is a generalization of Han et al method. The authors’ contributions are two: (1) they showed that the correlation=0 assumption under no heterogeneity is only valid in multiplicative model but not in liability threshold model and presented a correction for that. (2) they generalized the method to a) when other predicting variables than SNPs are used and b) when continuous phenotype is of interest.Overall, the paper is quite well written. The problem is interesting and important, and the solution is straightforward. I find contribution (2) quite interesting. Contribution (1) is also important, but there can be a bit of controversy. First, the authors say that the correlation would be negative if “logistic or liability threshold model” is true. In liability threshold model, it is clear that the correlation becomes negative. For logistic model, I didn’t understand why the correlation has to be negative. In fact, Risch’s multiplicative model can be presented as logistic model. Multiplicative nature of ORs of SNPs can be modeled as additive in logit space. This seems to be written in the latter part of Supplementary Note section 9.2, but the long derivation was hard to follow. Probably the authors can give an intuitive explanation about that? Second, I personally agree that liability threshold model more closely models the truth, but am not sure if it’s really the truth. The truth might be in-between of the two (liability threshold model and multiplicative). I feel that the popularity of liability threshold model was driven from the heritability estimation (where liability is a must for binary traits). But that’s because liability is one reasonable explanation that can model heritability, but not because liability is strictly true. In sum, no one knows if that’s true. I am not sure if there were any studies that tried to test if liability threshold model more closely models the truth in complex diseases. It would be better if the authors can do some literature search and cite some.  I agree that Han et al. method can be underpowered by non-multiplicative model (e.g. liability), but worry if CLiP can increase false positive rate if the truth would be in-between.In the method, I expected some equations to derive the negative expected correlations under the liability model, but was surprised that they were skipped directly to CLiP-X, leaving relatively short contents for the main CLiP. I feel that this part is as important as CLiP-X and Y, so hope that a summary of 9.4 can be in the main method, so that readers can easily implement the CLiP method using their own code.Minor comments:The title is confusing. I didn’t catch what “polygenic risk score predictor” means. Given title, I expected contents related to the (currently popular) usage of PRS for disease predictions. I understand that the authors did not want to use SNP or locus to emphasize that expressions can be used, but not sure if the current title is the best choice.The authors need to add more detailed and elaborated explanations about the “transcriptome-wide association study”. First, many geneticists might not be familiar with TWAS. The authors need to explain that there is an effort to associate the gene expression level of each gene with the phenotype. Second, to some people (like me), TWAS has double meaning: method name and study design name, so can be easily confusing.The method depends on the independency of SNPs. Did the authors do some LD pruning? Subtracting the control correlations might help controlling for long-range LD; was this the case in real data? Or controls are actually not needed?P9. Line 173: PRSs are expected to be zero than positive → you mean, negative?P11. Line 209: when the contents refer to Figure 3, I didn’t find it relevant. Is this a correct figure number?Reviewer #3: The manuscript considers a statistical method to detect phenotypic heterogeneity in GWAS cohorts by using individual-level genotype data on GWAS samples. The idea is that the correlation between genotypes at different SNPs in cases increases if the cases contain heterogeneous subgroups. The method is applied to schizophrenia data. The manuscript also extends the method to continuous traits but no real data examples are given.I find it difficult to evaluate the novel contribution of this work because the method is not presented very clearly (see below for details) and it is unclear how big a difference to the existing method is in realistic settings. The continuous versions CLiP-X and CLiP-Y seem experimental and no real data example is given. The current real data example with schizophrenia GWAS does not convincingly show how the method could conclude whether there is or is not heterogeneity in cohorts.About the term “controls”Unclear whether “controls” in this paper refers to a sample from the population or to proper disease-free controls. If former, then should talk about “population controls” and make clear that these are not proper disease-free controls. Theoretically, this has an important effect on whether risk SNPs are expected to be independent in “controls”. Typically, SNPs at different loci are independent in general POPULATION that is a mixture of cases and disease-free controls. And when risk SNPs are independent in population they are not independent either in cases nor in disease-free controls.Models:Three disease models are mentioned: “multiplicative Risch/binary model”, “logistic model” and “liability threshold model”.The manuscript does not define clearly “multiplicative (Risch/binary) model”, or rather what is its difference from the logistic model. This should be done in Methods.Best proxy is line 131 saying: “a multiplicative binary model, in which an individual's risk is the product of odds ratios of probability of disease for associated SNPs”First, risk is a product of relative risks, not odds-ratios. I assume that SNP effects are defined in terms of ORs and not RRs and so the multiplicative model should be formulated for odds of disease?Second, there needs to be some baseline risk for an individual without any risk allele on which each risk allele adds to. That together with relative risks or odds-ratios and genotype distribution in population define the prevalence in the population. Unclear what is the population prevalence in the example of Figure 1A and whether prevalence of disease is matched between the “multiplicative model” and “logistic