Two Different Reasons a Genotype May Be Unavailable
A genotype data set can lack a usable genotype for two fundamentally different reasons. A variant may not have been included in the assay at all, or it may have been assayed but produced no usable call for a particular sample. These situations can look similar if both are represented as an empty cell, but they describe different data-collection events and require different interpretations.
For sample \(i\) and variant \(j\), let \(G_{ij}\) denote the true genotype. At a biallelic, diploid locus, we can code \(G_{ij}\) as the number of copies of a designated alternate allele: 0, 1, or 2. This coding is useful for examples; the central distinction below applies more broadly. Let \(T\) be the set of variants included in the assay and \(U\) the set of target variants not included in it. A typed variant is in \(T\). A missing call is a failure to obtain a usable genotype at a typed variant for a particular sample.
Thus, a variant can be typed and have observed calls for most samples but a missing call for one sample. Conversely, a variant can be untyped for every sample in the study data. An absent variant row or column is not automatically equivalent to a typed locus with blank entries: the assay design and data-processing records determine which situation applies.
What Imputation Is Predicting
In genotype imputation, the usual target is a genotype at an untyped variant. The study has observed genotypes at other, typed markers. A statistical model uses those observed marker genotypes, along with information that connects markers to the target variant, to predict the unobserved target genotype. The target is unobserved because it was not assayed, not because the assay failed to call it in one sample.
The observed markers matter because genetic variants can carry information about one another: the pattern at observed loci can help distinguish which target genotypes are plausible. That relationship must be learned or supplied by an appropriate model and data. Imputation is therefore not simply a rule that replaces every blank with a value. A missing call at a typed locus may also be predicted in some workflows, but that is a distinct missing-call problem. In either case, a prediction is not a direct measurement.
The simplest way to keep the distinction clear is to track two statuses separately: whether a locus was assayed, and whether an individual sample received a usable call at that locus. A single missing-value code cannot convey both facts unless assay status is stored elsewhere.
Worked Example: Classifying Entries in a Small Genotype Table
Suppose a hypothetical study assayed variants V1, V2, and V3 in three samples. V4 was not included in the assay. The recorded table is:
| Sample | V1 (typed) | V2 (typed) | V3 (typed) | V4 (untyped) |
|---|---|---|---|---|
| A | 0 | 1 | 2 | — |
| B | 1 | — | 1 | — |
| C | 2 | 0 | 0 | — |
The dash at sample B, V2 is a missing call: V2 was assayed, but no usable genotype was recorded for that sample. The dashes in the V4 column indicate that V4 was untyped for all three samples. They do not mean that the assay attempted V4 and failed three times.
For V1, V2, and V3, there are \(3 \times 3=9\) possible sample-by-variant calls. One is missing, so the typed-call missingness rate is \(1/9=0.1111\), or 11.1%. V4 is not included in that denominator because it was not assayed. If the table format does not preserve the typed/untyped labels, the dashes alone cannot tell us which kind of unavailability occurred.
Why Observed Markers Are Needed
To predict an untyped target genotype, a model needs information that varies across samples and is informative about the target. A simple conceptual model might estimate the distribution of target genotypes conditional on an observed marker genotype. In notation, if \(G\) is the target genotype and \(M\) is an observed marker genotype, the relevant quantity is \(P(G=g\mid M=m)\). A useful marker has conditional distributions that differ across its genotype values. If the target distribution is essentially the same for every marker value, that marker contributes little predictive information.
This conditional distribution is not automatically known. It must be estimated from suitable data or supplied by a model that has information about the relationship between the observed markers and the target. For the simple frequency illustration below, assume the training data are correctly coded, the target genotypes are observed in those training data, and their marker-target relationships are sufficiently applicable to the study samples. Real analyses require careful attention to whether those assumptions are reasonable.
Worked Example: Predicting an Untyped Genotype From a Marker
Consider hypothetical training data from 100 individuals with both an observed marker \(M\) and a target genotype \(G\). The target variant is untyped in a new study, but the marker is observed. The training counts are:
| Marker genotype \(M\) | Target \(G=0\) | Target \(G=1\) | Target \(G=2\) | Total |
|---|---|---|---|---|
| 0 | 18 | 12 | 0 | 30 |
| 1 | 8 | 28 | 4 | 40 |
| 2 | 2 | 12 | 16 | 30 |
| Total | 28 | 52 | 20 | 100 |
For an individual whose observed marker genotype is \(M=2\), estimate the conditional frequencies by dividing the counts in that row by 30:
The three estimated frequencies sum to \(30/30=1\). The most frequent target genotype in this marker group is \(G=2\), with frequency \(16/30=0.5333\). If a single most-likely genotype were required for this simplified illustration, it would be 2. That is a model-based prediction, not an observed call; the conditional frequencies also show that the prediction is uncertain.
For comparison, the overall frequency of \(G=2\) in the training data is \(20/100=0.2000\). The marker group \(M=2\) has a higher observed frequency of \(G=2\), \(16/30=0.5333\), so the marker provides information in this example. This calculation illustrates the logic only; it does not specify a full imputation algorithm.
