EraSOR: Erase Sample Overlap in polygenic score analyses

  1. Shing Wan Choi
  2. Timothy Shin Heng Mak
  3. Clive J. Hoggart
  4. Paul F. O’Reilly

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Abstract

Background

Polygenic risk score (PRS) analyses are now routinely applied in biomedical research, with great hope that they will aid in our understanding of disease aetiology and contribute to personalized medicine. The continued growth of multi-cohort genome-wide association studies (GWASs) and large-scale biobank projects has provided researchers with a wealth of GWAS summary statistics and individual-level data suitable for performing PRS analyses. However, as the size of these studies increase, the risk of inter-cohort sample overlap and close relatedness increases. Ideally sample overlap would be identified and removed directly, but this is typically not possible due to privacy laws or consent agreements. This sample overlap, whether known or not, is a major problem in PRS analyses because it can lead to inflation of type 1 error and, thus, erroneous conclusions in published work.

Results

Here, for the first time, we report the scale of the sample overlap problem for PRS analyses by generating known sample overlap across sub-samples of the UK Biobank data, which we then use to produce GWAS and target data to mimic the effects of inter-cohort sample overlap. We demonstrate that inter-cohort overlap results in a significant and often substantial inflation in the observed PRS-trait association, coefficient of determination (R 2 ) and false-positive rate. This inflation can be high even when the absolute number of overlapping individuals is small if this makes up a notable fraction of the target sample. We develop and introduce EraSOR ( Era se S ample O verlap and R elatedness), a software for adjusting inflation in PRS prediction and association statistics in the presence of sample overlap or close relatedness between the GWAS and target samples. A key component of the EraSOR approach is inference of the degree of sample overlap from the intercept of a bivariate LD score regression applied to the GWAS and target data, making it powered in settings where both have sample sizes over 1,000 individuals. Through extensive benchmarking using UK Biobank and HapGen2 simulated genotype-phenotype data, we demonstrate that PRSs calculated using EraSOR-adjusted GWAS summary statistics are robust to inter-cohort overlap in a wide range of realistic scenarios and are even robust to high levels of residual genetic and environmental stratification.

Conclusion

The results of all PRS analyses for which sample overlap cannot be definitively ruled out should be considered with caution given high type 1 error observed in the presence of even low overlap between base and target cohorts. Given the strong performance of EraSOR in eliminating inflation caused by sample overlap in PRS studies with large (>5k) target samples, we recommend that EraSOR be used in all future such PRS studies to mitigate the potential effects of inter-cohort overlap and close relatedness.

Article activity feed

  1. GigaScience

    Background Polygenic risk score (PRS) analyses are now routinely applied in biomedical research, with great hope that they will aid in our understanding of disease aetiology and contribute to personalized medicine. The continued growth of multi-cohort genome-wide association studies (GWASs) and large-scale biobank projects has provided researchers with a wealth of GWAS summary statistics and individual-level data suitable for performing PRS analyses. However, as the size of these studies increase, the risk of inter-cohort sample overlap and close relatedness increases. Ideally sample overlap would be identified and removed directly, but this is typically not possible due to privacy laws or consent agreements. This sample overlap, whether known or not, is a major problem in PRS analyses because it can lead to inflation of type 1 error and, thus, erroneous conclusions in published work.Results Here, for the first time, we report the scale of the sample overlap problem for PRS analyses by generating known sample overlap across sub-samples of the UK Biobank data, which we then use to produce GWAS and target data to mimic the effects of inter-cohort sample overlap. We demonstrate that inter-cohort overlap results in a significant and often substantial inflation in the observed PRS-trait association, coefficient of determination (R2) and false-positive rate. This inflation can be high even when the absolute number of overlapping individuals is small if this makes up a notable fraction of the target sample. We develop and introduce EraSOR (Erase Sample Overlap and Relatedness), a software for adjusting inflation in PRS prediction and association statistics in the presence of sample overlap or close relatedness between the GWAS and target samples. A key component of the EraSOR approach is inference of the degree of sample overlap from the intercept of a bivariate LD score regression applied to the GWAS and target data, making it powered in settings where both have sample sizes over 1,000 individuals. Through extensive benchmarking using UK Biobank and HapGen2 simulated genotype-phenotype data, we demonstrate that PRSs calculated using EraSOR-adjusted GWAS summary statistics are robust to inter-cohort overlap in a wide range of realistic scenarios and are even robust to high levels of residual genetic and environmental stratification.Conclusion The results of all PRS analyses for which sample overlap cannot be definitively ruled out should be considered with caution given high type 1 error observed in the presence of even low overlap between base and target cohorts. Given the strong performance of EraSOR in eliminating inflation caused by sample overlap in PRS studies with large (>5k) target samples, we recommend that EraSOR be used in all future such PRS studies to mitigate the potential effects of inter-cohort overlap and close relatedness.

