Why Batch Matters in Rare-Variant Studies
A rare variant may appear more common in cases than controls because it is associated with the phenotype. But the same pattern can arise if cases and controls were sequenced or processed differently. For example, a batch with lower call quality may generate more false-positive rare calls, while a batch with better coverage may detect carriers more often. If cases are disproportionately represented in the first batch, the technical difference can look like biological enrichment.
This tutorial focuses on identifying that risk through batch-stratified diagnostics: comparing cases and controls within batches, examining how the groups are distributed across batches, and checking whether basic sequencing or calling summaries differ. These checks can flag a plausible artifact; they cannot, on their own, prove that a particular call is false or that a variant has no biological effect.
Let \(Y=1\) indicate that a sample is recorded as carrying a particular rare variant, and \(Y=0\) indicate that it is not. Let \(D\) denote case status and \(B\) the sequencing batch. The observed carrier-call proportion in a group is the number of samples with \(Y=1\) divided by the number of samples in that group. It is an observed-data quantity: it need not equal the true carrier prevalence if detection sensitivity or false-positive rates differ.
A useful starting point is to compare the observed proportions \(P(Y=1\mid D=1,B=b)\) and \(P(Y=1\mid D=0,B=b)\) separately for each batch \(b\). Also compare the batch distributions \(P(B=b\mid D=1)\) and \(P(B=b\mid D=0)\). The first comparison asks whether cases and controls look different under the same batch conditions; the second asks whether the two groups were exposed to different technical conditions.
How Batch Composition Can Create Apparent Enrichment
The pooled carrier-call proportion among cases is a weighted average of the within-batch proportions. The weights are the proportions of cases in each batch. The same identity applies to controls, but their batch weights may differ:
This identity explains an important diagnostic principle. Even if case and control call proportions are equal within every batch, the pooled proportions can differ when batch-specific call rates vary and case and control batch compositions are unequal. The derivation is direct: partition the event \(Y=1\) by the mutually exclusive batches, then add the joint probabilities \(P(Y=1,B=b\mid D=d)\). Each joint probability equals \(P(Y=1\mid D=d,B=b)P(B=b\mid D=d)\).
Worked Example: A Pooled Difference With No Within-Batch Difference
Suppose a hypothetical study reports carrier calls for one candidate rare variant. Batch A has a lower call rate than Batch B, perhaps because its processing produced fewer low-level erroneous calls. The table gives the observed data; assume for illustration that the batch difference is technical and that true carrier prevalence is the same in cases and controls within each batch.
| Batch | Cases with call | Cases total | Controls with call | Controls total |
|---|---|---|---|---|
| A | 1 | 20 | 4 | 80 |
| B | 12 | 80 | 3 | 20 |
Within Batch A, the case proportion is \(1/20=0.05\), or 5%, and the control proportion is \(4/80=0.05\), also 5%. Within Batch B, the proportions are \(12/80=0.15\), or 15%, and \(3/20=0.15\), also 15%. There is no case-control difference within either batch.
Pooling across batches gives \(13/100=0.13\), or 13%, among cases and \(7/100=0.07\), or 7%, among controls. The crude difference is \(0.13-0.07=0.06\), or 6 percentage points; the crude proportion ratio is \(0.13/0.07\approx1.86\). Those summaries suggest enrichment among cases, but they ignore the different batch mixtures.
Cases are 20% from Batch A and 80% from Batch B, whereas controls are 80% from Batch A and 20% from Batch B. To compare the groups under a common 50:50 batch distribution, calculate the standardized proportions:
Under these common weights, both proportions are 10%. The crude difference arose from the groups’ different batch composition combined with higher observed call rates in Batch B, not from a within-batch case-control contrast. This calculation diagnoses a possible distortion; the assumed technical explanation would still need evidence from quality summaries or other validation.
Stratified Diagnostics in Practice
A batch-stratified diagnostic is not just a request to “adjust for batch.” It is an inspection of the data structure and measurements within the relevant technical groups. The following sequence helps keep those questions separate.
Use a technical grouping that corresponds to a plausible shared source of measurement variation, such as a sequencing run or library-preparation plate. Record which samples belong to each group.
Tabulate case and control sample counts by batch. A marked imbalance warns that pooled comparisons may mix phenotype differences with technical differences.
For each batch with both cases and controls, calculate the two observed proportions and their difference. Look for a pattern that appears only after pooling or that changes substantially across batches.
Within batches and between batches, examine measures such as callable fraction, coverage summaries, and the fraction of calls flagged as low confidence. A case-control contrast in these summaries can support concern about differential measurement.
