UKB genetic data

UKB genotyped genetic variants were used for the simulation study whereas imputed genetic variants were used in analysis of UKB phenotypes. To obtain a genetic homogeneous study population we restricted our analyses to unrelated British Caucasians and excluded individuals with more than 5,000 missing variants or individuals with autosomal aneuploidy. Remaining (n = 335,532) White British unrelated individuals (WBU) were used for analyses. Genetic variants with minor allele frequency <0.01, call rate <0.95 and the variants deviating from Hardy-Weinberg equilibrium (-value ) were excluded. Further, we excluded genetic variants located within the major histocompatibility complex (MHC), having ambiguous allele (i.e., GC or AT), were multi-allelic or an indel [19]. This resulted in a total of 533,679 single nucleotide polymorphisms (SNPs).

For the imputed data, firstly genetic variants with genotype probability of 70% (hard-call threshold 0.7) were converted to genotypes followed by retaining variants with imputation score >= 0.8 using PLINK 2.0 [20]. The same quality control criteria were applied to the imputed genetic variants as for the genotyped data, except that we included MHC in the UKB phenotypes as this region contains many known disease-associated variants. After quality control of UKB imputed genetic data 6,627,732 SNPs were left for analyses.

Simulation of quantitative and binary phenotypes

Quantitative phenotypes.

To simulate genetic architectures from low to high polygenicity, we simulated quantitative phenotypes with heritability () of 30% and 10%, with two different proportions of causal SNPs (π), 0.1% and 1%, chosen randomly from the observed genotypes.

To reflect different underlying genetic architectures of the simulated phenotypes ( and ) two types of genetic architectures were simulated (genetic architecture 1 and 2, and ). In , causal SNPs effects (b) were sampled from a normal distribution (with mean of 0 and variance given by ) (Eq. 1):

(1)

where y is the phenotype for, is the estimate of the -th SNP effect. The such that is equal to . The residual, e, has a normal distribution with mean = 0 and variance = . The vector represents the i-th centered and scaled genotype (Eq. 2),

(2)

where, is the effect allele count at the -th SNP, is the allele frequency of the i-th SNP.

For genetic architecture 2 (), the effects of causal SNPs were sampled from a mixture of three normal distributions such that 93% of the causal SNPs would have small effect sizes and the remaining 5% and 2% of the causal SNPs would have moderate and large effect sizes respectively. The proportion of causal genetic variants in each class was designed in a similar way as by Lloyd-Jones et al. [14]. Eq. 3:

(3)

where, , , and are the effect of causal SNPs sampled from normal distribution with mean = 0 and variance = , , and , respectively [14].

For each simulation scenario (eight in total = two levels of , two values of π, and two genetic architectures), ten replicates were simulated. For each replicate within a given scenario, causal SNPs were randomly sampled without replacement. As a result, the likelihood of the same SNP being selected multiple times is extremely low. Even in the rare instance where this occurred, the simulated SNP effects would differ across replicates. The total sample of 335,532 were divided into ten replicates. Each replicate contained 80% of the randomly sampled data from the total samples.

Binary phenotypes.

To simulate the binary phenotypes, disease prevalence (PV) was introduced as simulation parameter. Two different PV of 5% and 15% were used. We simulated binary phenotypes from quantitative phenotypes. To simulate a binary phenotype with PV 5%, we chose top 5% of individuals with highest simulated quantitative values as cases and the remaining as controls for the total sample in a replicate. Each scenario of a quantitative phenotype gave rise to two different scenarios for binary phenotype, thus, resulting in 16 scenarios in total. Details on the different scenarios for the quantitative and the binary phenotypes are presented S1 Table. The flowchart of design of the simulations is presented in Fig 1.

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Fig 1. Flowchart illustrating the design of the simulation scenarios for both quantitative and the phenotypes, followed by fine mapping using Bayesian Linear Regression models.

The BLR models were implemented in different ways, and the resulting posterior inclusion probability (PIPs) for SNPs were used to estimate the F₁ classification score based on the credible sets.

https://doi.org/10.1371/journal.pgen.1011783.g001

Quantitative and binary phenotypes in UKB

For real data analysis five quantitative phenotypes and five binary phenotypes were selected for analysis (Table 1). The quantitative phenotypes were identified using specific field codes in the UKB data (see UKB showcase, Table 1). For all UKB phenotypes and covariates we used the first reported instance. We estimated the ratio of the waist circumference to the hip circumference (WHR). To define individuals as disease cases we used ICD10-codes from the data field “Diagnosis-main ICD10” along with codes from the self-reported information (Table 2). Individuals without the ICD10 diagnosis code for a particular disease were used as controls. Additional information, such as age at recruitment (p21022), biological sex at birth (p31), and the UKB assessment center (p54), was collected with the phenotypes. Detailed information regarding the number of samples, prevalence for the phenotypes is given in Tables 1 and 2.

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Table 1. Details of the data fields along with the total number of non-missing samples, age (mean and standard deviation), number (No) of females and average value for the quantitative phenotypes with standard deviation (sd) represented in brackets.

https://doi.org/10.1371/journal.pgen.1011783.t001

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Table 2. Details on cases definitions for the UKB binary phenotypes based on ICD10 codes and self-reported diseases, total number of cases, controls along with the distribution of age (mean and standard deviation [sd]) and number (No) of females within cases and controls.

https://doi.org/10.1371/journal.pgen.1011783.t002

For the subsequent analyses of the UKB phenotypes, the WBU UKB cohort was divided into five replicates of training (80%) and validation (20%).

