MetaGLIMPSE: Meta-imputation of low-coverage sequencing data for modern and ancient genomes

Summary

The advent of efficient and accurate imputation for low-coverage sequencing offers an unbiased alternative to SNP array imputation, increasing the accuracy of rare variant imputation across all populations. Since imputation accuracy generally increases with larger reference panels and closer ancestry match between target and reference samples, leveraging imputation from multiple reference panels improves imputation accuracy; however, individual reference panel genotypes are often privacy protected. Meta-imputation bypasses individual-level data by combining single-panel imputed genotypes through estimating panel- and marker-specific weights. We present a meta-imputation method, MetaGLIMPSE, that combines estimates from multiple reference panels for low-coverage sequencing imputation. Across all our scenarios, for both modern and ancient DNA samples, MetaGLIMPSE consistently outperforms the best single-panel imputation for coverages of 0.1×–8× and across all minor-allele frequencies, equaling the combined panel imputation for some parameters. Finally, MetaGLIMPSE is computationally efficient, meta-imputing 500 whole genomes in 16% of the time of GLIMPSE2.

MetaGLIMPSE is a meta-imputation method that improves rare-variant detection in low-coverage sequencing by combining multiple reference panels—without sharing individual genotype data. It outperforms single-panel imputation and offers rapid, privacy-preserving, and accurate genome imputation for both modern and ancient DNA.

Introduction

Genomic imputation is a cost-effective tool that powers downstream analysis, such as genome-wide association study (GWAS), fine-mapping, and meta-analyses.^{1,2,3,4,5,6,7} Earlier algorithms focused on SNP array data.^1,3,4 Nowadays, low-coverage sequencing is a growing alternative to SNP arrays due to decreasing sequencing costs.^8,9 Low-coverage sequencing involves shotgun sequencing at low mean depths between 0.1× and 8×.^8,9,10 While such read data are often insufficient to confidently call genotypes, imputation accuracy for low-pass sequencing at coverages as low as 0.5× is comparable to commonly used SNP arrays, and a coverage of 1× suffices for confident rare-variant detection.^9,10 Moreover, low-coverage sequencing is especially useful for non-European populations, as it provides unbiased coverage across the genome and eliminates ascertainment bias inherent in the design of SNP arrays,^8,9 which facilitates downstream analyses such as calculating polygenic risk scores.¹¹ This advantage has motivated large low-coverage sequencing efforts, such as blended genome exome (BGE), which has sequenced at least 53,000 samples at coverages between 1× and 4×.⁸ Furthermore, the lower cost and experimental considerations make low-pass sequencing attractive for the sequencing of ancient DNA (aDNA). Currently, at least 30,000 aDNA samples have been sequenced, of which only around 100 are at high coverage (B. Sousa da Mota, personal communication), leaving ∼29,900 samples with low-coverage sequencing data. Moreover, this number is likely to grow exponentially in the coming decades.^12,13

The challenge of low-coverage imputation is that individual genotypes are more uncertain, which precludes pre-phasing, a computation-time-saving strategy used in SNP array imputation.⁴ Thus, an algorithm for low-coverage imputation must handle both phasing and imputation with computational efficiency. A commonly used method for low-coverage imputation for both modern DNA and aDNA samples^{8,13,14,15,16,17,18} is GLIMPSE¹⁰ and its companion GLIMPSE2.¹⁹ GLIMPSE and GLIMPSE2 iteratively phase and impute using a Gibbs Sampler, resulting in phased genotypes.

Aside from algorithmic considerations, the two main determinants of imputation accuracy are ancestry match with target samples and reference panel size. The latter has a large benefit, in particular, on the imputation accuracy of rare variants, which are associated with substantial functional implications.² For this reason, the size of reference panels has grown over time; the largest ones broadly used are TopMed and Human Reference Consortium (HRC), representing 133,597 and 32,470^20,21,22 individuals, respectively. However, for underrepresented populations, imputing with an ancestry-specific panel may result in more accurate genotypes than imputing with a large, primarily European ancestry reference panel.^2,7,23,24 The optimal method leverages genotypes from multiple reference panels by combining the smaller panels into a “mega” panel and then imputing once with this mega-panel. However, creating such a panel is often not possible because the individual-level data are privacy protected. Furthermore, merging two reference panels, which are genotyped and quality controlled using different algorithms and parameters, is not trivial, as seen in the creation of the HGDP+1KG panel.²⁵ Finally, combining a small population-specific reference panel with a large nonspecific panel may cause rare population-specific haplotypes to be ignored in favor of more frequent haplotypes, reducing imputation accuracy. To address this challenge for imputation from individual-level genotyping data, Yu et al.⁷ proposed a “meta-imputation” method, MetaMinimac2, that combines imputation results generated from chip genotypes with multiple reference panels. Their method has been applied to improve imputation accuracy for multiple ancestries, including South Asian^26,27 and Korean²⁸ samples. However, MetaMinimac2⁷ cannot be applied to low-coverage sequencing data, as the input data are assumed to be phased genotypes without uncertainty.