    This work has been peer reviewed in *GigaScience *(see https://doi.org/10.1093/gigascience/giad043), which carries out open, named peer-review. These reviews are published under a CC-BY 4.0 license and were as follows:

    Samuel Lambert (revision 2)

    I commend the authors for doing these extra analyses focused on more real-world applications of the method and adding them to the paper. I think the discussion is better contextualised and my final recommendation is that these warnings/caveats are placed in the software documentation as well (https://choishingwan.gitlab.io/EraSOR/).

  2. GigaScience

    Background Polygenic risk score (PRS) analyses are now routinely applied in biomedical research, with great hope that they will aid in our understanding of disease aetiology and contribute to personalized medicine. The continued growth of multi-cohort genome-wide association studies (GWASs) and large-scale biobank projects has provided researchers with a wealth of GWAS summary statistics and individual-level data suitable for performing PRS analyses. However, as the size of these studies increase, the risk of inter-cohort sample overlap and close relatedness increases. Ideally sample overlap would be identified and removed directly, but this is typically not possible due to privacy laws or consent agreements. This sample overlap, whether known or not, is a major problem in PRS analyses because it can lead to inflation of type 1 error and, thus, erroneous conclusions in published work.Results Here, for the first time, we report the scale of the sample overlap problem for PRS analyses by generating known sample overlap across sub-samples of the UK Biobank data, which we then use to produce GWAS and target data to mimic the effects of inter-cohort sample overlap. We demonstrate that inter-cohort overlap results in a significant and often substantial inflation in the observed PRS-trait association, coefficient of determination (R2) and false-positive rate. This inflation can be high even when the absolute number of overlapping individuals is small if this makes up a notable fraction of the target sample. We develop and introduce EraSOR (Erase Sample Overlap and Relatedness), a software for adjusting inflation in PRS prediction and association statistics in the presence of sample overlap or close relatedness between the GWAS and target samples. A key component of the EraSOR approach is inference of the degree of sample overlap from the intercept of a bivariate LD score regression applied to the GWAS and target data, making it powered in settings where both have sample sizes over 1,000 individuals. Through extensive benchmarking using UK Biobank and HapGen2 simulated genotype-phenotype data, we demonstrate that PRSs calculated using EraSOR-adjusted GWAS summary statistics are robust to inter-cohort overlap in a wide range of realistic scenarios and are even robust to high levels of residual genetic and environmental stratification.Conclusion The results of all PRS analyses for which sample overlap cannot be definitively ruled out should be considered with caution given high type 1 error observed in the presence of even low overlap between base and target cohorts. Given the strong performance of EraSOR in eliminating inflation caused by sample overlap in PRS studies with large (>5k) target samples, we recommend that EraSOR be used in all future such PRS studies to mitigate the potential effects of inter-cohort overlap and close relatedness.

