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Fine-mapping from summary data with the “Sum of Single Effects” model

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Zou, Yuxin, Carbonetto, Peter, Wang, Gao, Stephens, Matthew·2022·PLOS Genetics
DOI 10.1371/journal.pgen.1010299PMC PMC9337707

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Abstract

In recent work, Wang et al introduced the “Sum of Single Effects” ( SuSiE ) model, and showed that it provides a simple and efficient approach to fine-mapping genetic variants from individual-level data. Here we present new methods for fitting the SuSiE model to summary data, for example to single-SNP z -scores from an association study and linkage disequilibrium (LD) values estimated from a suitable reference panel. To develop these new methods, we first describe a simple, generic strategy for extending any individual-level data method to deal with summary data. The key idea is to replace the usual regression likelihood with an analogous likelihood based on summary data. We show that existing fine-mapping methods such as FINEMAP and CAVIAR also (implicitly) use this strategy, but in different ways, and so this provides a common framework for understanding different methods for fine-mapping. We investigate other common practical issues in fine-mapping with summary data, including problems caused by inconsistencies between the z -scores and LD estimates, and we develop diagnostics to identify these inconsistencies. We also present a new refinement procedure that improves model fits in some data sets, and hence improves overall reliability of the SuSiE fine-mapping results. Detailed evaluations of fine-mapping methods in a range of simulated data sets show that SuSiE applied to summary data is competitive, in both speed and accuracy, with the best available fine-mapping methods for summary data.