Genome-wide association study

For the eight different simulated quantitative phenotypes, each with ten independent replicates, we conducted GWAS using the R package qgg [21,22]. A single SNP linear regression model was applied without including any covariates, as no covariates were simulated. We applied the same regression model without covariates for the quantitative phenotypes designed under “Two causal genetic variants”. For the 16 different simulated binary phenotypes each with ten independent replicates the GWAS was conducted using PLINK 1.9 [23] modelled as a logistic regression, again without adjustment for confounding effects.

For the real trait analyses of the UKB phenotypes, the GWAS were performed within the five replicates of training cohort. For T2D, the GWAS was also performed using the entire WBU UKB cohort to understand the biological mechanism underlying T2D (Fig 2). For the quantitative phenotypes we performed single SNP linear regression using the R package qgg [21,22], and for the binary phenotypes we used logistic regression within PLINK 1.9 [20]. We used top ten principal components (PCs) along with age, sex and the UKB assessment center as covariates in all GWAS of real traits. We computed PCs for WBU from 100K randomly sampled SNPs from the genotyped data after removing SNPs in the autosomal long-range LD regions [24] with pairwise correlation ()>0.1 in 500Kb region, using PLINK 2.0 [20].

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Fig 2. Flowchart illustrating the design of populations for the analysis of the UK Biobank phenotypes to determine the predictive abilities and features of credible sets across different models.

https://doi.org/10.1371/journal.pgen.1011783.g002

The statistical model for fine mapping

The BLR model can be written as a multiple linear regression model, Eq. 4,

(4)

where y is a vector phenotypic values, X is a matrix of centered and scaled genetic variants , with being the number of copies of the effect allele (i.e., 0, 1 or 2) for the i-th variant and is the allele frequency of the effect allele. The vector b is the estimated SNP effects for each genetic variant, and e, the residual, are a priori assumed to be independently and identically distributed multivariate normal with null mean and covariance matrix , where I is the identity matrix.

The key parameter of interest in the multiple regression model is the SNP effects, b, which can be obtained by solving Eq. 5:

(5)

where, is residual variance and is the SNP-effect variance.

To solve this equation system, individual level data (genotypes [X] and phenotypes [y]) are required. If these are not available, it is possible to reconstruct and from a LD correlation matrix B (from a population matched LD reference panel) and GWAS summary data [14] Eq. 6:

(6)

where if the genetic variants have been centered to mean 0, else if the genetic variants has been centered to mean 0 and scaled to variance of 1; thus, the diagonal elements of D represent the per variant sample size. The vector is marginal SNP effects obtained from a standard GWAS, with being the variance of the marginal effects from GWAS. The LD correlation matrix, B, can be obtained as the squared Pearson’s correlation (r²) among genetic variants.

BayesC.

In BayesC [12] the SNP effects, b, are a priori assumed to be sampled from a mixture distribution with a point mass at zero and univariate normal distribution conditional on SNP effect variance . To mimic a scenario where a limited numbers of causal genetic variants influence the trait variation additional variables are included to indicate if the i-th SNP has an effect or not. Thus, have a prior Bernoulli distribution with the probability π of being zero. Therefore, the hierarchy of priors is: (Eqs 7 and 8)

(7)(8)

where with because the variance of a t distribution is . In the fine-mapping analyses using the BayesC prior, we used initial values of .

BayesR.

In BayesR [13], the SNP effects, b, are a priori assumed to be sampled from a mixture distribution with a point mass at zero and univariate normal distributions conditional on common marker effect variance , and variance scaling factors, (Eq. 9):

(9)

where is a vector of prior probabilities and is a vector of variance scaling factors for each of C marker variance classes. The coefficients are prespecified and constrain how the common SNP effect variance scales within each mixture distribution. In the fine-mapping analyses using the BayesR prior, we used initial values of and .

The prior distribution for the SNP effect variance is assumed to be an inverse Chi-square prior distribution, . The proportion of genetic variants in each mixture class (π) follows a Direchlet distribution, where c is a vector of length C that contains the counts of the number of variants in each variance class and such that π is updated only using information from the data. Using the concept of data augmentation, an indicator variable , is introduced, where indicates whether the effect of the j’th genetic variant is zero or nonzero.

Fine mapping using summary statistics

We implemented BayesC and BayesR for fine mapping and compared the performance to the following external methods: FINEMAP [8], SuSiE-RSS [10], SuSiE-Inf and FINEMAP-Inf [6].

Model convergence

To assess the convergence of model parameters, namely , , and π, we used the metric Z-score. This involved calculating the difference between the average parameter values taken at the start and end of the iterations. This difference served as our metric to monitor the convergence of the desired parameter. Fine mapping regions with an absolute value of the Z-score, for any of the parameters, greater than three was further investigated by thorough evaluation of the trace plots of the parameters. We used the Geweke convergence diagnostic for Markov chains [26]. This diagnostic evaluates whether the means of the first and last segments of the chain (default settings: the first 10% and the last 50%) are equal. If samples are drawn from the stationary distribution, these means should be equal, and the test statistic follows an asymptotically standard normal distribution. The test statistic, a Z-score, is calculated as the difference between the two samples means divided by its estimated standard error. We used a threshold of 3.0 (i.e., ) to detect non-convergence. This diagnostic was employed for the following model parameters: SNP effect variance (), residual variance () and the proportion of causal variants (π). For densely positioned SNPs, we recommend using multiple independent runs of the Gibbs sampling algorithm. This is done using the nrun parameter in the gmap function from the qgg package (e.g., nrun = 10 will result in an average across ten independent runs).