model”. Both prevalence and ORs used in simulations should be realistic.Third, the logistic regression says that odds of disease increase multiplicatively with each copy of the risk allele, and multiplication happens independently across the SNPs. Thus I see no difference between “multiplicative model” and “logistic regression model” as statistical models. I assume that the difference is that the assumption about the population genotype distribution are different in settings where authors use these two models. In settings with “multiplicative model” the authors assume that risk SNPs are independent in CASES , whereas in settings with “logistic model” the assumption is that SNPs are independent in the whole POPULATION . However, when prevalence is low (a few percent or less) then independence between SNPs in population together with the logistic regression model lead to approximate independence of SNPs in CASES (as well as in disease-free CONTROLS), see e.g. Pirinen et al. Nat Gen 44, 848–851(2012). Thus, if prevalence is realistic for typical common diseases, I would not expect a large difference from independence in cases, and hence no large negative correlations between SNPs in cases. The paper should make clear whether the theoretically correct fact of negative risk SNP correlations in cases truly has a practical effect over earlier method (BUHMBOX) when prevalence is realistic. The simulations in Figure 1A should be done so that both settings (“multiplicative” and “logistic”) have the same population prevalence and ORs, and then it should be reported whether there is a practical difference after the correction for negative correlations in cases.Fig.2 “Colors indicate the total cohort size. All tests were conducted over 50,000 cases and 50,000 controls”Inconsistent that sample varies and is fixed to 50k.Methods section mentions one score: S_het, “modified heterogeneity score”. Is this what is used in all Figures? Then should use symbol “S_het” in main text to make this clear.L.136 “conventional, case-control score for heterogeneity”This is not defined anywhere in Methods.L. 138 “We simulated individual data using 100 independent SNPs”Independent in population, or in cases or in controls?L.140 “we assumed a variance explained of 1”Needs explanation. I assume that this means that the phenotype is deterministically defined from genotypes. ORs are now the same but do both models also lead to the same prevalence in the population?L. 141 “We evaluated the dichotomous-trait score relative to sample sizes for both homogeneous and heterogeneous groups.”Unclear what this means?“case cohorts were generated by repeatedly sampling control genotypes and selecting individuals whose PRS pass a threshold corresponding to a prevalence of 0.01”I assume that genotypes are sampled from POPULATION frequencies, not from CONTROL frequencies? Or if controls are population samples i.e. a mixture of cases and proper controls, then that should be said very clearly.L.153 “PRS over 108 genomewide-signicant SNPs with a total variance explained of 0.034”On which scale is this variance? And is it in population or in some case-control sample?L.185 CliP-Y section starts: “In practice, we found converting PRSs to percentiles improved performance for all learned weight functions, possibly because percentiles limit the domain of the PRS function over which the function must be 0, and they reduce the contribution to the score calculation by extreme PRS values.”Some kind of intro to what this section aims to do and what weight functions etc are should be stated before the sentence above, that currently is incomprehensible when first read by the reader who has not yet read the Methods that come only later.L 293. “the presence of distinct mixtures of cases within a cohort which have been identified as cases through different PRSs.”Unclear whether this means that the cases are identified through different PRSs or whether these cases happen to have heterogeneity and hence different distributions of PRSs?“misclassifcation, whereby a subset of individuals are not really cases, but have been rather labeled as such despite genetically being controls”Why there is word “genetically” there? Missclassification happens purely by mislabeling the phenotype, and is not informed by genotypes.L 296. “but it may also suggest distinct disease etiologies, some of which are not ascertained for the PRS of interest. Second, a mixture of unobserved sub-phenotypes with distinct PRSs.”What is the difference here? Both refer to a setting where sub-phenotypes of cases have different effect sizes (“distinct PRSs”).L 326. “The expected correlation among controls, E [R0jk], is always 0 in practice as SNPs are sampled independently, but is included below for clarity.”If you assume that SNPs are independent in POPULATION, and that the logistic model holds, then risk SNPs are independent neither in disease-free CONTROLS nor in CASES. Supplementary material:L.759-760 For which genotype group Is prevalence B given? Odds-ratios do not directly correspond to risk, but to odds.(27) and elsewhere would be clearer is conditioning on being case was explicitly written out.(28) This equation is based on the ASSUMPTION that p = p(x_i)*p(x_j) in cases. If this is the assumption of "Risch model", then that should be simply stated, and there is no need to show mathematically that the SNPs are independent if that is already assumed.(33) Assumes Hardy-Weinberg equilibrium in cases. It is not self-evident that this is true, so it should be made clear that this is an assumption.Formulas 776-778 should be corrected for “=0” parts.(35) Would benefit from middle steps that say that this is Bayes rule.Formulas (51) – (54) are not understandable as there are unexplained indexes (s and sc) and also likely something is missing.(55) conditions on X_i = b, and right hand side has alpha_i and X_i and T (which is not defined anywhere).I feel there is too much work left for reviewer trying to understand unclear and undefined notation and formulas. I haven’t read supplementary further.