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Fig 1 Example illustrating importance of identifying and correcting allele flips in fine-mapping. In this simulated example, one SNP (red triangle) affects the phenotype, and one SNP (yellow circle) has a different allele encoding in the study sample (the data used to compute the z-scores) and the reference panel (the data used to compute the LD matrix). Panel A shows the z-scores for all 1,002 SNPs. Panel B summarizes the results of running SuSiE-RSS on the summary data; SuSiE-RSS identifies a true positive CS (blue circles) containing the true causal SNP, and a false positive CS (green circles) that incorrectly contains the mismatched SNP. The mismatched SNP is also incorrectly estimated to have an effect on the phenotype with high probability (PIP = 1.00). The diagnostic plot (Panel C) compares the observed z-scores against the expected z-scores. In this plot, the mismatched SNP (yellow circle) shows the largest difference between observed and expected z-scores, and therefore appears furthest away from the diagonal. After fixing the allele encoding and recomputing the summary data, SuSiE-RSS identifies a single true positive CS (blue circles) containing the true-causal SNP (red triangle), and the formerly mismatched SNP is (correctly) not included in a CS (Panel D). This example is implemented as a vignette in the susieR package.
Fig 1 Example illustrating importance of identifying and correcting allele flips in fine-mapping. In this simulated example, one SNP (red triangle) affects the phenotype, and one SNP (yellow circle) has a different allele encoding in the study sample (the data used to compute the z-scores) and the reference panel (the data used to compute the LD matrix). Panel A shows the z-scores for all 1,002 SNPs. Panel B summarizes the results of running SuSiE-RSS on the summary data; SuSiE-RSS identifies a true positive CS (blue circles) containing the true causal SNP, and a false positive CS (green circles) that incorrectly contains the mismatched SNP. The mismatched SNP is also incorrectly estimated to have an effect on the phenotype with high probability (PIP = 1.00). The diagnostic plot (Panel C) compares the observed z-scores against the expected z-scores. In this plot, the mismatched SNP (yellow circle) shows the largest difference between observed and expected z-scores, and therefore appears furthest away from the diagonal. After fixing the allele encoding and recomputing the summary data, SuSiE-RSS identifies a single true positive CS (blue circles) containing the true-causal SNP (red triangle), and the formerly mismatched SNP is (correctly) not included in a CS (Panel D). This example is implemented as a vignette in the susieR package.CC BY · PubMed Central
Fig 2 Refining SuSiE model fits improves fine-mapping accuracy. Panels A, B and C show a single example, drawn from our simulations, that illustrates how refining a SuSiE-RSS model fit improves fine-mapping accuracy. In this example, there are 1,001 candidate SNPs, and two SNPs (red triangles “SNP 1” and “SNP 2”) explain variation in the simulated phenotype. The strongest marginal association (yellow circle, “SMA”) is not a causal SNP. Without refinement, the IBSS-ss algorithm (applied to sufficient statistics, with estimated σ2) returns a SuSiE-RSS fit identifying three 95% CSs (blue, green and orange circles); two of the CSs (blue, orange) are false positives containing no true effect SNP, one of these CSs contains the SMA (orange), and no CS includes SNP 1. After running the refinement procedure, the fit is much improved, as measured by the “evidence lower bound” (ELBO); it increases the ELBO by 19.06 (−70837.09 vs. −70818.03). The new SuSiE-RSS fit (Panel C) identifies two 95% CSs (blue and green circles), each containing a true causal SNP, and neither contains the SMA. Panel D summarizes the improvement in fine-mapping across all 600 simulations; it shows power and false discovery rate (FDR) for SuSiE-RSS with and without using the refinement procedure as the PIP threshold for reporting causal SNPs is varied from 0 to 1. (This plot is the same as a precision-recall curve after flipping the x-axis because precision=TP/(TP+FP)=1-FDR and recall = power.) Circles are drawn at a PIP threshold of 0.95.
Fig 2 Refining SuSiE model fits improves fine-mapping accuracy. Panels A, B and C show a single example, drawn from our simulations, that illustrates how refining a SuSiE-RSS model fit improves fine-mapping accuracy. In this example, there are 1,001 candidate SNPs, and two SNPs (red triangles “SNP 1” and “SNP 2”) explain variation in the simulated phenotype. The strongest marginal association (yellow circle, “SMA”) is not a causal SNP. Without refinement, the IBSS-ss algorithm (applied to sufficient statistics, with estimated σ2) returns a SuSiE-RSS fit identifying three 95% CSs (blue, green and orange circles); two of the CSs (blue, orange) are false positives containing no true effect SNP, one of these CSs contains the SMA (orange), and no CS includes SNP 1. After running the refinement procedure, the fit is much improved, as measured by the “evidence lower bound” (ELBO); it increases the ELBO by 19.06 (−70837.09 vs. −70818.03). The new SuSiE-RSS fit (Panel C) identifies two 95% CSs (blue and green circles), each containing a true causal SNP, and neither contains the SMA. Panel D summarizes the improvement in fine-mapping across all 600 simulations; it shows power and false discovery rate (FDR) for SuSiE-RSS with and without using the refinement procedure as the PIP threshold for reporting causal SNPs is varied from 0 to 1. (This plot is the same as a precision-recall curve after flipping the x-axis because precision=TP/(TP+FP)=1-FDR and recall = power.) Circles are drawn at a PIP threshold of 0.95.CC BY · PubMed Central
Fig 3 Discovery of causal SNPs using posterior inclusion probabilities—in-sample LD. Each curve shows power vs. FDR in identifying causal SNPs when the method (SuSiE-RSS, FINEMAP, DAP-G or CAVIAR) was provided with the in-sample LD matrix. FDR and power are calculated from 600 simulations as the PIP threshold is varied from 0 to 1. Open circles are drawn at a PIP threshold of 0.95. Two variants of FINEMAP and three variants of SuSiE-RSS are also compared: when L, the maximum number of estimated causal SNPs, is the true number of causal SNPs, or larger than the true number; and, for SuSiE-RSS only, when the residual variance σ2 is estimated (“sufficient data”) or fixed to 1 (“summary data”); see Table 1. The results for SuSiE-RSS with estimated σ2 is shown in both A and B to aid in comparing results. Note that power and FDR are virtually identical for all three variants of SuSiE-RSS so the three curves almost completely overlap in Panel A.
Fig 3 Discovery of causal SNPs using posterior inclusion probabilities—in-sample LD. Each curve shows power vs. FDR in identifying causal SNPs when the method (SuSiE-RSS, FINEMAP, DAP-G or CAVIAR) was provided with the in-sample LD matrix. FDR and power are calculated from 600 simulations as the PIP threshold is varied from 0 to 1. Open circles are drawn at a PIP threshold of 0.95. Two variants of FINEMAP and three variants of SuSiE-RSS are also compared: when L, the maximum number of estimated causal SNPs, is the true number of causal SNPs, or larger than the true number; and, for SuSiE-RSS only, when the residual variance σ2 is estimated (“sufficient data”) or fixed to 1 (“summary data”); see Table 1. The results for SuSiE-RSS with estimated σ2 is shown in both A and B to aid in comparing results. Note that power and FDR are virtually identical for all three variants of SuSiE-RSS so the three curves almost completely overlap in Panel A.CC BY · PubMed Central