Credible sets for simulations

Two different definitions of credible sets (CS) were used in this study, depending on the dataset. CS1 was applied to simulated data, where each fine-mapped region contained only one causal SNP. In this approach, SNPs were sorted by their PIP-value, and those contributing to a cumulative PIP of ≥ 90% formed a credible set [17]. This simplified procedure was used to evaluate methods based on their ability to identify a single causal SNP within a region. CS2, based on prior methods [10,27], was applied to both simulated and real data, potentially involving multiple causal variants per region. In CS2, individual SNPs with PIP ≥ 0.90 were first identified as single-SNP credible sets. Among the remaining SNPs, those in strong linkage disequilibrium (LD) (r² ≥ 0.5) with the SNP having the highest PIP were grouped into credible sets if their cumulative PIP reached ≥ 0.90. This process was repeated iteratively. The goal of CS2 was to assess methods based on their ability to identify multiple causal SNPs within a region. To enable comparison with the original methods, we also applied the credible set procedures implemented in FINEMAP, SuSiE-RSS, and SuSiE-Inf, which allow for multiple credible sets, using parameters similar to those used in CS2 (i.e., coverage of 0.9 and purity of 0.5). A flowchart detailing the CS design process is presented in S1 Fig. Detailed steps utilized to explore the presence of multiple CSs within a fine-mapped region are described in S1 Text.

Assessment of fine mapping models in simulations

We set out to benchmark the performance of fine-mapping methods using four evaluation metrics: F1 score, recall, precision, and area under the receiver operating characteristic curve (AUC), based on the credible set methods described previously.

The efficiency of different models was evaluated using PIP-values, focusing on AUC and the F1 score, which is the harmonic mean of precision and recall estimated for the credible sets (CS).

To directly compare the models, we quantified their ability to identify causal genetic variants by computing AUC values based on PIPs and an indicator vector denoting whether each variant was truly causal. We report the mean AUC within each simulation scenario across replicates.

In addition, we computed the F1 classification score for the fine-mapping regions based on the credible sets. Each region contained a simulated causal SNP (index SNP). The F1 score ranges from 0 to 1, with values closer to 1 indicating a model’s stronger ability to correctly identify true causal SNPs while minimizing false positives:

(10)

where, precision, and recall .

The F1 score was calculated for each replicate of a simulation scenario. For a given replicate, a true positive (TP) was defined as a credible set (CS) that contained the index SNP for its region (referred to as a true positive CS, or TP). A false positive (FP) was defined as a CS that met the significance threshold (alpha) but did not contain the index SNP (referred to as a false positive CS, or FP). A false negative (FN) was defined as a genomic region where the cumulative sum of PIPs did not exceed the alpha threshold (e.g., 0.9) and no CS was detected.

In addition to this standard definition of FN, we applied two additional criteria. First, regions where a method failed to converge were considered false negatives. Second, TP CSs that contained more than ten SNPs were also considered false negatives, as overly large credible sets provide limited value in pinpointing causal variants.

To assess model efficiency, we examined the number of SNPs in the true positive credible sets (TP), aiming to keep CS size as small as possible. The design of the CSs and the estimation of the F1 score are illustrated in Fig 3.

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Fig 3. Design of credible sets with a 0.90 threshold for the cumulative sum of Posterior Inclusion Probabilities (PIPs), and estimation of the F₁ classification score based on the credible sets.

https://doi.org/10.1371/journal.pgen.1011783.g003

We also evaluated model performance in fine-mapping regions containing two causal SNPs using the CS2 approach.

Credible sets for the UKB phenotypes

Unlike simulations where fine-mapping regions were not merged irrespective of overlaps, in the UKB phenotypes, fine-mapping regions were merged if they shared a 500kb overlap of SNPs. This approach increased the likelihood of containing multiple potentially causal SNPs within a single fine-mapped region. To capture multiple potentially causal SNPs, we utilized the CS2 algorithm as described in S1 Text. We applied this CS algorithm across all models in our study and compared the models’ performance. For each trait, non-converged fine-mapped regions were excluded across all the models. Afterwards, for each model, we determined the average total number of CSs, the average median CS size (SNP counts in a CS), and the average median value for the average correlations () among SNPs in the CS. To estimate , we excluded the sets with only one SNP as they were not informative, and we used absolute pair-wise correlations among SNPs in the CS. In case the size of CS exceeded 100, only randomly chosen 100 SNPs were used to obtain for that CS. In a fine-mapped region, SNPs with <= 0.001 was excluded before designing multiple CSs assuming that they would have little to no contribution in meeting the criterion of PIP.

Assessment of fine mapping models in the UKB phenotypes

Predictive ability.

For quantitative phenotypes, the predictive ability was determined by estimating the coefficient of determination, (). For binary phenotypes, the predictive ability was determined by estimating AUC [28].

Polygenic prediction of observed phenotypic values was performed by calculating a polygenic score (PGS) for each individual in the validation population, for each replicate. The PGS is computed as the sum of the number of effect alleles an individual carries, each weighted by its estimated effect size [29]:

(11)

where refers to the genotype matrix that contains an allelic count and is the estimated SNP effect for the i-th variant, m is the number of SNPs.

To quantify the accuracy of the PGS for real quantitative phenotypes, co-variates adjusted scaled phenotypes for validation population was regressed on the predicted phenotypes. The coefficient of determination, , from the regression was used as a metric to assess the predictive ability of the model. To quantify the accuracy of the PGS for real binary phenotypes, AUC [28] was reported. Difference in the estimates of and AUC (averaged across five replicates) among different methods was compared using TukeyHSD test.