    This work has been peer reviewed in *GigaScience *(see https://doi.org/10.1093/gigascience/giad043), which carries out open, named peer-review. These reviews are published under a CC-BY 4.0 license and were as follows:

    Samuel Lambert (revision 1)

    The revised manuscript is much clearer and better illustrates when and how to use the EraSOR method. However, I still think important analyses reflecting more common use cases are missing:- Use of EraSOR with multi-ancestry summary statistics- Use of EraSOR corrected sumstats with other PGS-derivation methods (e.g. LDpred or PRS-CS).- Providing results of a real sensitivity analysis for sample overlap. I understand that you won't know the true overlap in UKB but the difference in the adjusted and unadjusted SumStats performance in the presence of known overlap would be illustrative. Adding these analyses to the real UKB section would greatly benefit the manuscript and utility of the method. Apart from that I note that related to line 19, the impact of sample overlap was also outlined as a pitfall by Wray et al Nat Genet (2013, PMID:23774735).

  3. GigaScience

    Background Polygenic risk score (PRS) analyses are now routinely applied in biomedical research, with great hope that they will aid in our understanding of disease aetiology and contribute to personalized medicine. The continued growth of multi-cohort genome-wide association studies (GWASs) and large-scale biobank projects has provided researchers with a wealth of GWAS summary statistics and individual-level data suitable for performing PRS analyses. However, as the size of these studies increase, the risk of inter-cohort sample overlap and close relatedness increases. Ideally sample overlap would be identified and removed directly, but this is typically not possible due to privacy laws or consent agreements. This sample overlap, whether known or not, is a major problem in PRS analyses because it can lead to inflation of type 1 error and, thus, erroneous conclusions in published work.Results Here, for the first time, we report the scale of the sample overlap problem for PRS analyses by generating known sample overlap across sub-samples of the UK Biobank data, which we then use to produce GWAS and target data to mimic the effects of inter-cohort sample overlap. We demonstrate that inter-cohort overlap results in a significant and often substantial inflation in the observed PRS-trait association, coefficient of determination (R2) and false-positive rate. This inflation can be high even when the absolute number of overlapping individuals is small if this makes up a notable fraction of the target sample. We develop and introduce EraSOR (Erase Sample Overlap and Relatedness), a software for adjusting inflation in PRS prediction and association statistics in the presence of sample overlap or close relatedness between the GWAS and target samples. A key component of the EraSOR approach is inference of the degree of sample overlap from the intercept of a bivariate LD score regression applied to the GWAS and target data, making it powered in settings where both have sample sizes over 1,000 individuals. Through extensive benchmarking using UK Biobank and HapGen2 simulated genotype-phenotype data, we demonstrate that PRSs calculated using EraSOR-adjusted GWAS summary statistics are robust to inter-cohort overlap in a wide range of realistic scenarios and are even robust to high levels of residual genetic and environmental stratification.Conclusion The results of all PRS analyses for which sample overlap cannot be definitively ruled out should be considered with caution given high type 1 error observed in the presence of even low overlap between base and target cohorts. Given the strong performance of EraSOR in eliminating inflation caused by sample overlap in PRS studies with large (>5k) target samples, we recommend that EraSOR be used in all future such PRS studies to mitigate the potential effects of inter-cohort overlap and close relatedness.

    This work has been peer reviewed in *GigaScience *(see https://doi.org/10.1093/gigascience/giad043), which carries out open, named peer-review. These reviews are published under a CC-BY 4.0 license and were as follows:

    Samuel Lambert

    In this paper Choi et al. describe EraSOR, a new tool to remove the effects sample overlap between a set of summary statistics and a target dataset. EraSOR works by running a GWAS in the target dataset and then using LD-score regression techniques to estimate the heritability, genetic correlations of the phenotypes, and number of overlapping samples to decorrelate the effect sizes. The method is thoroughly described, and the simulation scenarios are relevant and well-motivated. However, the manuscript could better describe the inputs and characteristics of the decorrelated summary statistics, focusing more on the degree of bias in effect sizes rather than p-value inflation, and the practicalities of how the tool may be used.Specific Comments:* The results of Figure 1/Supp Figure 1 are highly motivating, but the p-value of the association doesn't seem like the perfect measure of inflation. Plots of the effect size of the PRS compared to its expected effect (0, based on heritability) would better illustrate this.* The paper proposes a method to remove the effects of sample overlap on summary statistics, but instead mostly focuses on how overlap biases the results of PRS prediction. Additional exploration of the decorrelated summary statistics themselves is needed to illustrate the validity of the method. Specifically, how different are the EraSOR adjusted summary statistics from the true summary statistics measured without sample overlap (e.g. distribution of effect sizes differences); what types of variants does EraSOR fail for or overcorrect (e.g. MAF differences between the summary statistics and the target cohort)? Are the results used as-is in other analyses, or do they have to be filtered in some way?* The PRS analyses in the paper all use PRSice to perform clumping+thresholding, selecting the best p-value and LD thresholds on the target datasets. This could be considered overfitting to the target data, and other derivation methods that do not require a sample to optimize hyperparameters (e.g. PRS-cs, LDpred-auto) could be used. It would be good to provide some additional analyses showing that EraSOR outputs also work with other methods of PRS derivation, and that the results are not sensitive to overfitting through hyperparameter optimization.* The PRS analysis of the real phenotype data in UKB should be expanded. Currently the analysis uses summary statistics derived in UKB with varying levels of overlap; however, this does not match the real scenario that EraSOR will likely be used in (applying EraSOR to an externally-sourced GWAS and applied to UK Biobank). The authors should perform a descriptive analysis to show that EraSOR is useful in this real-world scenario by downloading summary statistics from the GWAS Catalog (with and without inclusion of UK Biobank), applying EraSOR, and quantifying the difference in accuracy (r2) and effect size. On a related note: does the ancestry of the summary statistics have to perfectly match the target cohort? How well does EraSOR work with multiancestry summary statistics where the LD-panel might be mismatched?* The point about insufficient adjustment the authors raise on lines 336-42 is quite important. Proper signposting about the limits of the decorrelation is needed in the software description and the discussion. From this passage that the authors suggest that known sample overlap should be avoided and EraSOR should only be used as a sensitivity analysis to ensure that overlap does not exist? It would be useful to get the authors perspective on whether the evaluation of a PRS in a cohort derived using EraSOR-adjusted summary statistics can be seen as truly external to the source GWAS.* The paper should be accompanied by a more detailed user guide and some test data for the EraSOR tool. Are there any diagnostic plots that are produced that could be used to inspect the data quality?

  4. GigaScience

    Background Polygenic risk score (PRS) analyses are now routinely applied in biomedical research, with great hope that they will aid in our understanding of disease aetiology and contribute to personalized medicine. The continued growth of multi-cohort genome-wide association studies (GWASs) and large-scale biobank projects has provided researchers with a wealth of GWAS summary statistics and individual-level data suitable for performing PRS analyses. However, as the size of these studies increase, the risk of inter-cohort sample overlap and close relatedness increases. Ideally sample overlap would be identified and removed directly, but this is typically not possible due to privacy laws or consent agreements. This sample overlap, whether known or not, is a major problem in PRS analyses because it can lead to inflation of type 1 error and, thus, erroneous conclusions in published work.Results Here, for the first time, we report the scale of the sample overlap problem for PRS analyses by generating known sample overlap across sub-samples of the UK Biobank data, which we then use to produce GWAS and target data to mimic the effects of inter-cohort sample overlap. We demonstrate that inter-cohort overlap results in a significant and often substantial inflation in the observed PRS-trait association, coefficient of determination (R2) and false-positive rate. This inflation can be high even when the absolute number of overlapping individuals is small if this makes up a notable fraction of the target sample. We develop and introduce EraSOR (Erase Sample Overlap and Relatedness), a software for adjusting inflation in PRS prediction and association statistics in the presence of sample overlap or close relatedness between the GWAS and target samples. A key component of the EraSOR approach is inference of the degree of sample overlap from the intercept of a bivariate LD score regression applied to the GWAS and target data, making it powered in settings where both have sample sizes over 1,000 individuals. Through extensive benchmarking using UK Biobank and HapGen2 simulated genotype-phenotype data, we demonstrate that PRSs calculated using EraSOR-adjusted GWAS summary statistics are robust to inter-cohort overlap in a wide range of realistic scenarios and are even robust to high levels of residual genetic and environmental stratification.Conclusion The results of all PRS analyses for which sample overlap cannot be definitively ruled out should be considered with caution given high type 1 error observed in the presence of even low overlap between base and target cohorts. Given the strong performance of EraSOR in eliminating inflation caused by sample overlap in PRS studies with large (>5k) target samples, we recommend that EraSOR be used in all future such PRS studies to mitigate the potential effects of inter-cohort overlap and close relatedness.