In this paper, we introduce a method for meta-imputation of low-coverage sequencing data, called MetaGLIMPSE, which enables the imputation of low-coverage sequencing data with multiple reference panels. Through meta-imputation, we bypass accessing individual reference panel samples. We construct a hidden Markov model (HMM) to estimate weights, which are used to directly combine single-panel imputation results into a consensus genotype.

We evaluate our method on high-coverage sequencing data from 1000 Genomes²⁹ for 3 scenarios, downsampling to 0.1×–8×. First, we evaluate the case in which the target samples and reference panels originate from the same ancestry, modeling combining imputation results from two reference panels that have the same ancestry as the target sample. Second, we evaluate the case in which the target samples are an admixture of the ancestries in each reference panel, modeling imputing admixed individuals with two reference panels, each containing a different source population. Third, we evaluate the case where the target samples are aDNA and the reference panels are from two different modern populations. In all these cases, our method outperforms the best-available single-reference-panel imputation across all minor-allele frequencies (MAFs). In summary, MetaGLIMPSE delivers imputed genotypes that are more accurate than single-panel imputation at standard mean coverages (0.1×–8×) without knowing a priori which reference panel is the best.

Subjects and methods

MetaGLIMPSE combines multiple low-coverage sequencing imputation results by calculating each imputation result’s fit with the sequencing data. The imputation results, along with the genotype likelihoods, are inputs to an HMM that estimates weights for each panel at every imputed polymorphism. We leverage these weights to combine the single-panel imputation estimates into meta-imputed genotypes (Figure 1). This work has been conducted under UKBB project # 66995, the data for which is described in the supplemental methods.

Figure 1.

Model overview of MetaGLIMPSE

The workflow for MetaGLIMPSE is shown here for a single target sample with two markers in dark and light gray, respectively. The workflow starts from the read data, from which genotype likelihoods are called. Here, the most likely genotypes are A/A for the first marker and C/C for the second marker. Then, we phase and impute haplotypes based on the genotype likelihoods with two different reference panels separately, panel 1 in blue and panel 2 in yellow, via GLIMPSE2. The first panel imputes A|A, A|C, whereas the second panel imputes A|C, C|C. MetaGLIMPSE analyzes the imputed haplotypes and genotype likelihoods to estimate weights for each individual and marker, modeling the correlation of nearby markers by using an HMM. In this example, the first marker has a higher weight for panel 1 and the second marker has a higher weight for panel 2. Finally, MetaGLIMPSE outputs meta-imputed genotypes by generating a weighted average of each of the imputation estimates. In the example, MetaGLIMPSE imputes A\A, C\C as the best-guess genotypes, which derive from the higher weights on panels 1 and 2, respectively. MetaGLIMPSE can also output phased genotypes if the phasing option is used (supplemental methods).

Model description

In a dataset where variants have been called at M loci, we model sequencing data for each individual as genotype likelihoods GL_m = [GL(0), GL(1), GL(2)] at each called variant m. Let there be K distinct reference panels, and let (A_1,k,m, A_2,k,m) denote the imputation output for marker m (1 ≤ m ≤ M) with panel k (1 ≤ k ≤ K). (A_1,k,m, A_2,k,m) are the outputted phased dosages of any low-coverage sequencing algorithm, e.g., GLIMPSE2. Therefore, A_1,k,m + A_2,k,m is the unphased imputed genotype dosage for marker m and panel k. Finally, let G_m: 0 ≤ G_m ≤ 2 be the meta-imputed genotypes, obtained through estimating marker and panel-pair specific weights via HMM as described in the following sections.

Defining the HMM

Hidden and observed states

We define an HMM across all imputed genotypes m where the observed states are the genotype likelihoods GL_m and the hidden states are the “best” imputation results, denoted A^∗ = (A _p1, ^_∗, _m, A _p2, ^_∗, _m): A^∗[i] ∈ {A_{pj,k, m}: 1 ≤ k ≤ K; p_j ∈ {1,2}; 1 ≤ m ≤ M}, where p_j represents phasing status.