A Short Justification for Conditional Prediction
The frequency calculation above follows directly from the definition of conditional probability. For events \(A\) and \(B\) with \(P(B)>0\), \(P(A\mid B)=P(A\cap B)/P(B)\). Set \(A\) to the event \(G=g\) and \(B\) to the event \(M=m\). In a data set, the empirical counterpart is the number of individuals with both \(G=g\) and \(M=m\), divided by the number with \(M=m\):
The denominator is the number in the marker group, not the total number of individuals. In the example, the numerator for \(G=2\) and \(M=2\) is 16, and the denominator is 30, giving \(16/30\). This estimate is useful only insofar as the observed marker and target are related in the data used to make the prediction and that relationship applies to the study samples.
Worked Example: Keeping Missing-Call Rates and Untyped Loci Separate
A hypothetical genotyping run assays five variants in each of four samples, giving \(4\times5=20\) attempted sample-by-variant calls. Three calls are unavailable: one at variant 2 and two at variant 5. Separately, the analysis plans to predict two additional variants that were never assayed.
The missing-call rate among attempted calls is:
The two additional untyped variants do not add \(4\times2=8\) attempted calls to this denominator. No calls at those loci were attempted. Counting them as missing calls would answer a different question: how much of a combined typed-and-target data matrix is unobserved, rather than what fraction of assay attempts failed to produce calls.
The distinction also changes the next step. For the three unavailable calls at typed variants, one can investigate assay or sample call failures and decide whether a missing-call procedure is appropriate. For the two untyped variants, genotype imputation requires predictions based on observed marker information and a suitable model. Neither the 15.0% call-failure rate nor the mere existence of blank cells establishes that those target predictions will be accurate.
Assumptions, Diagnostics, and Failure Modes
The conceptual prediction from observed markers rests on several conditions. The variant and allele definitions must be consistent between the study data and the data used to learn the relationship. The marker genotypes used by the model must themselves be sufficiently reliable. The training information must cover the relevant marker and target patterns, and the learned relationship must be applicable to the study samples. If these conditions fail, a precise-looking prediction can still be wrong.
Diagnostics begin with the data structure. Confirm which variants were assayed, which sample calls are missing, and whether each target is genuinely untyped. Then inspect the amount and pattern of missingness at typed loci rather than treating all unobserved entries alike. For an imputation task, examine whether the observed markers provide informative and adequately represented patterns for the targets. Sparse or poorly represented patterns provide a warning that predictions may be weak. A lack of marker-target association, inconsistent allele coding, or unreliable marker calls can undermine the prediction even when the software returns an output.
A common failure is to equate a completed data table with complete measurement. A predicted genotype does not become an observed genotype merely because software writes a value into a file. Keep the original assay status and the imputed status identifiable, and interpret predicted values according to the uncertainty and quality information available from the procedure. Detailed uncertainty summaries and imputation-quality measures require methods beyond the basic distinction taught here.
| Situation | What is unavailable? | What the label means |
|---|---|---|
| Untyped target variant | The locus was not assayed in the study | Predict it from informative observed data and a suitable model |
| Missing call at a typed variant | A sample-specific genotype at an assayed locus | Investigate the failed call; any prediction is a missing-call problem |
| Observed call at a typed variant | Nothing at that sample-locus entry | A genotype was directly recorded, subject to ordinary data-quality checks |
Common Mistake
Wrong reasoning: “There is no genotype in this cell, so it is a missing genotype and can be filled in by genotype imputation.”
Correction: First establish whether the locus was assayed. If it was assayed but the sample has no usable call, the entry is a missing call. If the locus was not assayed, it is an untyped target. Imputation at an untyped target predicts genotype using information from observed markers and an appropriate model; it does not simply replace blanks without evidence. A predicted value remains a prediction, not a direct assay result.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A variant was included on an assay, but one sample has no genotype call there. Is the variant untyped or is that sample's call missing?
- A study assays 8 variants in 10 samples and has 4 unavailable calls. What is the missing-call rate among attempted calls? Should two unassayed target variants be added to its denominator?
- In a training set, among 25 individuals with marker genotype \(M=1\), the target genotypes are 0 for 5, 1 for 15, and 2 for 5. Estimate the conditional frequency of each target genotype for \(M=1\), and identify the most frequent class.
- Why is a predicted genotype at an untyped target not equivalent to a directly observed genotype?
Solutions. (1) The variant is typed; the particular sample has a missing call because the assay included the locus but did not yield a usable genotype for that sample. (2) There are \(10\times8=80\) attempted calls, so the rate is \(4/80=0.05\), or 5.0%. The two unassayed targets are excluded because no calls at those loci were attempted. (3) Divide each count by 25: \(\widehat{P}(G=0\mid M=1)=5/25=0.20\), \(\widehat{P}(G=1\mid M=1)=15/25=0.60\), and \(\widehat{P}(G=2\mid M=1)=5/25=0.20\). The most frequent class is \(G=1\). (4) The target was not measured in that sample. Its genotype is inferred from observed marker information and a model, so the result is a prediction whose reliability depends on the information and assumptions used.