    This work has been peer reviewed in *GigaScience *(see https://doi.org/10.1093/gigascience/giad043), which carries out open, named peer-review. These reviews are published under a CC-BY 4.0 license and were as follows: ** Jack Pattee **(revision 1)

    Thank you for your detailed responses; I have no further comments.

  5. GigaScience

    Background Polygenic risk score (PRS) analyses are now routinely applied in biomedical research, with great hope that they will aid in our understanding of disease aetiology and contribute to personalized medicine. The continued growth of multi-cohort genome-wide association studies (GWASs) and large-scale biobank projects has provided researchers with a wealth of GWAS summary statistics and individual-level data suitable for performing PRS analyses. However, as the size of these studies increase, the risk of inter-cohort sample overlap and close relatedness increases. Ideally sample overlap would be identified and removed directly, but this is typically not possible due to privacy laws or consent agreements. This sample overlap, whether known or not, is a major problem in PRS analyses because it can lead to inflation of type 1 error and, thus, erroneous conclusions in published work.Results Here, for the first time, we report the scale of the sample overlap problem for PRS analyses by generating known sample overlap across sub-samples of the UK Biobank data, which we then use to produce GWAS and target data to mimic the effects of inter-cohort sample overlap. We demonstrate that inter-cohort overlap results in a significant and often substantial inflation in the observed PRS-trait association, coefficient of determination (R2) and false-positive rate. This inflation can be high even when the absolute number of overlapping individuals is small if this makes up a notable fraction of the target sample. We develop and introduce EraSOR (Erase Sample Overlap and Relatedness), a software for adjusting inflation in PRS prediction and association statistics in the presence of sample overlap or close relatedness between the GWAS and target samples. A key component of the EraSOR approach is inference of the degree of sample overlap from the intercept of a bivariate LD score regression applied to the GWAS and target data, making it powered in settings where both have sample sizes over 1,000 individuals. Through extensive benchmarking using UK Biobank and HapGen2 simulated genotype-phenotype data, we demonstrate that PRSs calculated using EraSOR-adjusted GWAS summary statistics are robust to inter-cohort overlap in a wide range of realistic scenarios and are even robust to high levels of residual genetic and environmental stratification.Conclusion The results of all PRS analyses for which sample overlap cannot be definitively ruled out should be considered with caution given high type 1 error observed in the presence of even low overlap between base and target cohorts. Given the strong performance of EraSOR in eliminating inflation caused by sample overlap in PRS studies with large (>5k) target samples, we recommend that EraSOR be used in all future such PRS studies to mitigate the potential effects of inter-cohort overlap and close relatedness.