Emission and transition probabilities

The emission probability captures how well each imputation result fits with the observed sequencing data ((Equation 1), (Equation 2)). Let G be the genotypes possible in the genotype likelihood, G = {0,1,2}, and let g be a realization of G.

$$P\left({GL}_m|A_{p_1,k_1,m},A_{p_{2,}{k}_2,m}\right)={\sum }_{g\in G}{GL}_m\left(g\right)\ast P(G_m=\mathrm{g}|(A_{p_1,k_1,m},A_{p_{2,}{k}_2,m}))$$ (Equation 1)

$$P\left(G_m=\mathrm{g}|\left(A_{1,k_1,m},A_{p_2,k_2,m}\right)\right)=\{\begin{array}{c}\left(1-A_{p_1,k_1,m}\right)\left(1-A_{p_2,k_2,m}\right),ifg=0\\ \left(1-A_{p_1,k_1,m}\right)\left(A_{p_2,k_2,m}\right)+\left(A_{p_1,k_1,m}\right)\left(1-A_{p_2,k_2,m}\right),ifg=1\\ A_{p_1,k_1,m}\ast A_{p_2,k_2,m},ifg=2\end{array}$$ (Equation 2)

Due to the genotype uncertainty at each marker, we marginalize over the possible unphased genotypes in the emission probability. We also sum over phase since the imputation results are phased, whereas the genotype likelihoods are not. The transition probability is a function of marker distance based on the Li and Stephens³⁰ transition probabilities for diploid data.^5,31

$$P\left(A_{p_1,k_1,m},A_{p_2,k_2,m}\right)|\left(A_{p_1,k_1^{\text{'}},m-1},A_{p_2,k_2^{\text{'}},m-1}\right)=\{\begin{array}{c}\frac{{{\lambda }_m}^2}{|{K^{\ast }|}^2},if{k}_1\ne k_1^{\text{'}}and{k}_2\ne k_2^{\text{'}}\\ \frac{{\lambda }_m\left(1-{\lambda }_m\right)}{\left|K^{\ast }\right|}+\frac{{{\lambda }_m}^2}{|{K^{\ast }|}^2},if{k}_1\ne k_1^{\text{'}}and{k}_2=k_2^{\text{'}}or{k}_1=k_1^{\text{'}}and{k}_2\ne k_2^{\text{'}}\\ {\left(1-{\lambda }_m\right)}^2+\frac{2\left({\lambda }_m-{{\lambda }_m}^2\right)}{\left|K^{\ast }\right|}+\frac{{{\lambda }_m}^2}{|{K^{\ast }|}^2},if{k}_1=k_1^{\text{'}}and{k}_2=k_2^{\text{'}}\end{array}$$ (Equation 3)

Here, we assume that the switch from one imputation result being optimal to a different imputation result being optimal (i.e., $\left(A_{p_1,\ast ,m-1},A_{p_2,\ast ,m-1}\right)\ne \left(A_{p_1,\ast ,m},A_{p_2,\ast ,m}\right)$) is driven by the recombination process. Thus, λ_m = 1 − e^{−θ ∗d(m-1, m)}, and θ = 2 × 10⁻⁷ is the recombination rate between the variants.⁷ d(m-1, m) is the base-pair distance between the m^th and m-1^th markers. The probability of a transition between distinct hidden states increases as the distance between adjacent markers increases. We fix θ according to values found in the meta-imputation literature.⁷

Weight estimation and meta-imputed genotypes

We apply the forward-backward algorithm³² to this HMM, generating the marginal probability of each imputation panel pair being optimal at variant m. These probabilities serve as the weights, denoted as $W_{\left(A_{p_1,k_1,m},A_{p_{2,}{k}_2,m}\right)}$ (Equation 3), where the subscripts indicate the reference panels k₁ and k₂ used for the two haplotypes.

$$W_{\left(A_{p_1,k_1,m},A_{p_{2,}{k}_2,m}\right)}=P(A\ast =\left(A_{p_1,k_1,m},A_{p_{2,}{k}_2,m}\right)|{GL\left(g\right)}_1...{GL\left(g\right)}_M)$$ (Equation 4)

Using these weights, we compute the meta-imputed genotype at each marker by averaging the imputed genotypes from all possible panel pairs, weighted by their probabilities. Formally, for each marker m, we calculate G_m as follows (Equation 4):

$$G_m={\sum }_{k_1,k_2\in K^{\ast }:k_1\ne k_2}{W}_{\left(A_{p_1,k_1,m},A_{p_2,k_2,m}\right)}\left(A_{p_1,k_1,m}+A_{p_2,k_2,m}\right)$$ . (Equation 5)

This derives an expected genotype value that reflects a consensus across all panels, giving more weight to the panels that best fit the observed sequencing data.

Leveraging phasing information

MetaGLIMPSE can leverage the phase information on imputed genotypes by modifying the space of hidden states in the HMM. We describe two versions of MetaGLIMPSE. The default version, MetaGLIMPSE, leverages phasing, whereas “MetaGLIMPSE-plain” does not.