**********Have all data underlying the figures and results presented in the manuscript been provided?PLOS Geneticsdata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.Large-scale datasets should be made available via a public repository as described in the Reviewer #1: YesReviewer #2: YesReviewer #3: Yes**********what does this mean?). If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  and your responses to reviewer comments. If eligible, we will contact you to opt in or out. *Dear Dr Yuan,Thank you very much for submitting your Research Article entitled 'Leveraging correlations between variants in polygenic risk scores to detect heterogeneity in GWAS cohorts' to PLOS Genetics. Your manuscript was fully evaluated at the editorial level and by independent peer reviewers. The reviewers appreciated the attention to an important topic but identified some aspects of the manuscript that should be improved.We therefore ask you to modify the manuscript according to the review recommendations before we can consider your manuscript for acceptance. Your revisions should address the specific points made by each reviewer.In addition we ask that you:1) Provide a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript.archive. If your image is from someone other than yourself, please ensure that the artist has read and agreed to the terms and conditions of the Creative Commons Attribution License. Note: we cannot publish copyrighted images.2) Upload a Striking Image with a corresponding caption to accompany your manuscript if one is available (either a new image or an existing one from within your manuscript). 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Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org.While revising your submission, please upload your figure files to the data availability policy requires that all numerical data underlying graphs or summary statistics are included with the submission, and you will need to provide this upon resubmission if not already present. In addition, we do not permit the inclusion of phrases such as "data not shown" or "unpublished results" in manuscripts. All points should be backed up by data provided with the submission.Please be aware that our Similarity Check, powered by iThenticate, into its journal-wide submission system in order to screen submitted content for originality before publication. Each PLOS journal undertakes screening on a proportion of submitted articles. You will be contacted if needed following the screening process.PLOS has incorporated To resubmit, you will need to go to the link below and 'Revise Submission' in the 'Submissions Needing Revision' folder.[LINK]Please let us know if you have any questions while making these revisions.Yours sincerely,Samuli RipattiAssociate EditorPLOS GeneticsScott WilliamsSection Editor: Natural VariationPLOS GeneticsReviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #2: The authors have addressed my comments.The current version looks much better, particularly in describing the models (logistic / liability thres)Reviewer #3: I thank the Authors for expanding the manuscript and clarified the methods considerably. The manuscript has interesting methodological ideas that are useful for the field.Main comments:1. Such a clearly differing behavior of correlation between predictors under logistic and probit models seems surprising. I would still suggest that the Authors check that they are simulating data from the same populations under both models.In particular, on p.26 l.546-547 it sounds like the prevalence in logistic model has been set for the rare set of individuals who carry no risk alleles at all, and hence the population prevalence will become much larger than the prevalence in those genetically protected extreme individuals. (Unless genotypes have been mean-centered in logistic model as they seem to be in liability threshold model formula 3.) The same issue with Risch model where Authors say in their answers that “maximum possible risk is given by (0.05)*(1.16)^(2*10) = 0.97”, but with this approach the prevalence in the population would rather be23% = sum * 0.05 * 1.16^ (0:20) ) than target 5%.Similarly you could compute the population prevalence that the logistic regression model is imposing as the expectation of probability of being case (formula 2) over the population genotype distribution.If there are differences between population prevalence in logistic and liability threshold model simulation in Figure 1, that could affect the observed differences in SNP correlations in cases. My suggestion is that Authors check these simulations once more to make sure that both models are simulating genotype data from a population where the POPULATION PREVALENCE is 5% (or 1%) and the effect sizes are the same per allele.2. Terminology:Usually “probit model” means a liability threshold model with Gaussian CDF, and this model is often called simply “liability threshold model” as is done also in this manuscript. Logistic regression model is also a version of liability threshold model, although not typically called as such, but it seems confusing to me if logistic regression is now called a “probit model” as on p.7 l.151-152 and p.27 l. 564.The end of sentence on l.152 “dot product … sigma(1-sigma)” is unclear.3. Figure 1:Are the colors wrong way around in the figure? Or are the results wrong way around?In panel B, blue has larger negative bias but the legend says blue is logistic model and that in B logistic model is having "notably smaller negative bias"?Similarly in C, blue seems Normal and cyan seems logistic?4. l.754-755. Where is it shown that CliP score ~ N under the null. Section 4.2. does not mention that at all.Minor comments:p.28 “The case probabilities conditioned on SNP values P (y=1|X j ) are calculated from the liability threshold model in equation 3.”How do you get the effect sizes on liability scale? Refer to the equation that you use later in formula 29.Supp. TextL.993 “{1}^N” misses “0”L.995 One assumption not mentioned here is that genotypes at different loci are uncorrelated in the population.**********Have all data underlying the figures and results presented in the manuscript been provided?PLOS Geneticsdata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.Large-scale datasets should be made available via a public repository as described in the Reviewer #2: YesReviewer #3: Yes**********what does this mean?). 