SSimp
Summary¶
SSimp imputes GWAS summary statistics (effect sizes/Z-statistics) for untyped variants directly from the summary statistics of nearby tag SNVs and an external reference panel's LD structure, without needing to re-impute genotypes, rerun the association scan, and re-meta-analyze. Rüeger, McDaid & Kutalik (2018) extended the method to correctly handle variable sample size and missingness across SNVs (the norm in real meta-analyses), and benchmarked it against genotype imputation on 120,086 UK Biobank individuals before applying it to the GIANT consortium height GWAS, discovering 34 novel height loci [1].
Method¶
For a set of tag SNVs with known univariate GWAS effect estimates, the effect (or Z-statistic) of an untyped SNV is estimated as the conditional expectation of a multivariate normal distribution, using the LD (correlation) between the untyped SNV and tag SNVs from an external reference panel. The tag-SNV correlation matrix is shrunk (fixed λ = 0.1, or λ = 2/√n scaling with reference panel size n) to guarantee invertibility and control noise inflation. Imputation quality is reported as an r²_pred, adjusted for the ratio of effective tag-SNV count to reference panel size. All measured variants within 250 kb of a target SNV serve as tag SNVs, imputed in 1 Mb windows with 250 kb flanking regions for computational efficiency.
Handling variable sample size: because meta-analysis cohorts often use different chips or imputation panels, per-SNV sample size varies, which changes the true covariance between effect estimates (dropping to zero for SNVs measured in fully non-overlapping samples even under perfect LD). SSimp derives an adjusted correlation matrix that scales by each tag SNV's sample size relative to the maximum, under either a maximum-overlap assumption (D^(dep), recommended as the more conservative default) or an independence assumption (D^(ind)). Simulations on upsampled 1000 Genomes data (25,000 individuals, chromosome 15, HAPGEN2) showed both adjusted estimators had lower MSE than the naive/conventional estimator across missingness scenarios, with D^(dep) performing best under high missingness correlation and D^(ind) best under low overlap.
Benchmark: Summary Statistics Imputation vs. Genotype Imputation¶
Using 120,086 UK Biobank individuals with both directly genotyped and genotype-imputed data as ground truth, comparing 37,467 typed SNVs across 706 genomic regions (535 height-associated, 171 null):
- Accuracy: genotype imputation achieved near-perfect correlation and slope (~1) versus ground truth across all MAF/imputation-quality subgroups, while SSimp's correlation with ground truth ranged from 0.998 (well-imputed common variants) down to 0.928 (low-quality, low-frequency variants) for associated SNVs, and as low as 0.42–0.66 for badly-imputed null SNVs.
- RMSE: genotype imputation had 3–5-fold lower RMSE than SSimp overall (e.g., 0.093 vs. 0.33 for well-imputed common associated SNVs), with the gap widening as imputation quality or MAF decreased.
- Power: at fixed false-positive rates of 0.001, 0.01, and 0.05, SSimp showed 9%, 43%, and 35% lower power than genotype imputation, respectively, with the largest gaps for low-MAF, poorly-imputed variants.
Application: Novel Height Loci from GIANT Summary Statistics¶
SSimp was applied to impute >10 million UK10K variants (MAF ≥ 0.1%) from the GIANT HapMap-based height GWAS (Wood et al., 253,288 individuals, 423 loci), using the UK10K reference panel (3,781 individuals) for LD. After conditional analysis, 35 candidate loci were selected and checked against a GIANT exome-chip height study (Marouli et al., 120 loci) and an independent UK Biobank height GWAS (336,474 individuals) for replication:
- 1 of the 35 loci had already been reported by the exome-chip study (
rs28929474, SERPINA1) and replicated in UK Biobank. - Of the remaining 34 genuinely novel candidate loci, 19 replicated in UK Biobank (α = 0.05/35): 2 of 3 loci with no nearby reported HapMap variant, and 17 of 31 loci with a nearby borderline HapMap signal.
- Separately, imputing all 111 imputable variants from the 122-variant exome-chip study using only the HapMap-based summary statistics recovered 55 of 111 (including 4 with MAF ≥ 5%); 53 of the 83 high-confidence-imputed (r²≥0.7) variants were retrieved at the 0.05/111 threshold.
Availability¶
Software (SSIMP) is available at wp.unil.ch/sgg/summary-statistic-imputation-software; implemented in R (analysis) with UK Biobank association scans run via SNPTEST. The authors report SSimp imputing UK Biobank-scale data roughly 500× faster than genotype imputation with Minimac (4200 vs. 8.3 CPU-days).
Limitations¶
SSimp trades statistical power and accuracy for large computational savings versus genotype imputation, with the gap concentrated in low-MAF, poorly-imputed variants; it is best suited to rapid, cost-effective locus discovery and downstream analyses (Mendelian randomization, LD score regression, fine-mapping) rather than as a substitute for genotype imputation where individual-level data and compute are available.