Formally, let $\mathcal{S}$ be the set of all hidden states. For MetaGLIMPSE-plain, $\mathcal{S}$ = {(A₁₁,A₂₁),(A₁₂,A₂₂),…,(A_1k,A_2k)}, requiring that A_1^∗ and A_2^∗ originate from the same reference panel. For the default MetaGLIMPSE, we define $\mathcal{S}$ = {(A_1i,A_2j): 1 ≤ i,j ≤ k}, thus allowing A_1^∗ to originate from a different reference panel than A_2^∗. MetaGLIMPSE-plain has |$\mathcal{S}$| = K hidden states, whereas MetaGLIMPSE has |$\mathcal{S}$| = $\left(\begin{array}{l}2K\\ 2\end{array}\right)$ hidden states.

Deriving an estimated R² for assessing meta-imputation accuracy

We derive an estimated R² for each SNP j, denoted $\widehat{R_j^2}\text{,}$ for meta-imputation. This statistic is common to imputation algorithms.² We follow the definition of the Markov Chain Haplotyping algorithm (MACH)⁵-estimated $\widehat{R_j^2}$ in Marchini et al.⁶ Let the genotype be denoted as G ∈ {0,1,2} and g as a realization of G. Let N be the number of target samples. Let i denote the i^th individual, and let d_ij denote the meta-imputed dosage for SNP j and individual i. d_ij = P(G = 1) + 2 ^∗ P(G = 2). Let θ_j denote the allele frequency of SNP j: ${\theta }_j={\sum }_{i=1}^N\frac{d_{ij}}{2}$.

$$\widehat{R_j^2}=\{\begin{array}{c}\frac{\sum _{i=1}^N{d}_{ij}^2-{\left(\sum _{i=1}^N{d}_{ij}\right)}^2}{2{\theta }_j\left(1-{\theta }_j\right)}\\ 1,if{\theta }_j=0or{\theta }_j=1\end{array},if{\theta }_j\in \left(0,1\right)$$ (Equation 6)

We evaluate $\widehat{R_j^2}$ on variants that are present in both panels against the true per-marker R².

Evaluation

To assess the performance of MetaGLIMPSE and MetaGLIMPSE-plain in a variety of scenarios, we impute SNPs on chromosome 20 using the 2,495 samples unrelated to the 1^st degree in 1000 Genomes phase 3 resequenced at 30ײ⁹ as the source dataset for both modern target samples and reference panels. We also evaluate ten target aDNA samples, a subset of samples described in Sousa da Mota et al.¹³ but first published elsewhere^{33,34,35,36,37} (Table S1). We chose these ten for spatial diversity, with five Europeans, three Africans, and two Native Americans, and temporal diversity, as the samples range from 327 to 35,154 years before present. These samples also have relatively low C-to-T deamination rates. The maximum percentage of C→T transitions at reads’ ends across all samples is 18.5%, the mean is 4.7%, and the minimum is 0.8%. Three of the ten samples do not have reported deamination rates.¹³

To create our test datasets, we first align the aDNA FASTA files to hg38, unless the hg38-aligned BAM files already exist, which is the case for all modern samples. We use bwa-mem2 with the default settings, as recommended for aDNA.³⁸ All 1000 Genomes²⁹ samples include hg38-aligned BAM files. Then, from the 2,504 total modern samples, we remove samples that have any parents in the dataset, using the pedigree file from Byrska-Bishop et al.,²⁹ leaving 2,495 total samples unrelated to the 1^st degree. From these 2,495 remaining modern samples as well as the ten ancient samples, we generate low-coverage target samples by downsampling to a range of mean coverages {0.1×, 0.5×, 1×, 2×, 4×, 6×, and 8×} using samtools view v.1.19.2. For each sample and coverage, we calculate genotype likelihoods using bcftools mpileup v.1.19 at all bi-allelic sites for all 3,202 individuals in 1000 Genomes.²⁹ We call the genotypes of aDNA in the same manner as the modern samples since the choice of caller does not substantively impact imputation results.¹³

We create five reference panels by subsetting the samples for the following populations based on the 1000 Genomes²⁹ ancestry classification: Europeans half A (n = 249), Europeans half B (n = 249), Europeans (n = 498), Africans (n = 599, excluding African Americans, i.e., the African Ancestry in Southwest US [ASW] population in 1000 Genomes²⁹), and Africans + Europeans (n = 1,098, excluding African Americans). We generate European half A and European half B by randomly sampling half of the full European panel. We remove all SNPs that are singletons (i.e., minor-allele count of 1) across the 2,495 samples. Within each reference panel, we remove triallelic SNPs, and then we remove SNPs with a minor-allele count of 0. When inputting a target sample, we exclude that sample from the reference panel.

We impute the target African American and aDNA samples with downsampled coverage using the African, European, and African + European mega-panels. We impute the downsampled Europeans with each sample’s distinct European A, European B, and full European panels. In all three experiments, we impute in 6-cM-length chunks using the GLIMPSE 2.0.1 software -AP option branch for 19 burn-in iterations and 1 main iteration for each reference panel described above. We then meta-impute the modern African Americans, modern Europeans, and the aDNA samples using their respective single-panel imputations via MetaGLIMPSE.