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PLOS Genetics may also choose to issue a press release for your article. If there's anything the journal should know or you'd like more information, please get in touch via  9 Sep 2020PGENETICS-D-19-02004R2 Leveraging correlations between variants in polygenic risk scores to detect heterogeneity in GWAS cohorts Dear Dr Yuan, We are pleased to inform you that your manuscript entitled "Leveraging correlations between variants in polygenic risk scores to detect heterogeneity in GWAS cohorts" has been formally accepted for publication in PLOS Genetics! Your manuscript is now with our production department and you will be notified of the publication date in due course.The corresponding author will soon be receiving a typeset proof for review, to ensure errors have not been introduced during production. Please review the PDF proof of your manuscript carefully, as this is the last chance to correct any errors. 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Vaccinium macrocarpon Ait.) is a North American fruit crop domesticated less than 200 years ago. The USDA began the first cranberry breeding program in response to false-blossom disease in 1929, but after the first generation of cultivars were released in the 1950s, the program was discontinued. Decades later, renewed efforts for breeding cranberry cultivars at Rutgers University and the University of Wisconsin yielded the first modern cultivars in the 2000’s. Phenotypic data suggests that current cultivars have changed significantly in terms of fruiting habits compared to original selections from endemic populations. However, due to the few breeding and selection cycles and short domestication period of the crop, it is unclear how much cultivated germplasm differs genetically from wild selections. Moreover, the extent to which selection for agricultural superior traits has shaped the genetic and phenotypic variation of cranberry remains mostly obscure. Here, a historical collection composed of 362 accessions, spanning wild germplasm, first-, second-, and third-generation selection cycles was studied to provide a window into the breeding and domestication history of cranberry. Genome-wide sequence variation of more than 20,000 loci showed directional selection across the stages of cranberry domestication and breeding. Diversity analysis and population structure revealed a partially defined progressive bottleneck when transitioning from early domestication stages to current cranberry forms. Additionally, breeding cycles correlated with phenotypic variation for yield-related traits and anthocyanin accumulation, but not for other fruit metabolites. Particularly, average fruit weight, yield, and anthocyanin content, which were common target traits during early selection attempts, increased dramatically in second- and third-generation cycle cultivars, whereas other fruit quality traits such as Brix and acids showed comparable variation among all breeding stages. Genome-wide association mapping in this diversity panel allowed us to identify marker-trait associations for average fruit weight and fruit rot, which are two traits of great agronomic relevance today and could be further exploited to accelerate cranberry genetic improvement. This study constitutes the first genome-wide analysis of cranberry genetic diversity, which explored how the recurrent use of wild germplasm and first-generation selections into cultivar development have shaped the evolutionary history of this crop species.The cranberry ( Vaccinium macrocarpon Ait.) is a woody temperate perennial fruit crop native to the acidic bogs of North America  that correspond to second-generation selections, or first-generation hybrids, as well as 104 advanced selections (CLT2) derived from current breeding programs and that represent third-generation selections. This cranberry diversity panel is the largest and most complete collection of cranberry genotypes in the world and is currently housed at Rutgers University, Marucci Center for Blueberry and Cranberry Research and Extension Center in Chatsworth, NJ. Accession origin, a geographical infomap, pedigree, and additional information regarding these 362 accessions is provided in The cranberry diversity panel studied here included 362 accessions . From thGenotyping was performed using genotyping-by-sequencing (GBS), following 2; from that, 100 fruit were randomly selected and weighed to calculate average fruit weight, as described in The cranberry diversity panel was phenotyped for fruit yield, average fruit weight, fruit rot, total anthocyanin content (TACy), Brix degrees, and acids during 2006–2010 and 2014–2015 at Rutgers University. Total fruit yield per area was calculated by harvesting and weighing all the fruit within 0.09 mK), from 2 to 10 (with five replicates each), and selected a K value using a cross-entropy criterion computed by the package. Moreover, we performed hierarchical clustering using the Ward clustering algorithm implemented in the hclust function in R, as in Population structure of the 362 cranberry accessions was assessed using a Structure-like population genetic analysis with the R package LEA . We testprcomp R function. Principal components 1–10 were used in further analysis.Genetic relationship among accessions were also investigated using principal component analysis (PCA) in R. The complete SNP dataset was converted into a numeric format  using sommer , and theFST) values between all subgroup pairs using the pegas package  was computed per chromosome using non-overlapping windows of 10 Kb length. The intra-chromosomal genome-wide linkage disequilibrium decay rate was estimated separately for all four subgroups. Linkage disequilibrium calculations were made using in-house R scripts. Association mapping was conducted for all phenotypic traits using mixed linear models, where PC1-10 from the PCA analysis, population structure probabilities, and an additive relationship matrix computed with the A.mat function of the rrBLLUP package (Pairwise linkage disequilibrium (LD) explained by pairwise correlation coefficient . Then, 21,179 SNPs (average site depth was 23.16 reads) uniquely assigned to a genomic position were finally selected after filtering for missing data and MAF. An average of 1764.20 SNP markers were obtained per chromosome . The average gap between SNP markers was 22.19 Kb . PolymorThe distribution of MAF across markers was fairly consistent across subgroups. A large portion of markers showed MAFs <0.1 . In partK = 2  suggested that the genetic relationships among accessions are highly reticulated . Similarly, out of the 121 advanced selections (CLT2), 51 had an accession of NS origin.FST