Application of BLR for fine mapping in T2D

We performed single SNP logistic regression in PLINK 1.9 [23] leveraging the entire UKB cohort for T2D (Table 1), followed by adjustments of the marginal summary statistics with the BayesR model. Fine mapping regions were created as for the UKB phenotypes were defined as described in the S1 Text.

To validate the results obtained from BayesR model for T2D, we conducted non-exhaustive comparison of our findings with the external study. Also, using the R package “gact”, we performed a gene set enrichment analysis to identify diseases enriched for T2D-associated genes and tissue-specific expression Quantitative loci (eQTLs) enrichment analysis to identify tissues enriched for T2D.

In the initial step, we mapped SNPs from multiple CSs to genes using the Ensembl Gene Annotation database available at https://ftp.ensembl.org/pub/grch37/release109/gtf/homo_sapiens/Homo_sapiens.GRCh37.87.gtf.gz. This mapping targeted SNPs within the open reading frame (ORF) of a gene, including regions 35kb upstream and 10kb downstream of the ORF, due to their potential regulatory role in controlling main ORF translation.

Performance in simulation scenarios

Comparison between methods.

We evaluated the mean performance (± standard error) of several fine-mapping methods across multiple metrics. Statistical significance was assessed using one-sample t-tests comparing each method’s mean performance to the overall metric average, as well as ANOVA on a linear model in which the performance metric (e.g., F1 score) was regressed on method, while adjusting for other simulation design parameters (Figs 4 and S3–S10 Figs). These results were further supported by rank-based analyses (S11 and S12 Figs). To explore the influence of simulation design parameters in more detail, we present F1 scores across all simulation scenarios for both quantitative (S3 Fig) and binary phenotypes (S7 Fig).

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Fig 4. Method-wise performance (mean ± 95% CI) across four evaluation metrics using the CS1 credible set procedure in one-causal-variant simulation scenarios.

Forest plots display F1-score, Recall, Precision, and AUC for each method. CS1 is applied uniformly to all methods. Points are colored by method and shaped to reflect whether performance differs significantly from the overall mean (p < 0.05). Error bars represent 95% confidence intervals. Methods are ordered by their mean score.

https://doi.org/10.1371/journal.pgen.1011783.g004

Using the simple credible set method (CS1), our results revealed consistent differences in performance across all simulation settings. The bR2 method demonstrated the strongest performance when assessed by F1 classification score (mean = 0.339, p = 0.004), significantly outperforming the overall mean (Fig 4A). In contrast, bCgw (mean = 0.261, p = 0.015) and FINEMAP-Inf (mean = 0.265, p = 0.033) performed significantly worse than average. All other methods, including SuSiE-RSS, SuSiE-Inf, FINEMAP, bC2, and bR1, showed no statistically significant deviations from the mean, suggesting similar F1 performance. In terms of Recall, bR2 again achieved the highest value (0.454, p < 1 × 10 ⁻ ⁸), followed by bC2 (0.394, p = 0.013), both significantly above the mean performance (Fig 4B). bC1 (0.295), bCgw (0.292), and FINEMAP-Inf (0.265) performed significantly below average. The remaining methods showed no significant difference from the overall mean. None of the methods differed significantly in mean precision, indicating comparable ability to identify true positives. Mean values ranged narrowly, from bR2 (lowest at 0.308, p = 0.264) to bRgw (highest at 0.334, p = 0.475) (Fig 4C). FINEMAP-Inf, SuSiE-RSS, and SuSiE-Inf displayed significantly higher AUC than the average (p < 0.05), reflecting stronger classification accuracy (Fig 4D). In contrast, bCgw and bC1 showed significantly lower AUC values, with bCgw performing the worst overall. Other methods, including bR2 and FINEMAP, did not differ significantly from the average.

The rank-based evaluation confirmed that bR2 consistently achieved the highest ranks in both F1 and Recall, with perfect mean values for these metrics, indicating strong and stable performance (S11 Fig). We generally observed a performance trend of bRgw < bR1 < bR2 in both F1 and Recall, except in cases of high polygenicity. Similar pattern was observed among the BayesC-based models. SuSiE-RSS also performed well, particularly in F1 and Precision, while SuSiE-Inf excelled in Precision. FINEMAP showed moderate performance with variability in AUC, whereas FINEMAP-Inf performed poorly in F1 and Recall but ranked well in AUC, suggesting imbalanced performance. bC1 ranked lowest overall, while bC2 and bR1 showed mixed results. Overall, bR2 emerged as the most robust method, followed by SuSiE-RSS and SuSiE-Inf, depending on the metric.

Under the CS1 procedure, credible set sizes were generally small but varied across methods (S2A Fig). SuSiE, SuSiE-Inf, and bR2 had the largest average sizes (2.15–2.23), while bCgw and FINEMAP-Inf produced the smallest (1.34–1.42). Among BLR models, bC1, bCgw, and bRgw yielded the most compact sets. Several methods, including FINEMAP-Inf and multiple BLR models, differed significantly from the overall mean (p < 0.05).

To further enable comparison with the original fine mapping methods, we also applied the credible set procedures implemented in FINEMAP, SuSiE-RSS, and SuSiE-Inf, which allow for multiple credible sets, using parameters similar to those in CS2 (i.e., coverage of 0.9 and purity of 0.5). The overall performance rankings remained largely unchanged. bR2 and bR1 continued to show strong performance, while FINEMAP again underperformed in sparse architectures, although the significance of its underperformance was slightly less consistent (S1 Fig). The differences between SuSiE-RSS and SuSiE-Inf remained minor, while bC1 and bC2 consistently showed lower performance. Under the CS2 procedure, all methods produced small credible sets, with mean sizes ranging from 1.22 (bC1) to 1.79 (FINEMAP) (S2B Fig). SuSiE-based models and BLR methods showed similar performance (means ~1.24–1.29). Compared to CS1, CS2 yielded more compact sets, likely due to LD-based filtering. All methods differed significantly from the overall mean (p < 0.05), indicating consistent differences in set size across methods.