    This work has been peer reviewed in GigaScience (see Description), which carries out open, named peer-review. These reviews are published under a CC-BY 4.0 license and were as follows:

    ** Jack Pattee**

    Overall, I think that this manuscript is strong and describes a well-formulated method to address a relevant problem. There are a few outstanding questions about the performance of the EraSOR method from my perspective, which I'll detail as follows.My understanding of reference [16] indicates that equation (3) of this manuscript only holds for null SNPs, i.e. if SNP g is not associated with the outcome Y. If this is the case, then this should be discussed in the manuscript. I wonder if this can partially explain the 'under-estimation' behavior we see in the application to real data in Supplementary Figure 3. In particular, I am referencing the behavior where the EraSOR correction will under-estimate the predictive accuracy of the PRS in the target data, i.e. where delta-R^2 is negative. This behavior is not seen in the simulation and warrants further investigation and discussion. While the bias appears small, for some cases delta-R^2 approaches -.025, which corresponds to an under-estimation of Pearson's r by roughly .15; this is substantial. Could it be the case that, for highly polygenic traits such as height and BMI, the null-SNP assumption is unreliable and the performance of EraSOR is degraded? Does a fundamental assumption of sparse genetic association underlie EraSOR?I recommend that the real data application play a larger role in the manuscript narrative and be moved out of the supplementary. The simulations are appreciated and helpful, but there is nuance in the analysis of real data that cannot be replicated in simulation.I believe the reference to "Supplementary Figure 2" on line 346 should actually be "Supplementary Figure 3". I believe that the axis labels in Supp Figure 3 are flipped.Lines 82 and 83 reference genetic stratification and subpopulations; I think the relevance of these concepts should be introduced more clearly and they should be defined in this context. EraSOR concerns the overestimation of predictive accuracy and association incurred by sample overlap between the base and target GWASs; to this reader, it's not clear what this central issue has to do with population stratification. I realize that the derivation of the LD score method is motivated heavily by correcting for stratification; however, these concepts should be introduced more clearly in this manuscript.Line 88: consider defining LD score l_j.Lines 94-96: consider outlining the mathematical consequence of the assumption that "the two outcomes and cohorts are identical." It's the case that N_1 = N_2 = N_c = N, correct?Line 109 / equation (11): My understanding is that the relevant quantity of this derivation is N_c / sqrt(N_1 N_2), which allows us to define the correct matrix C in expression (4). If this is the case, perhaps the quantity of interest should be moved to the LHS of the equation in the final line of the expression, for clarity.As discussed in the manuscript, the estimated heritability is in the denominator of the expression for N_c / sqrt(N_1 N_2). The authors correctly discuss that the method should not be applied when there is doubt as to whether the heritability is different from zero. I would take this a step further; in cases where the heritability is zero, we cannot meaningfully apply the EraSOR correction, and thus I am not sure of the utility of the 'type I error' simulations in the manuscript. Perhaps an explicit test for h^2 > 0 should be worked into the EraSOR workflow?Line 148 / expression (12): If beta has a normal distribution here, it is the case that all SNPs in the simulation are associated with the outcome Y. This is a somewhat unusual choice for the distribution of SNP effects in a simulation; other applications such as LDPred (Vilhjalmsson et al, AJHG 2015) and LassoSum (TSH Mak et al, Genetic Epi 2017) use a point-normal distribution for simulated SNP effects, which effectively simulates the sparsity frequently observed in nature. Is there a reference or justification for the non-sparse simulation structure here?Line 215: there may be a typo in the expression for the variance of the residual term. Is it the case that the variance of the residual depends on the variance of a covariance term? If so, I am confused as to the derivation.Line 241: 'triat' should be 'trait'.The simulation results in this paper are based on clumping and thresholding for PRS, which does not estimate joint SNP effects i.e. account for LD. Methods such as LDPred and LassoSum do so. Is there any reason to believe the results would be different for a method such as LassoSum?I am confused by the very low Fst between the simulated Finnish and Yoruban samples in simulation. As detailed on line 385: the reported Fst is > .1, but the simulated Fst is essentially zero. This seems likely to be an undesirable simulation artefact, and potentially invalidates the simulation study (or, at least, doesn't provide evidence that EraSOR functions correctly when Fst is large, which was the ostensible motivation for this simulation). Is there no way to effectively simulate populations with a larger Fst?