estimates , followed by WLD vs. CLT1 (FST = 0.034), NS vs. CLT2 (FST = 0.023), NS vs. WLD (FST = 0.013), NS vs. CLT1 (0.010), and CLT2 vs. CLT1 (0.007). Additionally, FST 95th percentiles, based 1000-iteration permutation tests (resampling memberships between two subgroups), were 0.35 (WLD vs. CLT1), 0.33 (NS vs. CLT1), 0.32 (CTL1 vs. CLT2), 0.12 (WLD vs. CLT2), 0.12 (NS vs. WLD) and 0.11 (NS vs. CLT2). Some genomic regions presented FST values considerably higher than FST 95th percentiles; for example, single SNP FST estimates were as a high as 0.594 (for WLD vs. CLT2), 0.550 (for WLD vs. CTL1), and 0.403 (for NS vs. CLT2).Using allele stimates , which mstimates . Based oTo infer the effects of domestication and breeding on the genetic diversity of cranberry, we computed the reduction of diversity (ROD), based on the ratio of diversity between subgroups we assumed corresponded to the progression of domestication and breeding . We defiFor maximum ROD (ROD = 1), there were 42 SNPs for step 1 (NS/WLD comparison), 1649 SNPs for step 2 (CLT1/NS comparison), 560 SNPs for step 3a (CLT2/CLT1 comparison), and 1152 SNPs for step 3b (CLT2/NS comparison). SNPs with ROD ≥0.8 and <1 were fewer than for ROD = 1. Steps 1, 2, 3a, and 3b had 180, 114, 318, and 823 SNPs, respectively. Finally, for low or null ROD , most of the steps had consistently high number of SNPs and very few differences .P = 0), TACy (P = 0.003), Brix degrees (P = 0), and acid (P = 7.149e-8). In contrast, we did not observe significant differences for fruit rot (P = 0.2735). Average fruit weight and total fruit yield were highly correlated ; Brix degrees were moderately correlated with both average fruit weight  and total fruit yield ; fruit rot and TACy showed low correlation , as well as acid and total fruit yield  and acid and average fruit weight . Other trait comparisons were not significantly correlated  during 2006–2010 and 2014–2015 . Fruit yr2 between all pairs of SNP markers (To estimate the linkage disequilibrium (LD) patterns in the different cranberry subgroups, we calculated  markers . LinkageK = 3), principal components (PC 1-10), and kinship (additive relationship matrix) to account for population stratification. Using a threshold of FDR = 0.1, we identified one marker-trait association (MTA) for total fruit yield (chromosome 7) and five for average fruit weight . Nevertheless, when we visually inspected each of these MTAs, we found that some of the associations may be spurious due to the high stratification of the subgroups utilized. Particularly, CLT1 and CTL2 accessions had considerably higher values for total fruit yield and average fruit weight than the other two subgroups, and the models used to account for population stratification may not allow the breaking down of this structure. For example, in 10P = 5.83; as illustrated in the small boxplot inside the panel, the G allele seems to increase average fruit weight. However, when inspecting average fruit weight variation by both genotype and subgroup, we found that the significance of this association could be caused by a high number of WLD accessions with AA genotype, which in this case presented lower average fruit weight. Nevertheless, some these suspicious MTA for total yield and average fruit weight partially co-localized with QTLs previously identified using biparental populations, which may require further confirmation and testing . Importantly, this collection includes accessions from the most important states in the United States, commercially and historically, for cranberry production . The anaFST = 0.042, Our analyses in cranberry, including MAF, population structure , PCA Fi, fixatioActinidia chinensis var. chinensis or A. chinensis var. deliciosa , a close relative of cranberry, there is ≤1 chiasma formed per chromosome arm pair during meiosis  higher total yield and average fruit weight compared with the other subgroups. On the other hand, except for anthocyanins, fruit metabolite data showed mixed or little differentiation among wild and modern subgroups, indicating neutral selection, reflecting limited directional improvement. For TACy, the only significant (P < 0.01) differences were between WLD vs. CLT2 and WLD vs. NS. For Brix degrees, differences were attributable only to CLT2 having significantly higher values than the other three subgroups . A similar tendency was observed for acid, although the differences were more subtle . In general, the metabolite accumulation differences between subgroups did not show directional and gradual changes as observed for fruit weight and yield, where modern germplasm are characterized by heavier fruits and more productive varieties. Furthermore, wild and cultivated cranberries still share many morphological similarities and ability to grow well in the same environments. In fact, at the phenotypic level, modern cranberry materials do not exhibit marked differences compared with wild germplasm as in other fruit crops such as kiwifruit  and total yield, fruit color was also emphasized to some extent . Based oThis is the first cranberry genetic diversity study involving a very diverse and large collection of germplasm, which captures early domestication events as well as further genetic improvement through breeding. All of the analyses performed here revealed clear pattern of ongoing genetic change characterized by the gradual reduction of wild alleles and transition into elite materials. We hypothesize that the recent domestication of cranberries and the use of recurrent introgression of wild germplasm into cultivars or advanced selections, reduced number of breeding, i.e., recombination, cycles, together with the intricacies of breeding long-lived perennials, has slowed the genetic differentiation between wild and new cranberry materials. Additionally, the wide use of wild germplasm in today’s commercial cranberry production has also likely contributed to slow the implementation of recently released cultivars. The genetic diversity analyses performed in this study collectively revealed important insights into the domestication and breeding history of cranberry and provide a valuable resource for breeding and further genetic improvement of this crop.10.6084/m9.figshare.13208360.The original contributions presented in the study are publicly available. This data can be found here: doi: LD-G, GC-P, NV, and JZ conceived and designed the experiments, revised and approved the final manuscript. NV, JJ-C, and GC-P collected the data. LD-G and JZ analyzed the data and wrote the manuscript. All authors contributed to the article and approved the submitted version.The authors declare that this study received funding from Ocean Spray Cranberries, Inc. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication.