Performance in simulations with two causal variants.

We evaluated the performance of fine-mapping methods using simulations with two causal variants, varying sample sizes (200k, 250k, 300k), and effect size configurations. This analysis used the credible set procedures implemented in FINEMAP, SuSiE-RSS, and SuSiE-Inf, as well as the credible set procedure for the BLR models, which allows for multiple credible sets.

F1 scores improved with increasing sample size across all methods (Fig 5). In the two large-effect scenario (LL), bR1, bR2, bC2, and SuSiE-RSS achieved the highest performance (F1 > 0.75 at n = 300k). In the mixed-effect scenario (LS), bR2 and bC2 maintained relatively strong performance, while all methods struggled under the small-effect (SS) setting. Nonetheless, bR and bC variants generally outperformed SuSiE-Inf and FINEMAP in the SS scenario.

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Fig 5. F1-score performance (mean ± standard error) for fine-mapping methods across sample sizes and causal configurations in two-causal-variant simulation scenarios.

Points represent mean F1-scores by method, with causal configurations grouped as LL (two large effects), LS (one large and one small effect), and SS (two small effects). Error bars show ±1 SE.

https://doi.org/10.1371/journal.pgen.1011783.g005

Ranking analyses across all settings showed that bC2 and bR2 achieved the best average F1-score ranks (2.5 and 2.7, respectively), followed by SuSiE-RSS and bR1 (S16 Fig). In contrast, FINEMAP, SuSiE-Inf, and bC1 ranked lowest (mean ranks ~5.0–5.4), indicating weaker overall performance. Most methods performed similarly in terms of Recall (S13 Fig), Precision (S14 Fig), and AUC (S15 Fig). However, the poorer F1-score performance of FINEMAP is primarily due to its lower Precision (see S6B and S7C Figs).

Across all methods, the average credible set size was similar, ranging from approximately 3.77 to 4.43 variants (S17 Fig). FINEMAP produced the largest average credible sets (mean = 4.43), followed by bR2 (4.20) and bC2 (4.15). SuSiE-Inf yielded the smallest average set size (mean = 3.77), with SuSiE and bR1 also producing relatively small sets (3.82 and 4.02, respectively). These results indicate that, in the presence of two causal variants, all methods produced compact credible sets of comparable size, with minor differences across models.

Application to UKB phenotypes

Predictive ability.

We observed a significant decrease in the (averaged across all the continuous phenotypes) of BayesC and BayesR relative to SuSiE-Inf and FINEMAP-Inf for the phenotypes BMI, WC, HC and WHR (Fig 6). No significant difference in the was observed between BayesR compared to SuSiE-Inf and FINEMAP-Inf for height, whereas a significant decrease was observed for BayesC compared to these models. We observed significant improvement in the of BayesR relative to SuSiE-RSS for height. All the methods could predict height better compared to other quantitative phenotypes. Prediction (averaged across all the binary phenotypes) with BayesR increased by 0.40%, 0.16%, 0.08%, 0.05% compared to SUSIE-RSS, BayesC, FINEMAP-Inf and SuSiE-Inf, respectively (Fig 7). We did not observe any significant differences between the (averaged across all the replicates) of models compared pairwise for any binary phenotypes except for HTN. For HTN, BayesR improved the significantly compared to SuSiE-RSS. The highest estimate of the was observed for T2D followed by HTN for all the models. The lowest estimate of the was observed for RA. Prediction (averaged across all the quantitative phenotypes) with BayesR decreased by 5.32% and 3.71% compared to SuSiE-Inf and FINEMAP-Inf, whereas increased by 7.93% and 8.3% compared to SuSiE-RSS and BayesC. BayesR model improved the (averaged across all the replicates) significantly compared to BayesC model for all the quantitative phenotypes except for WHR.

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Fig 6. Prediction accuracies estimated from fine mapped regions.

Box plot of prediction accuracy, represented by the coefficient of determination (R²), averaged across five replicates for the UKB quantitative phenotypes: body mass index (BMI), hip circumference (HC), standing height (Height), waist circumference (WC), and waist-hip ratio (WHR). The models used in the fine mapping can be identified by the colors in the legend associated with each model. For each method within a trait, corresponding mean of R2 or AUC across five replicates and standard error is written on the top of the boxplot.

https://doi.org/10.1371/journal.pgen.1011783.g006

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Fig 7. Prediction accuracies estimated from fine mapped regions.

Box plot of prediction accuracy, represented by the Area under the Curve (AUC), averaged across five replicates for the UKB binary phenotypes: coronary artery disease (CAD), hypertension (HTN), psoriasis (PSO), rheumatoid arthritis (RA), and type 2 diabetes (T2D). The models used in the fine mapping can be identified by the colors in the legend associated with each model. For each method within a trait, corresponding mean of R2 or AUC across five replicates and standard error is written on the top of the boxplot.

https://doi.org/10.1371/journal.pgen.1011783.g007

Credible sets.