Fig 4 Assessment of 95% credible sets from SuSiE-RSS, FINEMAP and DAP-G with different LD estimates, and different LD regularization methods. For in-sample LD, two variants of SuSiE-RSS were also compared (see Table 1): when the residual variance σ2 was estimated (“sufficient data”), or fixed to 1 (“summary data”). We evaluate the estimated CSs using the following metrics: (A) coverage, the proportion of CSs that contain a true causal SNP; (B) power, the proportion of true causal SNPs included in a CS; (C) median number of SNPs in each CS; and (D) median purity, where “purity” is defined as the smallest absolute correlation among all pairs of SNPs within a CS. These statistics are taken as the mean (A, B) or median (C, D) over all simulations; error bars in A and B show two times the standard error. The target coverage of 95% is shown as a dotted horizontal line in Panel A. Following [17], we discarded all CSs with purity less than 0.5.
Fig 4 Assessment of 95% credible sets from SuSiE-RSS, FINEMAP and DAP-G with different LD estimates, and different LD regularization methods. For in-sample LD, two variants of SuSiE-RSS were also compared (see Table 1): when the residual variance σ2 was estimated (“sufficient data”), or fixed to 1 (“summary data”). We evaluate the estimated CSs using the following metrics: (A) coverage, the proportion of CSs that contain a true causal SNP; (B) power, the proportion of true causal SNPs included in a CS; (C) median number of SNPs in each CS; and (D) median purity, where “purity” is defined as the smallest absolute correlation among all pairs of SNPs within a CS. These statistics are taken as the mean (A, B) or median (C, D) over all simulations; error bars in A and B show two times the standard error. The target coverage of 95% is shown as a dotted horizontal line in Panel A. Following [17], we discarded all CSs with purity less than 0.5.CC BY · PubMed Central
Fig 5 Discovery of causal SNPs using posterior inclusion probabilities—Out-of-sample LD. Plots compare power vs. FDR for fine-mapping methods with different LD matrices, across all 600 simulations, as the PIP threshold is varied from 0 to 1. Open circles indicate results at PIP threshold of 0.95. Each plot compares performance of one method (CAVIAR, DAP-G, FINEMAP or SuSiE-RSS) when provided with different LD estimates: in-sample (R^=R), or out-of-sample LD from a reference panel with either 1,000 samples (R^=R^1000) or 500 samples (R^=R^500). For out-of-sample LD, different levels of the regularization parameter λ are also compared: λ = 0; λ = 0.001; and estimated λ. Panels C–F show results for two variants of FINEMAP and SuSiE-RSS: in Panels C and E, the maximum number of causal SNPs, L, is set to the true value (“L = true”); in Panels D and F, L is set larger than the true value (L = 5 for FINEMAP; L = 10 for SuSiE-RSS). In each panel, the dotted black line shows the results from SuSiE-RSS with in-sample LD and estimated σ2, which provides a baseline for comparison (note that all the other SuSiE-RSS results were generated by fixing σ2 to 1, which is the recommended setting for out-of-sample LD; see Table 1). Some power vs. FDR curves may not be visible in the plots because they overlap almost completely with another curve, such as some of the SuSiE-RSS results at different LD regularization levels.
Fig 5 Discovery of causal SNPs using posterior inclusion probabilities—Out-of-sample LD. Plots compare power vs. FDR for fine-mapping methods with different LD matrices, across all 600 simulations, as the PIP threshold is varied from 0 to 1. Open circles indicate results at PIP threshold of 0.95. Each plot compares performance of one method (CAVIAR, DAP-G, FINEMAP or SuSiE-RSS) when provided with different LD estimates: in-sample (R^=R), or out-of-sample LD from a reference panel with either 1,000 samples (R^=R^1000) or 500 samples (R^=R^500). For out-of-sample LD, different levels of the regularization parameter λ are also compared: λ = 0; λ = 0.001; and estimated λ. Panels C–F show results for two variants of FINEMAP and SuSiE-RSS: in Panels C and E, the maximum number of causal SNPs, L, is set to the true value (“L = true”); in Panels D and F, L is set larger than the true value (L = 5 for FINEMAP; L = 10 for SuSiE-RSS). In each panel, the dotted black line shows the results from SuSiE-RSS with in-sample LD and estimated σ2, which provides a baseline for comparison (note that all the other SuSiE-RSS results were generated by fixing σ2 to 1, which is the recommended setting for out-of-sample LD; see Table 1). Some power vs. FDR curves may not be visible in the plots because they overlap almost completely with another curve, such as some of the SuSiE-RSS results at different LD regularization levels.CC BY · PubMed Central
Fig 6 Discovery of causal SNPs using posterior inclusion probabilities—Out-of-sample LD and larger effects. Each curve shows power vs. FDR for identifying causal SNPs with different effect sizes (total PVE of 0.5%, 10% and 30%). Each panel summarizes results from 600 simulations; FDR and power are calculated from the 600 simulations as the PIP threshold is varied from 0 to 1. Open circles depict power and FDR at a PIP threshold of 0.95. In addition to comparing different methods (SuSiE-RSS. FINEMAP, DAP-G, CAVIAR), two variants of FINEMAP and SuSiE-RSS are also compared: when L, the maximum number of estimated causal SNPs, is set to the true number of causal SNPs; and when L is larger than the true number. SuSiE-RSS with estimated residual variance σ2 and in-sample LD (dotted black line) is shown as a “best case” method against which other methods can be compared. All other methods are given an out-of-sample LD matrix computed from a reference panel with 1,000 samples, and with no regularization (λ = 0). The simulation results for 0.5% PVE (top-left panel) are the same as the results shown in previous plots (Figs 3 and 5), but presented differently here to facilitate comparison with the results of the higher-PVE simulations.
Fig 6 Discovery of causal SNPs using posterior inclusion probabilities—Out-of-sample LD and larger effects. Each curve shows power vs. FDR for identifying causal SNPs with different effect sizes (total PVE of 0.5%, 10% and 30%). Each panel summarizes results from 600 simulations; FDR and power are calculated from the 600 simulations as the PIP threshold is varied from 0 to 1. Open circles depict power and FDR at a PIP threshold of 0.95. In addition to comparing different methods (SuSiE-RSS. FINEMAP, DAP-G, CAVIAR), two variants of FINEMAP and SuSiE-RSS are also compared: when L, the maximum number of estimated causal SNPs, is set to the true number of causal SNPs; and when L is larger than the true number. SuSiE-RSS with estimated residual variance σ2 and in-sample LD (dotted black line) is shown as a “best case” method against which other methods can be compared. All other methods are given an out-of-sample LD matrix computed from a reference panel with 1,000 samples, and with no regularization (λ = 0). The simulation results for 0.5% PVE (top-left panel) are the same as the results shown in previous plots (Figs 3 and 5), but presented differently here to facilitate comparison with the results of the higher-PVE simulations.CC BY · PubMed Central