To compare the performance of single-panel imputation, mega-imputation, and meta-imputation, we identify SNPs that are present in both single-panel imputations. This results in ∼344,000 and ∼281,000 SNPs in both the Europeans half A and Europeans half B panels and both the African and European panels, respectively. Using these SNPs, we calculate the accordance of each imputation result with the high-coverage genotypes. For the modern samples, we use the 30× genotypes called in 1000 Genomes.²⁹ For the ancient samples, we call the validation genotypes using the “five filter approach,”^13,34 resulting in ∼257,000 SNPs. Of these, ∼60,000 SNPs are present in both the European and African panels, respectively.

To calculate imputation accuracy, we bin SNPs by MAF and determine the aggregated Pearson R² between the high-coverage genotypes and the imputed genotype estimates in each bin. Aggregated R² combines the true genotypes into one vector and the estimated genotypes into a second vector and calculates the correlation between these two vectors.¹⁰ This metric accounts for the relatively small number of target samples we impute, since the Pearson R² per SNP is not defined when the variance of either the true or imputed genotypes is zero.³⁹ We use aggRSquare v.1.0.0⁷ to compute the aggregated R², and we set the allele frequency of an SNP to its value across all unrelated samples in the 30× resequenced phase 3 1000 Genomes dataset.²⁹

Results

We evaluate MetaGLIMPSE across sequencing coverages ranging from 0.1× to 8×, considering a variety of realistic scenarios with two available reference panels. These scenarios include instances where (1) target samples share ancestry with both reference panels; (2) admixed individuals are present, with each panel representing one ancestral background; (3) aDNA samples are imputed with modern reference panels; and (4) one reference panel is large (supplemental notes).

For each scenario, we generate four distinct imputed datasets for the target samples: initially, two imputed cohorts are generated, each using one of the available reference panels. A third cohort is then created via mega-imputation, where both panels are merged into a unified reference. The fourth cohort is produced by applying MetaGLIMPSE to combine the two individually imputed cohorts.

Meta-imputing with reference panels from the same population

A common use of meta-imputation is to combine imputation results from several reference panels, such as TopMed²² and HRC,²¹ that cannot be merged in a mega-imputation framework, due to privacy reasons. We model this challenge by splitting the unrelated 30× European samples (n = 499) in 1000 Genomes²⁹ into two reference panels while excluding the target sample from either panel. We imputed each of our 499 target samples with its distinct set of three reference panels separately: European mega-panel (n = 498), European half A (n = 249), and European half B (n = 249). We then combined the results from European half A imputation and European half B imputation using MetaGLIMPSE. We compared MetaGLIMPSE to the two half-panel imputations and the one mega-imputation.

Across all coverages, mega-imputation, unsurprisingly, achieves the highest overall aggregated R², with high accuracy for common variants that rapidly declines as alleles become rarer. European panels half A and half B have an almost identical aggregated R² that is consistently lower than the aggregated R² of the mega-imputation, with larger differences for uncommon and rare variants. MetaGLIMPSE provides more accurate imputation results than either of the individual European panels across all MAFs and all sequencing depths (Figures S4 and S5).

At 2× coverage, aggregated R² values for all imputation scenarios are within 0.01 of each other for variants with MAFs > 1%. The difference in imputation quality increases between MAFs of 0.1% and 1%. For MAFs between 0.1% and 0.2%, the mega-imputation maintains an R² of 0.68, while the individual panels drop to 0.62. MetaGLIMPSE gives an R² of 0.65, recovering 45% of the performance increase of mega-imputation compared to the best single-panel imputation (Figures 2A and 2B). Phasing also plays an important role in MetaGLIMPSE. At 2×, for MAFs between 0.1% and 0.2%, MetaGLIMPSE performance drops to 0.64, a difference of 0.01, when we do not leverage phasing (Figures S4 and S5).

Figure 2.

Meta-imputation of European target samples with two European reference panels

We impute 499 Europeans from 1000 Genomes, downsampled to 2× and 4×, using two European reference panels (n = 249). We evaluate MetaGLIMPSE by calculating the aggregated R² between the (meta-)imputed genotypes and true genotypes. We plot both the aggregated R² by MAF (A) and the difference between the aggregated R² from mega-imputation and the aggregated R² for each of the other imputations by MAF (B).

At 4× coverage, MetaGLIMPSE’s performance compared to mega-imputation improves noticeably compared to that at 2×. For MAFs between 0.1% and 0.2%, mega-imputation produces an aggregated R² of 0.75, while MetaGLIMPSE delivers 0.73, recovering 62% of the performance gain by mega-imputation compared to the best single-panel imputation (Figures 2A and 2B).