The average total number of fine-mapped regions across five replicates for the quantitative phenotypes ranged from 135.2 for WHR to 461 for Height and for the binary phenotypes ranged from 4 for RA to 137.4 for HTN (Table 1). The highest averaged non-converged regions were observed for RA (55%) followed by PSO (29.62%). For other phenotypes, the non-converged regions ranged from 1.22% to 6.42%.

BayesR identified the highest average number of CSs for Height, CAD, HTN and T2D, whereas SuSiE-RSS found the highest average number of CSs for BMI, HC, WC and WHR (Table 1). For the above-mentioned phenotypes, FINEMAP-Inf identified the smallest average number of CSs. All the models obtained a similar average number of CSs for PSO (9–12) and RA (1.8 to 2.2).

The BLR models showed the smallest average median CS size across all the phenotypes compared to the external fine-mapping models (Table 3). BayesR showed the smallest average median size of CS for BMI, Height, WC, WHR, PSO, RA and T2D. BayesC showed the smallest average median size of CS for CAD. Both BayesC and BayesR showed the same average median size for HC and HTN. The highest average median CS size was shown by SuSiE-Inf for BMI, Height, WC, CAD, PSO, RA and T2D. For other phenotypes, SuSiE-RSS showed the highest value for the median CS size.

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Table 3. Average for the total number of fine mapped regions (FMR) and non-converged regions for the UKB phenotypes along with the total number of credible sets (CSs), median size of the CSs, and median of the average correlations (r²) of the CSs for all the models.

https://doi.org/10.1371/journal.pgen.1011783.t003

The average median for for the BLR models was smaller compared to the external models. BayesC showed the largest average median value compared to BayesR across all the phenotypes.

Application of BLR model in T2D

We identified a total of 117 CSs for T2D across 69 fine-mapped regions with a median CS size of 2 (range:1–297), and the median of was 0.80 (range: 0.49 to 1). We identified 53 CSs of size 1 (1 SNP counts), 47 CSs of size between 2–50, and the remaining 17 CSs of size more than 50 SNPs.

BLR as a fine mapping methodology

BayesC and BayesR share the same assumptions regarding the prior variance of marker effects but differed in their implementation in our study. Specifically, we compared their performance when applied either genome wide—using all SNPs—or region wide—restricted to predefined fine-mapping regions based on simulated causal variants. To our knowledge, this is the first study to systematically compare BayesC and BayesR in both contexts. We evaluated several variants of BLR models, which differed along two main dimensions: (1) whether the prior proportion of non-zero effects (π) was fixed or estimated, and (2) whether the model was applied at the region level or genome wide. For BayesR, bR1 estimates π from the data, while bR2 uses a fixed value during model fitting. Similarly, for BayesC, bC1 estimates π, whereas bC2 uses a fixed π. Overall, bC2 and bR2 outperformed bC1 and bR1 in terms of F1 classification score and Recall, suggesting that using a fixed π may improve performance under certain conditions. All models estimated the marker effect variance. A smaller estimate of this variance can lead to better model fit either by assigning small effects to a larger number of SNPs or by concentrating larger effects on fewer SNPs, depending on the underlying genetic architecture. Further investigation is needed to determine whether improved control of hyperparameters, particularly those governing π and marker effect variance, can enhance fine mapping accuracy.

To further explore the effect of modeling scope, we also included genome-wide versions of the models: bCgw and bRgw, which analyze the entire genome in a single model rather than being restricted to predefined fine-mapping regions. We generally observed a performance trend of bRgw < bR1 < bR2 in both F1 and Recall, except in cases of high polygenicity; a similar pattern was observed among the BayesC-based models. This improvement in Recall and F1 appeared to come at a slight cost to Precision, although the differences were not statistically significant compared to the overall mean.

Together, this suggests that applying BLR models at the region level can improve fine mapping resolution by providing better estimates of local marker effect variances. In contrast, genome-wide models may be more appropriate for highly polygenic traits or for settings where regional boundaries are poorly defined, and they tended to improve Precision. Our framework allowed us to systematically evaluate how the choice of prior specification, the treatment of π, and the modeling scope influence the accuracy and efficiency of fine mapping.

Comparison of the BLR models to external models

Our results demonstrate that Bayesian Linear Regression models, particularly bR2, can outperform widely used fine-mapping methods such as FINEMAP and SuSiE-RSS under a range of simulation scenarios. bR2 consistently showed superior performance in F1 score and Recall, indicating a better balance between sensitivity and precision when identifying true causal variants. In contrast, external methods such as FINEMAP-Inf and SuSiE-Inf often showed imbalanced performance, strong in AUC but weaker in Recall, suggesting limitations in identifying true positives despite good overall classification.

Among the BLR variants, models with fixed π (bR2, bC2) generally outperformed those that estimate π from the data (bR1, bC1), suggesting that fixed priors may improve model stability and fine-mapping accuracy. In particular, bC1 consistently ranked lowest among all methods, while bC2 showed moderate but improved performance. We used in-sample LD, while using external summary statistics in-sample LD is not always available [34]. Hence, the recall may decrease while using an external reference LD panel.

While SuSiE-RSS and SuSiE-Inf performed competitively in Precision and AUC, they did not consistently outperform the best BLR models. Similarly, FINEMAP showed moderate performance overall but underperformed in sparse genetic architectures.

Our findings were robust to different credible set procedures, with performance rankings remaining consistent across both simple (CS1) and multiple-set (CS2-like) methods. While bR2 maintained strong performance, bR1 and bC2 also demonstrated reliability across metrics, suggesting they may serve as viable alternatives depending on the analysis context.