Microbial genome-wide association studies (mGWAS) are a new and exciting research field that is adapting human GWAS methods to understand how variations in microbial genomes affect host or pathogen phenotypes, such as drug resistance, virulence, host specificity and prognosis. Several computational tools and methods have been developed or adapted from human GWAS to facilitate the discovery of novel mutations and structural variations that are associated with the phenotypes of interest. However, no comprehensive, end-to-end, user-friendly tool is currently available. The development of a broadly applicable pipeline presents a real opportunity among computational biologists. Here, (i) we review the prominent and promising tools, (ii) discuss analytical pitfalls and bottlenecks in mGWAS, (iii) provide insights into the selection of appropriate tools, (iv) highlight the gaps that still need to be filled and how users and developers can work together to overcome these bottlenecks. Use of mGWAS research can inform drug repositioning decisions as well as accelerate the discovery and development of more effective vaccines and antimicrobials for pressing infectious diseases of global health significance, such as HIV, TB, influenza, and malaria. Helicobacter pylori  are a new area of research aimed at identifying genetic variants in microbial genomes that are associated with host variation in or microbe phenotypes, for example genetic variation affecting phenotypes such as carriage  in humanr pylori  and to er pylori .Staphylococcus aureus  genomes, while Escherichia coli.Successful applications of mGWAS include identifying genetic determinants of pyomyositis in s aureus  which res aureus  showed tMycobacterium tuberculosis isolates to 11 anti-TB drugs and reported 13 non-canonical loci that were associated with resistance. Another study  functioning as DNA probes -based methods for identifying all genetic associations with phenotypic variation . Early GA probes . BecauseA probes . These cA probes . As a rengitidis , 2008, Mrculosis  and P. flciparum  with higlciparum  and thatlciparum , paving Campylobacter to cattle and chickens, they had to create a novel method as naively applying the Fishers exact tests would result in many spurious associations. Similarly, in a separate study by M. tuberculosis (MTB), the haplotype-based tests could not be used as diversity in MTB mainly arises from clonal expansion and homologous recombination Single Nucleotide Polymorphisms (SNPs) and INDELs- which are point mutations or small insertions and deletions (indels) that occur within the genome of an organism Gene presence-absence occurs when entire genes are lost or gained. Several processes are responsible for gene presence-absence. These include speciation events (n events  horizontn events . MGEs ann events . The dif(c)Copy Number Variations (CNVs) and Sequence Inversions (SIs). They contribute to adaptation and phenotypic variation of microbes , minor allele frequencies (MAF), effect size (beta for quantitative traits/odds ratio for binary traits) and standard error (SE). To help with interpretation, results are normally visualized using a Manhattan plot whose x-axis is the SNP position and y-axis negative log10 p-value or -log of the SNP. A horizontal line in the plot delineates genome-wide significance threshold. All sample p-values above the line are considered statistically significant. A single SNP passing the significance threshold is often considered a genotyping error owing to the expectance of linkage disequilibrium (LD) s observed in the study and expected distribution under the null hypothesis, a quantile-quantile (QQ) plot is used. From the QQ plot, population stratification or polygenicity can be inferred  see  Part 1b.inferred . The outPrevious research describes in detail the important analytical considerations for microbial GWAS . Here, wRecombination rate refers to the frequency of recombination which generally varies widely among microorganisms such as bacteria and viruses and can thus limit the ability of GWAS to pinpoint specific variants responsible for the phenotype if not accounted for There is evidence that for some pathogens within-host genetic diversity is common . It occuMultiple testing is a source of false positives intrinsic to GWAS. The Bonferroni correction is usually used to correct for multiple testing. However, it is overly strict for densely genotyped and imputed studies where correlations between variants exist  and requk-mers are able to pick up the effect of multiple SNPs. Moreover, they also assign importance to each rule that quantifies how much it affects the phenotype predictions made by the model, while TreeWAS accounts for this by allowing each SNP to contribute only partially to the phenotype. Finally, HAWK reports all SNPs that present a strong effect on the phenotype without determining how much each SNP is contributing.Polygenicity or multiple SNP effects on a phenotype is based on the assumption that many SNPs with small effect sizes will fail the stringent cutoff used for genome-wide significance, however, together their cumulative effect will explain a large amount of the variance in risk  hence prk-mer-based methods, for example in a study analyzing Campylobacter. jejuni, multi-allelic k-mers were tested for association with host preference  versus other environmental factors . In mGWAIn most phylogenetic analyses, beyond heritability, accounting for the heterogeneity in evolutionary patterns across sites is particularly important . PartitiSample size, unlike in human GWAS, mostly poses a subtle problem as most variants in microbial genomes are under strong selection and therefore present large effect sizes even with small datasets. Subtle traits resulting from many low effect variants, however, require larger sample sizes in order to detect significant associations . For phyTraditional microbial-based GWAS tools can be broadly categorized into three categories: (a) phylogeny, (b) non-phylogeny and (c) hybrid tools that