In general, as coverage increases, MetaGLIMPSE recovers more of the performance gain by mega-imputation, especially for rare variants. At 0.1×, MetaGLIMPSE recovers 25% of the performance increase at MAFs between 0.1% and 0.2%. At 8×, for the above MAFs, MetaGLIMPSE recovers 67%. At 8×, for MAFs > 1%, the performances of mega-imputation and MetaGLIMPSE are practically equal (Figures S4 and S5).

Meta-imputing admixed samples

Meta-imputation facilitates imputation for admixed populations by combining imputation results from reference panels that each contain a different source population. We model imputation for admixed targets by imputing 57 unrelated African Americans from 1000 Genomes²⁹ using three imputation panels also from 1000 Genomes²⁹: an African population panel without African Americans (n = 599), a European population panel (n = 499), and a mega-panel (n = 1098), which is a concatenation of the African and European reference panels. We generate meta-imputation results by combining the African panel imputation results and European panel imputation results through MetaGLIMPSE and comparing them to mega-imputation and the two single-panel imputations.

Across all MAFs and coverages, the mega-imputation has the highest aggregated R², and the European panel nets the lowest aggregated R². Across all coverages, for MAFs > 2%, the performance of MetaGLIMPSE is indistinguishable from the performance of the African panel. For MAFs < 2%, MetaGLIMPSE performs better than the African panel alone (Figures S6 and S7).

At 2× coverage, for MAFs between 0.5% and 1%, mega-imputation achieves an aggregated R² of 0.66, and MetaGLIMPSE has an aggregated R² of 0.62. The best single-panel imputation nets an aggregated R² of 0.60. Across all MAFs and coverages, MetaGLIMPSE performs at least as well or better than the best single-panel imputation, which is the African panel (Figures 3A and 3B).

Figure 3.

Meta-imputation of African American target samples with an African and a European reference panel

We impute 57 African Americans from 1000 Genomes, downsampled to 2×, using an African (n = 599) and a European (n = 499) reference panel. We evaluate MetaGLIMPSE by calculating the aggregated R² between the (meta-)imputed genotypes and true genotypes. We plot both the aggregated R² by MAF (A) and the difference between the aggregated R² from mega-imputation and the aggregated R² for each of the other imputations by MAF (B).

MetaGLIMPSE’s performance gain compared to the African panel imputation remains roughly constant as coverage increases. For instance, at both 0.1× and 8×, for MAFs between 0.5% and 1%, MetaGLIMPSE recovers 26% and 21%, respectively, of the performance increase by mega-imputation compared to the African panel imputation.

We also find that phasing has an important role in meta-imputation. Across all coverages, when MetaGLIMPSE leverages phasing, it has a higher aggregated R² compared to when it does not—we denote this version MetaGLIMPSE-plain. For example, at 2×, for variants with MAFs between 0.5% and 1%, MetaGLIMPSE-plain achieves an aggregated R² of 0.61, which is 0.01 less than MetaGLIMPSE (Figures S6 and S7).

We evaluate the per-marker estimated R² on this scenario at 0.1× coverage, which is the most challenging depth for meta-imputation. The estimated R² tends to overestimate the true R² (mean [true R² − estimated R²] = −0.1) and has a correlation of 0.81 with the true R² across all MAFs, which is highly significant (p < 2e−16) (Figure S8).

Meta-imputing aDNA

MetaGLIMPSE facilitates imputation for aDNA, which is often sequenced at low coverage and imputed with modern-day reference panels.^13,40,41 We emulate this scenario through (meta-)imputing a diverse set of ten target aDNA samples in Sousa da Mota et al.¹³ with the 1000 Genomes²⁹ African and European panels, as described above. These ten aDNA samples are of European, African, or Native American ancestry. We evaluate MetaGLIMPSE for these targets by comparing its performance with the mega-panel and the two single-panel imputations.

Across all MAFs and coverages, the mega-imputation has the highest aggregated R², followed by MetaGLIMPSE. The single-panel imputations have the lowest aggregated R². The relative performance of each single-panel imputation depends on the MAF (Figures S9 and S10).

At 2× coverage, mega-imputation has the highest aggregated R² across MAFs, and the single-panel imputations have the lowest. Unlike scenarios with modern targets, mega-imputation has a noticeable performance gain compared to the best single-panel imputation at both rare and common variants. For rare MAFs between 0.2% and 0.5%, MetaGLIMPSE recovers 71% of this performance gain and achieves an aggregated R² of 0.45, while the best single-panel imputation drops to 0.28. At common MAFs between 10% and 20%, MetaGLIMPSE has an aggregated R² of 0.92, while the aggregated R² of the best single-panel imputation drops to 0.91. MetaGLIMPSE recovers 57% of the performance gain by meta-imputation over the best single-panel imputation (Figures 4A and 4B).

Figure 4.