When estimating Recall (and F1 classification scores), in addition to requiring that a set surpasses a cumulative PIP threshold of 0.90 to be considered a credible set, any credible set containing a causal SNP but exceeding 10 SNPs in size was treated as a false negative (FN), thereby penalizing overly large sets. While this threshold is strict and somewhat arbitrary, it reflects the limited value of large CSs in sparse genetic data. Results may vary with different thresholds, and it would be interesting to assess model performance under alternative CS size cutoffs.

In simulations with two causal variants, BLR models, particularly bC2 and bR2, consistently demonstrated strong and reliable performance across varying sample sizes and effect-size configurations. While all methods benefited from larger sample sizes, BLR models maintained an advantage even in challenging scenarios with small-effect variants, where external methods like FINEMAP and SuSiE-Inf underperformed. These results highlight the robustness of BLR models with fixed π, especially in sparse or heterogeneous genetic architectures, and support their use in diverse fine-mapping contexts.

These findings highlight the advantages of BLR models, especially bR2, in scenarios where accurate identification of causal variants is critical. They also emphasize the importance of modeling assumptions, such as the treatment of π and model scope, in influencing fine-mapping outcomes. Our results suggest that BLR models can serve as strong alternatives, or even preferred options, to established external methods in fine mapping applications.

To our knowledge, this is the first study comparing the BayesR model to leading fine mapping methods, including FINEMAP, SuSiE-RSS, SuSiE-Inf, and FINEMAP-Inf. A previous study by de Los Campos et al. [34] evaluated BayesC against various methods, including SuSiE-RSS and FINEMAP, and found that BayesC performed comparably to SuSiE-RSS and outperformed FINEMAP in terms of Recall and false discovery rate across multiple simulation scenarios. Our results are consistent with those findings. There are, however, differences in study design. The previous study applied models at the whole-genome level using a local regression approach, whereas our analysis was restricted to specific regions defined by simulated causal SNPs, which did not necessarily span the entire genome. Additionally, we compared SuSiE-RSS (an extension of SuSiE that operates on GWAS summary statistics) along with BayesC and FINEMAP, using summary statistics with in-sample LD. In contrast, de Los Campos et al. [34] used individual-level data for BayesC and SuSiE, and summary statistics with in-sample LD only for FINEMAP. Despite these differences in data and scope, we did not expect, nor observe, major discrepancies in results.

Credible set size comparison

Across both CS1 and CS2 procedures, BLR models (bC1, bC2, bCgw, bR1, bR2, bRgw) produced comparable or more compact credible sets than external methods (FINEMAP, FINEMAP-Inf, SuSiE, SuSiE-Inf, and SuSiE-RSS) (S2 and S17 Figs).

In regions with one causal variant, CS1, based solely on PIP ranking, resulted in the smallest credible sets for BLR models such as bC1, bCgw, and bRgw (mean size 1.34–1.52), while external methods like SuSiE and SuSiE-Inf produced larger sets (2.15–2.23). Under CS2, which supports multiple credible sets per region and applies LD-based filtering (e.g., purity ≥ 0.5), all methods produced smaller sets overall (1.22–1.79). However, the size advantage of BLR models persisted, with bC1 and bR2 producing some of the most compact sets (1.22 and 1.29, respectively), while FINEMAP yielded the largest (1.79).

In regions with two causal variants, credible set sizes increased slightly across methods (3.77–4.43), but similar patterns remained. bR1 and SuSiE-based methods produced the smallest sets, while FINEMAP, bR2, and bC2 generated the largest. These results demonstrate that BLR models consistently produce concise credible sets, particularly when using LD-aware procedures like CS2, while maintaining competitive fine-mapping performance.

Influence of parameters in simulations

Simulation design parameters had a strong influence on fine mapping performance. Across models, the best results were observed under moderate heritability (h² = 0.3), low polygenicity (π = 0.001), and simple genetic architectures (GA₁), particularly for continuous traits and binary traits with higher prevalence (PV = 15%). In contrast, scenarios with low heritability, high polygenicity, or complex genetic architectures led to significantly lower F1 scores.

ANOVA confirmed that polygenicity had the largest impact on performance, followed by heritability and genetic architecture. The effect of polygenicity likely reflects the increased difficulty of detecting many small-effect variants, which contribute weak signals and reduce the precision of credible sets. As expected, scenarios with fewer causal variants sampled from a larger marker effect variance produced stronger signals and higher PIPs, making causal SNPs more likely to be captured in credible sets. These findings underscore the importance of genetic architecture and trait characteristics—such as heritability, prevalence, and polygenicity, when evaluating or applying fine mapping methods. They also highlight the need to consider simulation design carefully when benchmarking models or interpreting results.

The UKB phenotypes, accuracy and fine mapping, credible sets

BayesR showed significantly higher prediction accuracy (R²) than BayesC for four out of five quantitative phenotypes. These findings are consistent with previous studies. Zhu et al. reported improved prediction ability using BayesR over BayesC across several economically important cattle traits [35], while Mollandin et al. observed similar results in simulations for traits with high heritability [36]. In our analysis, BayesR also produced more, and smaller credible sets compared to BayesC, suggesting that its assumptions about genetic architecture may be better suited for predicting polygenic traits where a range of effect sizes is present.

Despite this, the average prediction accuracy for both BayesR and BayesC was significantly lower than that of SuSiE-Inf and FINEMAP-Inf for traits like BMI, HC, WC, and WHR. The higher prediction performance of the infinitesimal models may be explained by our use of SNP effects from both the sparse and infinitesimal components in SuSiE-Inf and FINEMAP-Inf. This contrasts with a previous study [6], where only the sparse components were used to compare prediction accuracy. Because infinitesimal components account for small effects across all SNPs, they may better capture the genetic signal underlying complex traits. Notably, BayesR’s performance approached that of the infinitesimal models, reinforcing its suitability for modeling polygenic architectures.