  6. GigaScience

    Background Polygenic risk score (PRS) analyses are now routinely applied in biomedical research, with great hope that they will aid in our understanding of disease aetiology and contribute to personalized medicine. The continued growth of multi-cohort genome-wide association studies (GWASs) and large-scale biobank projects has provided researchers with a wealth of GWAS summary statistics and individual-level data suitable for performing PRS analyses. However, as the size of these studies increase, the risk of inter-cohort sample overlap and close relatedness increases. Ideally sample overlap would be identified and removed directly, but this is typically not possible due to privacy laws or consent agreements. This sample overlap, whether known or not, is a major problem in PRS analyses because it can lead to inflation of type 1 error and, thus, erroneous conclusions in published work.Results Here, for the first time, we report the scale of the sample overlap problem for PRS analyses by generating known sample overlap across sub-samples of the UK Biobank data, which we then use to produce GWAS and target data to mimic the effects of inter-cohort sample overlap. We demonstrate that inter-cohort overlap results in a significant and often substantial inflation in the observed PRS-trait association, coefficient of determination (R2) and false-positive rate. This inflation can be high even when the absolute number of overlapping individuals is small if this makes up a notable fraction of the target sample. We develop and introduce EraSOR (Erase Sample Overlap and Relatedness), a software for adjusting inflation in PRS prediction and association statistics in the presence of sample overlap or close relatedness between the GWAS and target samples. A key component of the EraSOR approach is inference of the degree of sample overlap from the intercept of a bivariate LD score regression applied to the GWAS and target data, making it powered in settings where both have sample sizes over 1,000 individuals. Through extensive benchmarking using UK Biobank and HapGen2 simulated genotype-phenotype data, we demonstrate that PRSs calculated using EraSOR-adjusted GWAS summary statistics are robust to inter-cohort overlap in a wide range of realistic scenarios and are even robust to high levels of residual genetic and environmental stratification.Conclusion The results of all PRS analyses for which sample overlap cannot be definitively ruled out should be considered with caution given high type 1 error observed in the presence of even low overlap between base and target cohorts. Given the strong performance of EraSOR in eliminating inflation caused by sample overlap in PRS studies with large (>5k) target samples, we recommend that EraSOR be used in all future such PRS studies to mitigate the potential effects of inter-cohort overlap and close relatedness.

    This work has been peer reviewed in *GigaScience *(see https://doi.org/10.1093/gigascience/giad043), which carries out open, named peer-review. These reviews are published under a CC-BY 4.0 license and were as follows:

    Christopher C. Chang Reviewer Comments to Author: This paper addresses a significant need that has arisen in the interaction between privacy rules and ever-larger genomic datasets, and I find the results to be very promising and clearly worth publishing. I just have a few comments on some methodological details:line 130: Have you compared the effectiveness of this algorithm with plink2 --king-cutoff?lines 145-155: If I understand this correctly, these simulated quantitative traits are still normally distributed, they just aren't standardized to mean 0 variance 1. If the intent is to "simulate phenotypes that [do] not follow the standard normal distribution", I'd expect it to be more valuable to look at e.g. the log-normal case, where an alert user might transform the phenotype to normal, but some users may fail to do so. A mixture distribution may also be worth looking at.lines 238-239: Have you considered using the "cc-residualize" option of plink2 -glm, which removes most of the computational cost of including PCs in your binary trait analysis?lines 383-387: This is interesting; there is some room for follow-up investigation here. Thanks for posting all the scripts needed for another researcher to easily reproduce this Fst=0.00639 value; this could help facilitate development of a better genotype-simulation tool.Also, some minor copyedits:line 84: "subpopulation" -> "subpopulations"line 342: "overlaps" -> "overlap"line 363: "ErasOR" -> "EraSOR"line 376: "different level of environmental stratifications" -> "different levels of environmental stratification"line 384: "population" -> "populations"line 402: "capture" -> "captured"

  7. Version published to 10.1101/2021.12.10.472164v1 on bioRxiv