Meta-imputation of aDNA target samples with an African and a European reference panel

We impute ten aDNA samples used in Sousa da Mota et al., downsampled to 2×, using an African (n = 599) and a European (n = 499) reference panel. We evaluate MetaGLIMPSE by calculating the aggregated R² between the (meta-)imputed genotypes and true genotypes. We plot both the aggregated R² by MAF (A) and the difference between the aggregated R² from mega-imputation and the aggregated R² for each of the other imputations by MAF (B).

As the coverage increases from 0.1× to 8×, MetaGLIMPSE recovers more of the performance gain by mega-imputation over the single-panel imputation for rare variants while staying essentially constant for common variants. At 0.1×, MetaGLIMPSE recovers 21% and 67% of the performance gain at rare variants between 0.2% and 0.5% MAFs and common variants between 10% and 20% MAFs, respectively. While at 8×, MetaGLIMPSE recovers 66% of the performance gain at rare variants with MAFs between 0.2% and 0.5% and, at common variants, between 10% and 20% MAFs (Figures S9 and S10).

Computation time

Computation time is an important consideration in (meta-)imputation algorithms due to the large number of markers processed.^2,4,7 For HMMs, computation time is linear with the number of markers and quadratic with the number of reference panel pairs. Therefore, for K reference panels and M markers, the computation time, without file reading and writing, for MetaGLIMPSE is O(K⁴M), whereas it is O(K²M) for MetaGLIMPSE-plain because it has fewer possible configurations for reference panel pairs than MetaGLIMPSE.

We report the computation times for MetaGLIMPSE, including file reading and writing time, by the number of samples and markers processed. MetaGLIMPSE computes the underlying HMM in 30,000-marker chunks to allow for parallelization, which significantly speeds up the computation time. The number of markers assigned to each chunk is customizable.

MetaGLIMPSE with 1 sample and 900,000 markers takes a total time of 4.42 s on an Intel Xeon Platinum 8176 CPU @ 2.10 GHz with 1 core—if we run all 30 chunks in parallel. For 500 samples and ∼900,000 markers, MetaGLIMPSE takes a total time of 32 min and 7 s. By comparison, GLIMPSE2 for 500 samples takes 3 h 15 min and 45 s. 900,000 markers are roughly the size of the union set of polymorphic markers between the African and European panels in 1000 Genomes²⁹ on chromosome 20. Since chromosome 20 comprises roughly 2% of the genome, the time for MetaGLIMPSE on a whole genome will be 3 min and 41 s (Table 1).

Table 1.

Grid of computation times for MetaGLIMPSE by the number of samples (N) and the number of markers (M) while running all chunks in parallel

N	M = 900,000	M = 1 genome
1	4.42 s	3 min and 41 s
50	2 min and 50 s	2 h, 21 min, and 51 s
500	32 min and 7 s	26 h, 45 min, and 42 s

Discussion

We present a meta-imputation framework for low-coverage sequencing that enables imputation with multiple reference panels. MetaGLIMPSE is efficient and improves accuracy, achieving consistently better aggregated R² than the best single-panel imputation for a wide range of coverages and allele frequencies. This improvement is largest for rare variants, where the performance difference between the mega-imputation and the individual reference panels is also the largest. This result is consistent with observations elsewhere that the imputation quality of rare variants is dependent on reference panel size and the extent of shared ancestry with target samples.² We observe this improved performance over single-panel imputation for a wide variety of scenarios, including meta-imputing samples with the same ancestry as the reference panels, admixed populations with the source populations as reference panels, and aDNA targets imputed with modern reference panels.

These scenarios model a wide range of applications. First, the scenario of meta-imputing targets with the same ancestry as the reference translates to combining imputation results for, e.g., European target samples from several reference panels, such as TopMed²² and HRC,²¹ that cannot be used in a mega-imputation framework for logistic reasons. The results are relevant for, e.g., meta-imputing European targets sequenced using BGE.⁸ Since BGE is sequenced at 1×–4× coverage,⁸ our results suggest that meta-imputation of the low-coverage regions would be nearly equal to mega-imputation. Second, our scenario of imputing admixed samples with the source populations separately indicates that MetaGLIMPSE would facilitate imputing admixed samples, such as those in the Mexican Biobank. There, the best reference panel for imputing a given sample depends on its global ancestry composition.⁴² Our results illustrate that combining imputation results will never reduce the quality of the imputation, and so meta-imputation with MetaGLIMPSE is a powerful strategy if the best reference panel is unknown or if different panels are better in different parts of the genome. Third, the scenario of imputing aDNA from samples that are spatially and temporally diverse using two modern reference panels from different ancestries directly applies to aDNA imputation, where the available reference panels consist of modern humans.^13,14,17 Meta-imputing aDNA with 1000 Genomes,²⁹ as well as a population-specific panel more closely related to the target sample, could improve the imputation accuracy of aDNA. For instance, for ancient European targets, this additional reference panel could be UK Biobank 200K,⁴³ which is publicly available to anyone approved to use UK Biobank data.