The predictive accuracies we observed for UK Biobank phenotypes were lower than those reported in other studies. For traits such as BMI, height, HC, WHR, and T2D, the R² values reported by Lloyd-Jones et al. using SBayesR and approximately 1.1 million SNPs were notably higher than those obtained with BayesR in our analysis [14]. This discrepancy is likely due to differences in SNP coverage and model scope. Our predictions were based only on imputed SNPs within fine mapped regions, whereas previous studies used genome-wide SNP sets.

Additionally, for highly polygenic traits like height and BMI, prior work [37] has shown enrichment of heritability from rare variants (MAF < 0.01), which we excluded in our study to focus on common SNPs. Moreover, we excluded non-converged regions from our prediction and credible set analyses, which may have further impacted the overall predictive accuracy.

Validation of BLR model

Compared to the recent meta-GWAS on T2D [30], we identified 10 genes to overlap with the 53 genes, which were categorized as novel loci in [30]. This finding demonstrates the effectiveness of BayesR model combined with credible sets in identifying potential causal variants, even in studies with comparatively smaller size. This limited number of overlapping genes could be attributed to our study’s smaller scale (25,828 cases and 309,704 controls compared to 74,124 cases and 824,006 controls in [30]), which could limit ability to detect especially rare variants, and the exclusion of rare variants (excluding SNPs with < 1% MAF in our study). Additionally, the discrepancies in how SNPs were mapped to a gene between our study and that of [30] might also contribute to this limited overlap.

TCF7L2 (Transcription Factor 7-like 2) explained the highest genetic variance (0.035) in our study. This gene plays a crucial role in Wnt signaling pathway, which regulates pancreatic islet cell proliferation and survival [38]. In TCF7L2, rs7903146 is the largest-effect common variant signal for T2D in Europeans [30]. Observation of multiple signals for T2D at TCF7L2 in addition to rs7903146 in [30] was the first evidence according to this study. In addition to the rs7903146, we also identified SNP rs34855922 associated to T2D similar with [30], which again demonstrates the effectiveness of BayesR model combined with CSs. The rs7903146 and rs34855922 are two of the eight SNPs that mark regulatory elements within TCF7L2 locus [39]. The rs7903146 coordinate regulation of TCF7L2 expression and overlaps histone modification marks and an annotated enhancer in the pancreas [39]. Our study also identified an intronic variant (rs145034729) at the TCF7L2 locus. The effect of this intronic SNP is uncertain. However, it may function as an enhancer element, modulating the expression of distal genes without necessarily affecting the function of TCF7L2 itself. The discovery of multiple variants within the TCF7L2 locus is interesting, as Nyaga et al., suggests that it acts as a regulatory hub for genes implicated in the etiology of T2D [39]. Identifying these variants in this locus offers valuable insights into the biological mechanisms underlying T2D.

The gene set enrichment analysis for diseases provided further support for the efficacy of BayesR model in T2D. This analysis revealed significant enrichment of our gene set for diseases such as T2D, hyperglycemia (diabetes-like symptoms), hyperinsulinism (one of the processes leading to hyperglycemia [40]. Significant enrichment to other types of diabetes and diseases may reflect shared genetic factors (via pleiotropic genes or common pathways) influencing the etiology of diverse conditions (diseases) through different mechanisms. For instance, Tian et al., noted an increased risk of diabetes mellitus incidence in individuals with RA [41], highlighting the potential role of inflammatory pathways in the T2D pathogenesis.

For tissue enrichment analysis, our findings indicate that T2D related eQTLs exhibit tissue-specific effects on gene expression. The implications of our results can be viewed from multiple perspectives. Our results may suggest a complex interplay of regulatory regions in significantly enriched tissues leading to T2D predisposition. Our results may also suggest individuals with T2D might experience adverse effects in these tissues, potentially leading to a range of complications. For instance, Hemerich et al., explored the association of significantly enriched tissue specific T2D associated eQTLs with different T2D complications [42]. Here we delve into the cerebellar hemisphere region of the brain, the most significant enriched tissue. This region, part of the cerebellum (another significant tissue in our study), has been linked to cognitive impairments when abnormal. Roy et al., highlighted significant cognitive impairments in T2D individuals [43], correlating these deficits with considerable loss in gray matter volume in brain regions associated with these functions. The decline in insulin transport and resistance in the cerebral cortex, an area dense with high insulin receptor, may impair regional glucose metabolisms, leading to gray matter volume changes potentially leading to structural and functional changes in brain in T2D individuals.

No association with pancreatic tissue was found, likely due to the GTEx database’s limitations. The pancreatic tissue in GTEx represents mostly (97%) exocrine cells that mask islets signals [44]. Pancreatic islets are clusters of specialized endocrine cells that are essential to maintain glucose homeostasis and play a central role in etiology of T2D.

Our study was confined to the cis-eQTLs database from GTEx consortium. Torres et al., have shown that trans-eQTLs contribute significantly to T2D heritability, suggesting that further exploration of trans-eQTLs could enhance the understanding of gene expression and cellular functions across different tissues [45].

In conclusion, we observed that the performance of the BLR models was comparable to the state-of-the-art external models. The performance of BayesR prior was closely aligned with SuSiE-Inf and FINEMAP-Inf models. Results from both simulations and application of the models in the UKB phenotypes suggest that the BLR models are efficient fine mapping tools.