implement a combination of statistical and phylogenetic methods. An emerging fourth group that is gaining traction comprises tools that apply machine learning to the prediction of phenotypes from genotype data. The main limitation of machine learning tools is their performance however, as more whole genome sequences become available, their predictive accuracy is expected to improve. In this review we profile eleven traditional microbial GWAS tools and two machine learning applications.CCTSWEEP and VENN ((1) and VENN  use phyland VENN .Bacillus anthracis in inbred mouse strains. VENN successfully identified 11 SNPs from 4 chromosomes  performed better than those that did not include phylogenetic information. Using GWAMAR on the two datasets also allowed for the identification of novel mutations putatively associated with drug-resistance ((2) bacteria . It compsistance . HoweverSequence Element Enrichment (SEER) Analysis is a k-mer based tool that counts variable length k-mers using a distributed string-mining algorithm implemented in C ++   in C ++ . It provallation .Scoary is a tool that scores the components of the pan-genome  for associations to observed phenotypic traits while accounting for population stratification  at genome-wide significance with a modest sample size of 21 isolates ((4) fication . It doesble data . Scoary isolates .Bugwas is a robust bacterial GWAS end-to-end pipeline implemented in R, Python, and C ++  to identify and correct for population structure. The LMM’s are implemented using Genome-wide Efficient Mixed Model Association (GEMMA)  and C ++ . It is c (GEMMA) , a fast eumoniae . It succTreeWAS is a phylogenetic method implemented in an R package that measures the statistical associations between a phenotype and genotype at all loci while correcting for the confounding effects of clonal population structure and homologous recombination without losing statistical power to detect associations (Neisseria meningitidis to identify penicillin resistance and invasive disease-associated variants (penA) gene that encodes penicillin-binding proteins and in three additional genes. For invasive meningococcal disease, it located 12 genes and 7 SNPs that were significantly associated. Considering the complexity of the invasiveness phenotype, the results show that the package is well suited for detecting loci with subtle and complex phenotypes which may not be entirely determined by genetic factors. A limitation of TreeWAS is that being implemented in R requires users to have basic knowledge of the programming language, which often may not be the case for many researchers.(6) ciations . The treciations , a softwvariants . For penPhenotypeSeeker is a machine learning tool for the prediction of host-phenotypes from associated bacterial genotype data (PhenotypeSeeker modeling) and another for prediction (PhenotypeSeeker prediction). The modeling module applies the Welch’s two-sample t-test if the phenotype is continuous and a chi-squared test if it is binary. It then constructs a regression or linear model which is consumed by the prediction model and used to predict phenotypes. It optionally performs weighting of strains using a distance matrix of the strains to account for population structure. The final output is a complete list of statistically significant candidate variations. It is both easy to install and easy to use, requiring just two commands to run a complete analysis. Only searching for the k-mers in the regression model makes PhenotypeSeeker very fast. However, in the presence of novel mutations when using the models, this would become a limitation.(7) ype data . The sofKover is a reference-free method for the identification of biomarkers that relies on the k-mer representation of genomes and the set covering machine learning algorithm to produce intelligent multivariate models  e models , 2016. Tcategory . Additiocategory .k-mer  and phenotype. To control for population structure, it performs multi-dimensional scaling of a pairwise distance matrix and the components are included as fixed effects in the model. After adjusting for multiple testing, significant k-mers can be mapped to a reference annotation to find regions of the genome associated with the phenotype. PySEER also allows for testing of association of SNPs and indels called against a reference genome and implements machine learning prediction with a regularized regression approach/elastic net. Interactive visualizations are generated using an implementation of Phandango ((9) PySEER is a direct Python reimplementation of SEER (see above) with several enhancements . It useshandango . Finallyhandango . Unlike MAGNAMWAR is an R package for assessing genotype-phenotype relationships using orthologous genes in bacteria (Drosophila melanogaster (fruitfly) phenotypes ((10) bacteria . The pacenotypes  which thenotypes . This, cenotypes . It consenotypes  and a phHitting Associations with k-mers (HAWK) is a k-mer based tool that uses logistic regression to determine k-mers which are significantly associated with a phenotype of interest ((11) interest . It has E. coli dataset for ampicillin resistance. It uses principal component analysis to detect and correct population structure. HAWK accepts raw FASTQ files as input and requires the reads for each sample to be in a separate directory. Using the same pipeline, one is able to map associations to different types of variants including SNPs, INDELs and structural variations such as copy number variations (CNVs). Future work of interest to the developers that is likely to add value to the community of users include modeling stochasticity in counts, incorporating confounders as well as extending the approach to quantitative phenotypes as future work.The tool has been tested on an De Bruijn Graph GWAS (DBGWAS) is a freely available k-mer based tool that produces interpretable genetic variants associated with distinct phenotypes  graphs (k-mers connected by edges to compact and abstract the complexity behind k-mers while providing a relatively easy to understand representation of the results. Compacted DBGs (cDBGs) eliminate local redundancy, reflect genome variations, and characterize the genomic environment of a k-mer at population level. It takes as input a set of contigs and phenotype data. It relies on bugwas, to test significant associations between unitigs and phenotypes.