What an INFO Score Summarizes
An imputation program usually does not know a participant's genotype at an untyped variant. Instead, it estimates probabilities for the possible genotypes. The dosage is the expected genotype under those probabilities; it is useful precisely because it retains uncertainty that would be discarded by selecting a single hard call. The earlier material on genotype posteriors and dosage \(R^2\) provides this background. An INFO score compresses aspects of imputation uncertainty into a variant-level summary, but the meaning of the score depends on how the software defines it.
For a biallelic, diploid variant, let \(G_i\in\{0,1,2\}\) be the number of copies of the allele being counted for individual \(i\), and let \(Y_i\) denote that individual's observed data used by the imputation model. Write \(\pi_{ig}=P(G_i=g\mid Y_i)\) for the posterior probability of genotype \(g\). The dosage \(d_i\) is the posterior mean, and \(v_i\) is the posterior variance. Both are calculated for each individual before a variant-level score is formed.
A common posterior-uncertainty definition of INFO compares the average posterior genotype variance with the variance expected under a binomial-genotype benchmark. If \(\hat p=\sum_i d_i/(2n)\) is the allele frequency estimated from dosages, that benchmark is \(2\hat p(1-\hat p)\). One common form is:
How to Read the Score
For the uncertainty-based definition, less posterior variance relative to the benchmark gives a higher score. A value near 1 indicates that posterior genotype uncertainty is small on this scale; a lower value indicates greater average uncertainty relative to the benchmark. It does not mean that a particular percentage of genotypes is correct, nor that every individual's genotype has the same level of certainty. INFO is an aggregate over individuals at a variant.
The denominator is a reference scale, not a direct measurement of the actual genotype variance in this particular cohort. The expression \(2\hat p(1-\hat p)\) is the genotype variance for a binomial genotype with two independent allele copies and allele frequency \(\hat p\). The comparison therefore relies on that benchmark being suitable for the score's intended use. In finite samples, or when the cohort's genotype distribution differs from the benchmark, INFO need not behave like a simple percentage. A score can even be negative if the average posterior variance exceeds the chosen benchmark.
A different, common quantity is based on the across-individual variation in dosages. Under a population-moment convention, define:
This ratio compares observed dosage variation with the same allele-frequency benchmark. It is often called dosage \(R^2\), and some software or file formats label related quantities “INFO.” It is not the same formula as posterior-uncertainty INFO. In particular, dosage \(R^2\) describes variation among expected genotypes, whereas uncertainty INFO directly summarizes posterior variance. Software may also use a sample-variance correction or a different frequency estimate, which changes the numerical result. Always identify the actual estimator before comparing scores across programs.
Worked Example: Feasible Posterior Summaries and Two Scores
Suppose four hypothetical individuals have dosages \(0.2,\ 0.8,\ 1.2,\) and \(1.8\), and each has posterior genotype variance \(0.20\). These are feasible summaries for \(G\in\{0,1,2\}\). For example, dosage \(0.2\) and variance \(0.20\) can arise from posterior probabilities \(P(G=0)=0.82,\ P(G=1)=0.16,\ P(G=2)=0.02\); the other listed dosages can likewise be paired with valid probabilities.
First calculate the dosage mean and allele frequency:
The benchmark genotype variance is \(2\hat p(1-\hat p)=2(0.5)(0.5)=0.5\). The average posterior variance is \(0.20\), so the uncertainty-based score is:
For dosage \(R^2\), the dosage deviations from 1.0 are \(-0.8,-0.2,0.2,0.8\). Their squared values sum to \(0.64+0.04+0.04+0.64=1.36\), so the population-moment dosage variance is \(1.36/4=0.34\). Therefore:
The scores differ because one measures average posterior uncertainty and the other measures variation among dosages. Neither number says that exactly 60.0% or 68.0% of the imputed genotypes are correct.
Why the Two Formulas Can Differ
The distinction follows from the law of total variance. For a random genotype \(G\) and observed data \(Y\), the variance of \(G\) is the variance of its conditional expectation plus the expected conditional variance. In imputation notation, the conditional expectation is dosage and the conditional variance is posterior uncertainty.
If the genotype variance in the relevant population exactly equals \(2p(1-p)\), and the dosage and posterior-variance terms are computed on a compatible scale, this identity implies that the dosage-variance ratio and the uncertainty-based score are complements: \(R^2_{\mathrm{dos}}=1-\operatorname{INFO}_{\mathrm{unc}}\). That equality is conditional on the matching variance benchmark and definitions. In an observed finite cohort, the posterior-predictive genotype variance need not equal the binomial benchmark, and software conventions may differ. The first worked example illustrates this: the two reported quantities do not add to one.
This relationship is a useful check on interpretation, not a rule that every pair of fields labelled INFO and \(R^2\) must obey. A discrepancy can reflect different estimators, frequency estimates, variance divisors, or cohort features rather than an arithmetic error.
