Imputation

Imputation is the statistical inference of genotypes at positions you never measured, done by matching the stretches of your chromosome you did measure against a reference panel of sequenced haplotypes and copying over what those matching haplotypes carry.

A genotype is what you have at one position on the two copies of a chromosome: the pair of alleles, written 0/0 (two reference), 0/1 (one of each), 1/1 (two alternate) ¹. A genotyping array measures maybe 650,000 of those positions directly. A human genome contains tens of millions of common and rare variable positions ². Imputation fills the gap between the two.

How it works

Chromosomes are inherited in blocks. Recombination breaks them up slowly enough that if you share a few hundred kilobases of measured markers with someone in a reference panel, you likely share the whole segment, including the variants nobody typed on your chip. The standard implementation is a hidden Markov model where the hidden state is “which reference haplotype am I copying right now,” transitions correspond to recombination, and emissions allow for mutation and genotyping error. The Li and Stephens framework underlies IMPUTE2, minimac, and Beagle alike ³.

The workflow has two stages. First phasing: resolve your unordered genotype calls into two ordered haplotypes (SHAPEIT5 or Beagle 5.4 are the current choices). Then imputation against a panel. Scaling matters here. IMPUTE2 introduced selecting a custom subset of reference haplotypes per sample, which made panels of thousands of genomes tractable ³. minimac2 got further speedups by collapsing reference haplotypes that are identical over a given region into single states, which cuts redundant HMM computation dramatically on large panels ⁴.

Panels grew from HapMap to 1000 Genomes to HRC to TOPMed (roughly 97,000 sequenced samples, ~300 million variants). Bigger panel, better rare-variant coverage, more ancestry representation.

In your own data

Open your imputed VCF and look at the INFO field. You will see something like:

chr9 22125504 rs1333049 C G . PASS AF=0.47;MAF=0.47;R2=0.98;IMPUTED GT:DS:GP 0|1:0.99:0.01,0.97,0.02

Three things to read:

• IMPUTED vs TYPED. TOPMed and Michigan Imputation Server tag which sites were on your input chip. Everything else was inferred.
• R2 (or INFO from IMPUTE2, or DR2 from Beagle). This is the estimated squared correlation between the imputed dosage and the true genotype. Standard filter is R² ≥ 0.3 for association testing, R² ≥ 0.8 if you care about a single variant. Below 0.3 the variant carries almost no information.
• DS and GP. DS is the alternate allele dosage, 0 to 2, a continuous quantity. GP is the posterior probability over the three genotypes. The hard call GT is just the argmax of GP and throws away the uncertainty. If you are computing a polygenic score, use DS, not GT.

Common mistakes, in the order we see them:

1. Strand and reference mismatch. Array data is often on the forward strand of the probe design, not the reference. A/T and C/G sites are ambiguous and get flipped silently. Run the panel’s checking script (the HRC/1000G HRC-1000G-check-bim.pl is still the workhorse) before uploading anything.
2. Wrong build. Arrays ship in GRCh37 more often than you would expect. Lift over with CrossMap or Picard LiftoverVcf and expect to lose a small percentage of sites.
3. Filtering on R² after computing an allele frequency across a filtered set. R² is frequency-dependent: rare variants have low R² almost by construction, so a flat threshold removes rare variants preferentially and biases anything frequency-stratified.
4. Treating an imputed genotype at a clinically actionable site as a result. It is not. Confirm with targeted sequencing, and interpret with a clinician.

Limitations

Accuracy tracks how well the panel represents your ancestry. Imputation is most accurate in European-ancestry samples and degrades in African-ancestry samples, where shorter haplotype blocks and higher diversity mean each measured marker constrains less of the surrounding region ⁵. Admixed individuals do better with a diverse panel than with a single-population one.

Rare variants impute poorly regardless of panel. Below roughly 0.5% minor allele frequency, R² drops fast because few reference haplotypes carry the allele. Structural variants, repeat expansions, and anything in segmental duplications or the MHC are effectively unimputable without a panel built for the region.

Method choice matters less than panel choice. Comparisons of imputation algorithms find that differences between well-implemented HMM methods are small next to differences in reference panel size and match ⁶. Methods that skip the reference panel entirely and impute from linkage disequilibrium within the study sample exist, mainly for organisms without one ⁷.

The simple way out, if you can afford it: sequence. 30x whole-genome sequencing observes the variants directly, and imputation becomes a step you never run.

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