Distinguish a diagnostic signal from a conclusion about a variant’s truth or biological effect. If case status and batch are nearly or completely confounded, acknowledge that the observed data may not separate them.
Worked Example: Interpreting Batch-Level Quality Summaries
In a second hypothetical study, cases are more common in Batch B and controls are more common in Batch A. Suppose each sample has a recorded fraction of candidate calls flagged as low confidence. The group means are:
| Batch | Cases (n) | Case low-confidence fraction | Controls (n) | Control low-confidence fraction |
|---|---|---|---|---|
| A | 20 | 0.5% | 80 | 0.5% |
| B | 80 | 3.0% | 20 | 3.0% |
Within each batch, the displayed mean is the same for cases and controls. However, the rate is higher in Batch B than in Batch A. The weighted mean across cases is
or 2.5%. For controls, the corresponding calculation is
or 1.0%. The pooled difference is 1.5 percentage points, despite equal case and control means within each batch. This is a useful warning that low-confidence calls are concentrated in a batch that contains more cases. It does not establish that every low-confidence call is erroneous; it identifies a pattern that warrants scrutiny of the candidate calls and the technical process.
When Batch and Case Status Do Not Overlap
Within-batch comparison requires both cases and controls in a batch. If every case was processed in one batch and every control in another, batch and case status are completely confounded in the observed data. The data then contain no direct comparison of cases and controls under the same batch conditions. A numerical adjustment cannot manufacture that missing comparison.
Worked Example: Complete Confounding Limits Interpretation
A hypothetical study has 50 cases sequenced in Batch C and 50 controls sequenced in Batch D. Four cases receive a call at a candidate rare locus, compared with one control. The observed proportions are \(4/50=0.08\), or 8%, in cases and \(1/50=0.02\), or 2%, in controls. The crude difference is \(0.08-0.02=0.06\), or 6 percentage points.
But Batch C contains no controls, and Batch D contains no cases. It is therefore impossible to calculate a within-batch case-control difference in either batch. The observed 8% versus 2% contrast is compatible with a biological difference, a batch-dependent difference in call detection, or both. These data alone do not distinguish those explanations.
A useful next step is to seek evidence that breaks the confounding, such as sequencing or validating samples from both groups under comparable technical conditions. Until then, report the observed contrast as an association in these processed data, not as evidence that the variant causes disease or that the difference is necessarily biological.
Why These Diagnostics Matter
Rare-variant analyses are especially sensitive to a small number of calls: a handful of extra calls can noticeably change a carrier proportion when true carriers are uncommon. Technical differences can affect both sides of the calling process. Lower sensitivity can hide true carriers; a higher false-positive rate can add apparent carriers. If either difference tracks case status through batch allocation, the resulting pattern may resemble rare-variant enrichment.
Batch-stratified comparisons help reveal whether a pooled finding is stable within technical groups. Quality summaries provide context for interpreting those comparisons. Neither should be treated as a substitute for sound study design. Ideally, cases and controls are distributed across batches so that each batch contains both groups, and technical processing is comparable. If this balance is absent, the limitation should be explicit.
Common Mistakes
- Wrong: “The pooled case proportion is higher, so the variant is enriched in cases.” Correction: First compare proportions within batches and inspect how cases and controls are distributed across them. A pooled difference can reflect batch composition.
- Wrong: “The within-batch proportions look similar, so there is no technical concern.” Correction: Batches can have different overall call rates or quality summaries. Similar case-control proportions within batches do not make those batch differences irrelevant when group composition is imbalanced.
- Wrong: “Adding batch to a model resolves complete confounding.” Correction: If no batch contains both cases and controls, the observed data lack a within-batch contrast. Statistical adjustment cannot identify a comparison absent from the data.
- Wrong: “A low-confidence call is definitely false.” Correction: A quality flag is diagnostic evidence, not a definitive verdict on an individual call. Interpret it with the other available evidence.
Check Your Understanding
Use the distinctions between pooled comparisons, within-batch comparisons, and technical diagnostics to answer these questions.
- Why can pooled case and control carrier-call proportions differ even when the within-batch proportions are equal?
- In a study, cases are mostly in Batch A and controls mostly in Batch B. Name two batch-stratified checks that would help assess possible technical distortion.
- What does it mean if no batch contains both cases and controls, and why can adjustment not create the missing comparison?
- A quality summary differs between batches but is similar for cases and controls within each batch. What does this suggest, and what does it not prove?
- Why should an observed carrier call not automatically be interpreted as a true biological rare-variant association?