(12) enotypes . The mai) graphs  i.e., a k-mer based GWAS and (v) it is memory efficient and can scale to very large datasets. To perform GWAS, DBGWAS uses the bugwas  the need for enough sequences for a well powered GWAS. (b) high variability of viral genomes, especially RNA viruses  causing Protozoa and fungi on the other hand, have highly conserved genomes and very low mutation rates  making iWith a large number of existing tools, and several others that are still in development, it can be quite challenging for users to determine which one is most suitable for their research. It can also be a non-trivial problem to determine optimal parameters to use in order to guarantee the best results. Below we present the important features and parameters that researchers must consider.k-mer based tools are able to detect all forms of variation making them prime candidates. The main challenge when working with k-mers however, is that they are less compact than SNPs and thus require additional computational resources to process  which comprise overlapping fragments that together spell a common sequence and do not overlap fragments with sequences that dispute, or contest, the common sequence. Each unitig contains on average about 30 fragments. There are 100 times fewer overlaps between unitigs than overlaps between fragments  Select a tool that supports the analysis of all/most forms of variation as they offer the advantage of testing multiple hypotheses. This is important because a single isolate can be affected by multiple forms of variation. For example, it can acquire SNPs, indels as well as MGEs. For such an isolate, testing only for SNPs misses out MGEs. And yet these MGEs could potentially be the driving force behind the phenotype . k-mer b process . In the  process . Majoritragments . Unitigs(2) While it is important to control for population structure in microbial GWAS, power to detect significant associations is lost using some methods. Prominent methods used to control for population structure include clustering, linear mixed models (LMM) and, for more clonal species, phylogenetic relatedness. The effect of recombination on several microbial organisms makes phylogenetic methods less effective and reduces their power to detect associations. In selecting a pipeline, we recommend one that implements LMMs as they offer biological insights at both locus and lineage specific levels. It will also identify groups of loci which are collectively significant, even though individually insignificant, without sacrificing the power to detect locus-specific associations. When the sample used is homogenous, the effect of population structure is less pronounced . Perform(3) Inconsistent ordering of samples between variant call, phenotype file, and population structure adjustment can result in spurious results, especially among tools that implement LMMs. Unfortunately, several tools do not check ordering and therefore leave much room for error. We recommend using a tool that automatically checks for inconsistent labels and notifies the user if they occur. Of the tools that we reviewed, PySEER was able to automatically match labels and report the intersection of samples used .k-mer used impacts speed and accuracy inversely. Longer lengths increase the sensitivity of the test and guarantee more accurate results. However, they are also associated with a significant increase in the amount of memory and processor usage  The length of or usage . Most stor usage , especia(5) Converting continuous or quantitative phenotypes into categorical values (binning) can be costly in terms of power to detect significant associations , We recoThe significant and systemic genomic differences between human and microbial genomes call for substantial adaptations of older, human GWAS workflows to microbial GWAS. Here we propose a general workflow and highlight the major steps critical to a study’s success .Even though copy number variants and structural inversions have been shown to be quite frequent in some microbes and to contribute significantly to phenotypic variation, methods to perform GWAS on them remain underexplored as compared to gene presence-absence or SNPs and INDELS . A well-Machine learning enables the prediction of phenotypes from genomic data as new data is made available. In this article, we cite three tools  currently implementing machine learning methods. Models created by Kover were found to have error rates as low as 10% . Some ofLong range linkage disequilibrium (LD) is a common phenomenon in microbial genomes . It occuPre-processing of raw data prior to performing any form of analysis is an important step to avoid spurious results. Many of the tools presented here depend on pre-processed results from other tools implying, that burden of ensuring appropriate input is left on the user. Extending these tools to integrate pre-processing tools for raw sequencing data through transparent calls to existing software or improved implementation of existing methods will greatly enhance the utility of the tools. In a similar manner, integration or implementation of post GWAS methods will also contribute immensely to the utility of existing tools. For example, MAGNAMWAR , providep-values  had a single pull request where a user shares an improvement to the countKmers script. To improve the utility of existing tools, we recommend more collaborative efforts among the developer community.4 and GitHub which are free and reliable general-purpose, open-access platforms designed for scholars and researchers.Furthermore, we encourage open data sharing to improve the quality of testing and thus solve the problem of overfitting of tools to specific datasets or organisms. For machine learning, data sharing enables training of models that predict anti-microbial resistance (AMR) phenotypes without relying on a database of preexisting AMR genes or mutations . We recoSignificant strides have been made to advance the field of microbial GWAS. Several tools and methods have been developed targeting the analysis of microbial genomes however, the need for a complete, freely available and easy to use tool for microbial GWAS still remains. Biological researchers and software developers will need to work together to achieve this important cause.JS and TO conceived and structured the manuscript. All authors generated the content and wrote the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.