Imputation Dosages and Their Contribution to SNP Heritability

Why Imputation Quality Matters for Heritability

A heritability estimate can only capture genetic variation represented by the variants and genotypes used in the analysis. When genotypes are imputed, the data usually contain dosages rather than certain allele counts. A dosage is informative about a genotype, but it can be less precise than directly observed genotype data. That uncertainty can reduce the genetic signal available to an individual-level or summary-statistic estimator.

The central distinction is between the underlying variant set and the information about that set in the analysis data. Removing a poorly imputed variant changes which variants are included in the estimated quantity. Retaining it with a noisy dosage may leave the target set unchanged, but make some of its genetic signal harder to measure. Neither effect is described adequately by saying that imputation quality simply “multiplies heritability” by one universal factor.

A dosage can be fractional, such as 0.35 or 1.72, because it represents uncertainty about the allele count rather than a fractional biological genotype. Under Hardy–Weinberg equilibrium, the variance of the true allele count is \(2p_j(1-p_j)\), where \(p_j\) is the allele frequency. For a well-calibrated dosage, \(\operatorname{Var}(D_{ij})\) is no greater than \(\operatorname{Var}(G_{ij})\), so \(q_j\) lies between zero and one. A value near one indicates that dosage variation closely tracks genotype variation; a value near zero indicates little genotype information in the dosage.

How Dosage Uncertainty Reduces Captured Signal

The variance ratio has a direct interpretation under calibrated imputation. Write \(I\) for the information used to impute a genotype, so \(D=E(G\mid I)\). Because \(D\) is determined by \(I\), \(E(GD)=E\{E(G\mid I)D\}=E(D^2)\). After centering, this gives \(\operatorname{Cov}(G,D)=\operatorname{Var}(D)\). Thus the dosage is correlated with the true genotype, but its variance is smaller when uncertainty remains.

This identity explains why dosage quality is relevant to association and heritability analyses. For a single variant with phenotype model \(Y=\beta G+\varepsilon\), where the residual \(\varepsilon\) is uncorrelated with \(G\) and \(D\), the linear projection of \(Y\) on dosage captures \(\operatorname{Cov}(D,Y)^2/\operatorname{Var}(D)\) of phenotype variance. Since \(\operatorname{Cov}(D,Y)=\beta\operatorname{Var}(D)\), this is \(\beta^2\operatorname{Var}(D)\), compared with \(\beta^2\operatorname{Var}(G)\) for the true genotype. Under these assumptions, the dosage captures a fraction \(q\) of the variant’s additive variance contribution.

Consequences for Individual-Level GREML

In GREML, the additive genetic component is represented through a genomic relationship matrix (GRM) constructed from the genotypes in the analysis. A common form uses centered allele counts scaled by their expected genotype variance. With dosages, a corresponding matrix is built by substituting dosage values for allele counts. For example, under a conventional scaling,

Here \(M\) is the number of included variants. The matrix is intended to summarize genetic similarity based on those variants. When dosages are uncertain, they are imperfect measurements of the genotype patterns that would produce that similarity. In turn, the data may contain less information for estimating the genetic variance component than they would if the genotypes were known accurately.

The exact effect on a fitted GREML estimate depends on how the GRM is constructed, the pattern of dosage uncertainty across people and variants, linkage disequilibrium (LD), and the model. In particular, the single-variant variance ratio does not imply that every GREML estimate is exactly multiplied by the average INFO score. Per-variant scaling can also affect the GRM: scaling dosages by their observed variance rather than the expected genotype variance changes the relative contribution of variants. Analysts should know how their software constructs the matrix and what variant set it uses.

A useful simplified model makes the role of quality explicit. Suppose variants are independent, each contributes additive variance \(\beta_j^2\operatorname{Var}(G_j)\), dosage errors are calibrated, and there are no other genetic correlations to account for. The variance in the dosage-based genetic predictor is then \(\sum_j\beta_j^2\operatorname{Var}(D_j)\). Its fraction of the true additive variance is a contribution-weighted average of \(q_j\), not necessarily an unweighted average across variants. Variants that contribute more true genetic variance receive more weight in that comparison.

Consequences for Summary-Statistic Estimation

LD Score regression uses GWAS summary statistics to relate association statistics across variants to their LD scores. In a simplified form, the expected chi-squared statistic at variant \(j\) is modeled as a baseline plus a genetic-signal term that depends on sample size, SNP heritability, and the LD score. This interpretation depends on having appropriate LD information and on the assumed relationship between association signal and LD.

If the GWAS used dosages, uncertainty can reduce association signal. At a directly tested variant with no LD to other causal variants, the noncentrality of its association statistic is approximately proportional to \(N\beta^2\operatorname{Var}(D)/\sigma^2\), where \(N\) is sample size and \(\sigma^2\) is residual variance. Relative to using the true genotype, this is reduced by \(q\), under the same calibrated single-variant assumptions as above. When a tested variant tags other causal variants through LD, the association also depends on the covariance between its dosage and those causal genotypes. A single INFO value cannot describe that whole pattern.

For summary-statistic heritability estimation, imputation quality can therefore alter the relationship between observed association statistics and the LD scores used in the regression. If the LD scores come from an accurately genotyped reference panel but the GWAS dosages are noisy, the measured association signal and the reference LD information need not describe exactly the same effective marker set. Matching ancestry and LD reference panels remains important, and analysts should also apply consistent variant inclusion criteria and inspect how the GWAS handled imputation quality.

The single-variant example gives a clear \(q\)-based reduction only when a variant is tested directly and the stated assumptions hold. Across many variants, variable quality, LD, sample size, and variant filtering mean there is no universal rule that an LDSC heritability estimate should be divided by mean INFO. A quality-weighted or “effective” LD description may be useful in a particular model, but it must be justified for that model rather than assumed from the definition of dosage.

Filtering Changes the Estimand

Excluding poorly imputed variants is often sensible because their dosages may provide little reliable information and may behave poorly under the analysis assumptions. But filtering also changes the variant set. SNP heritability is defined relative to a specified set of variants, so an estimate after filtering pertains to the retained set, not automatically to the full set before filtering. For summary-statistic methods, the number of variants and their LD scores must correspond to the retained analysis set.

A filter can also select variants unevenly. Imputation quality may vary with allele frequency, genomic region, ancestry, and reference-panel representation. If excluded variants have distinct effects or LD patterns, the retained set can represent a different share or pattern of genetic variance. A filtered estimate can be more reliable for the retained set while capturing less of the genetic contribution represented by the original broader set.

Common Mistake

A common mistake is to multiply an estimated SNP heritability by the average INFO score—or divide by it—to “correct” for imputation. The reasoning is that each dosage captures a fraction \(q_j\) of its genotype variance, so one average factor should restore the missing signal. This fails because variants differ in their genetic contributions, dosage quality, and LD; the relevant weights are not generally equal, and the analysis method’s scaling matters. Filtering also changes the set whose heritability is being estimated.