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Metadata

Authors
Zou, Y., Carbonetto, P., Wang, G., & Stephens, M.
Affiliations
  • University of Chicago (US)
  • Columbia University (US)
Corresponding author
Stephens, Matthew
ORCID
Venue
PLOS Genetics
Publisher
Public Library of Science (PLoS)
Published
2022-07-19
Volume
18
Issue
7
Pages
e1010299
ISSN
  • 1553-7390 (ISSN-L)
  • 1553-7404
DOI
10.1371/journal.pgen.1010299
PMC
PMC9337707
OpenAlex
W4286218496
Semantic Scholar
9397075def54e53ddb3d934e9e45679c4cdb0422
Cited by
429
References
52
Citations by year
2026: 134 · 2025: 123 · 2024: 103 · 2023: 50 · 2022: 18
FWCI
45.68
Type
journal article
Language
en
Update notices
new_version (2022-07-29)
Open access
Licence
Locations
  • PLoS Genetics (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Knowledge@UChicago (University of Chicago) (submittedVersion, cc-by-nc-nd)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • University of Chicago (cc-by)
Funders
  • National Human Genome Research Institute (R01HG002585)
  • Gordon and Betty Moore Foundation
  • National Institute on Aging (U01AG072572)
  • Thompson Family Foundation Initative (TAME-AD)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Mapping and Diversity in Plants and Animals
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic and phenotypic traits in livestock
Keywords
fine mapping, summary data, linkage disequilibrium, caviar, model fitting, model refinement, genetic association studies
MeSH terms
Models, Genetic, Reproducibility of Results, Linkage Disequilibrium, Likelihood Functions, Polymorphism, Single Nucleotide

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