Our results also encourage creating an aDNA reference panel. As of now, aDNA is imputed with modern reference panels, most commonly 1000 Genomes.^13,14,17,29 The current literature on imputing aDNA^{13,14,31,40,44,45} does not exploit the 10,000+ and growing set of aDNA samples,¹² from which one could create an aDNA reference panel. Meta-imputing aDNA with both a small aDNA-only panel and a large modern panel would leverage these aDNA samples. Due to their lower coverage and higher genotyping error rate^31,45,46 than modern reference panel genomes, aDNA might not be selected as the best template haplotype by imputation algorithms. MetaGLIMPSE, which explicitly allows for aDNA as templates in imputation algorithms, could provide a substantial benefit—especially for older ancient genomes, which have undergone many subsequent population replacements.⁴¹

The imputation accuracy gained by MetaGLIMPSE compared to the best single-panel imputation leads to increased GWAS power. Aggregated R² represents the effective sample size loss in a GWAS from imputing rather than using true genotypes.² For instance, for the European targets, at 2×, for variants with MAFs between 0.05% and 0.1%, the single-panel imputation requires 1.15× the sample size to achieve the same power as the mega-imputation, whereas MetaGLIMPSE requires only 1.06× the sample size.

We also present an estimated R² metric that facilitates empirical evaluation of meta-imputation. The correlation between the estimated and true R² is comparable to that of the estimated R² for imputation algorithms.⁴⁷ The estimated R² tends to overestimate the true R², which is consistent with evaluations of the $\widehat{R_j^2}$ metric elsewhere.⁴⁸

Our method is easily adaptable to other low-coverage sequencing imputation algorithms other than GLIMPSE2, such as Beagle 4.1⁴⁹ and QUILT.⁵⁰ Furthermore, MetaGLIMPSE could also meta-impute samples imputed with multiple low-coverage sequencing algorithms. Some algorithms impute certain variants better than others,⁴⁵ necessitating meta-imputation.

We made several choices during our analysis. We handle variants missing in only one of the two reference panels by setting their genotype to the reference. Deciding how to handle variants that are not present in all reference panels is a challenging consideration for meta-imputation.⁷ Setting the missing variant to the reference is correct in the vast majority of cases. However, as a missing variant tends to indicate a monomorphism, individuals of the same ancestry as those in the reference panel that have a non-reference allele might not have been sequenced. This is especially important for meta-imputing a larger reference panel paired with a smaller reference panel, such as for UK Biobank 200K⁴³ and 1000 Genomes East Asians²⁹ (Figure S1), where the number of variants that are not present in all panels is a larger proportion of the total number of variants processed. Future work would involve constructing a more robust strategy to handle such variants. Finally, we note that the most challenging situation for MetaGLIMPSE is when one reference panel is vastly superior to the others. However, as long as mega-imputation is superior to the best single-panel imputation, meta-imputation is a reasonable strategy.

In summary, we propose a method to combine low-pass imputation results that consistently outperforms the best single-panel imputation for a wide range of scenarios—including target samples and reference panels from the same ancestry, admixed target samples with reference panels from each source population, and aDNA target samples with modern reference panels. MetaGLIMPSE is especially useful for increasing imputation accuracy of rare variants, and we expect that our method will increase the imputation accuracy for samples of diverse ancestries and time periods by allowing for privacy-protected imputation with multiple reference panels.

Data and code availability

The code for MetaGLIMPSE, along with a tutorial and instructions, is publicly available at https://github.com/karinkumar/MetaGLIMPSE.

Acknowledgments

This work was funded by the NIH grants R01 HG011031 and R01 HG005855 to S.Z. We acknowledge Ketian Yu and Jean Morrison for helpful conversations and support. We also thank the individuals, both modern and ancient, whose genomic data we used in our analyses.

Author contributions

K.H.K. and S.Z. developed the ideas. K.H.K. and S.Z. wrote the manuscript with contributions from S.R., who also developed the inputs for the software, performed the UKBB panel imputation, and designed the UKBB experiment in conjunction with S.Z. and K.H.K. K.H.K. wrote the software and performed the rest of the analyses.

Declaration of interests

The authors declare no competing interests.

Published: March 5, 2026

Web resources

• bwa-mem2, https://github.com/bwa-mem2/bwa-mem2)

• bcftools and samtools, https://www.htslib.org/

• GLIMPSE2 branch ap-option, https://github.com/odelaneau/GLIMPSE/tree/ap-field

• Phasing of the UK Biobank whole genome sequencing data interim release of 200,031 samples, https://docs.google.com/document/d/1EJmh-JcR8HBvu3rjBtREw_50kDIW-sOW2EcC6zweuTc/edit?tab=t.0#heading=h.yo8wu55p88nn

• TOPMed Imputation Server, https://imputation.biodatacatalyst.nhlbi.nih.gov