Worked Example: Same Dosage, Different Uncertainty
Consider four hypothetical individuals, each with posterior probabilities \(P(G=0)=0.5,\ P(G=1)=0.5,\ P(G=2)=0\). Each dosage is \(d_i=0.5\), and each posterior variance is:
The allele frequency is \(\hat p=0.5/2=0.25\), giving benchmark variance \(2(0.25)(0.75)=0.375\). The uncertainty-based INFO score is:
All four dosages are identical, so their dosage variance is zero and \(R^2_{\mathrm{dos}}=0/0.375=0\). The score difference is coherent: there is no variation among expected genotypes, while every individual remains uncertain between two possible genotypes. INFO and dosage \(R^2\) summarize different features of the imputation output.
Assumptions, Diagnostics, and Limitations
Before interpreting a reported score, establish what it summarizes. The formulas above concern biallelic, diploid genotypes coded \(0,1,2\), posterior probabilities over those genotypes, and a specified allele-frequency benchmark. They presume that posterior probabilities are meaningful under the imputation model and that the individuals and frequency estimate are defined consistently. Ploidy, missing results, variant representation, or the software's handling of frequency and variance can alter the calculation. The score is not directly comparable across different definitions simply because the columns share a name.
Useful checks include confirming that posterior probabilities for each individual sum to one, dosages lie between 0 and 2, posterior variances are nonnegative, and the allele frequency calculated from dosages is between 0 and 1. Also check the software documentation for whether the reported field is posterior-uncertainty based, dosage-variance based, or another estimator. If a calculated uncertainty score is unexpectedly negative or outside the range you anticipated, inspect the benchmark, frequency, sample inclusion, and definition before treating the value as a coding mistake. Some programs may constrain or transform their output; do not assume they do so.
Most importantly, INFO is not a direct comparison with true genotypes. It summarizes the imputation model's output, and that model can be overconfident or misspecified. A reference panel that poorly represents the target population, incorrect variant matching, or other input problems can produce confident posterior probabilities that are nevertheless wrong. A high score is therefore not an accuracy guarantee. Assessing accuracy requires information that bears on truth, such as an appropriate validation comparison; a summary score alone cannot supply it.
Worked Example: Interpreting a Reported INFO Field
Suppose a hypothetical imputation report gives a variant an INFO field of 0.92, but the documentation says this field is a dosage-variance ratio. A researcher describes the result as “92% of calls are correct.” That conclusion does not follow from the reported quantity.
Under the documented definition, the value says that dosage variation is 0.92 times the specified benchmark variance, subject to the program's conventions. It is not a count of correct genotype calls, a probability that the variant is accurate, or a guarantee about any individual's genotype. The appropriate next step is to report the estimator and benchmark, then use a validation measure if the research question concerns accuracy.
The same caution applies if the report instead uses posterior-uncertainty INFO. A value of 0.92 then indicates relatively low average posterior variance compared with its reference scale, not a 92% correctness rate. The definition changes the interpretation, but neither version provides a truth-based accuracy guarantee on its own.
Common Mistakes and Comparisons
| Quantity | What it summarizes | What it does not establish |
|---|---|---|
| Posterior-uncertainty INFO | Average posterior genotype variance relative to a benchmark | The fraction of calls that are correct |
| Dosage \(R^2\) | Across-individual dosage variance relative to a benchmark | A direct comparison with true genotypes |
| Validation accuracy measure | Agreement or association with genotypes treated as truth in validation data | Guaranteed accuracy in every target sample or population |
The main alternative to an INFO summary is not another name for the same statistic: dosage \(R^2\) captures dosage spread, while validation directly evaluates imputed results against observed genotypes in a suitable validation set. The first two are available from imputation outputs alone; validation requires suitable truth data and a design that makes the comparison informative. Each answers a different question.
- Wrong reasoning: “INFO is 0.90, so 90% of genotypes are correct.” Correction: State the software's estimator and interpret the number as a relative uncertainty or dosage-variance summary, not a correctness percentage.
- Wrong reasoning: “INFO and dosage \(R^2\) must be identical.” Correction: Their numerators differ. They are complements only under compatible definitions and a matching variance benchmark.
- Wrong reasoning: “A high INFO score proves the imputation model is reliable.” Correction: A model can be confidently wrong; INFO alone does not compare posterior predictions with truth.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- For an uncertainty-based INFO score, what does a value near 1 indicate, and what does it not indicate?
- A variant has \(\hat p=0.5\) and average posterior variance \(0.10\). Calculate the uncertainty-based INFO score using the stated formula.
- Why can dosage \(R^2\) be zero even when posterior-uncertainty INFO is positive?
- Under what condition does the variance decomposition imply that dosage \(R^2\) and uncertainty-based INFO are complements?
- A software field is called INFO, but its documentation defines it as dosage variance divided by a benchmark. What should be checked before interpreting or comparing it?
Solutions. (1) It indicates relatively little average posterior variance on the score's benchmark scale; it does not mean that the same percentage of calls is correct. (2) The benchmark is \(2(0.5)(0.5)=0.5\), so INFO is \(1-0.10/0.5=0.800\). (3) If all dosages are equal, their across-individual variance is zero, while the posterior distributions may still assign uncertainty to multiple genotypes. (4) The genotype variance must match the \(2p(1-p)\) benchmark, and the dosage and posterior-variance terms must use compatible definitions and scales. (5) Check the documented estimator, frequency and variance conventions, sample handling, and whether the intended comparison uses the same definition; this field is dosage \(R^2\)-type information, not automatically posterior-uncertainty INFO or a correctness percentage.