Why Calibration Diagnostics Matter
A structural-variant association can look compelling even when the recorded genotypes partly reflect sequencing or calling behavior rather than biological variation. A deletion, duplication, or other structural variant may be harder to call in some samples than others. If that difficulty tracks case status, sequencing batch, or another feature related to the phenotype, the resulting association can be misleading. Calibration diagnostics look for such patterns before an association is treated as credible.
No single check establishes that a signal is genuine. Instead, several checks address different failure modes: whether callability differs between phenotype groups, whether it varies across batches, whether apparently null tests show systematic departures from expectation, and whether negative controls produce unexpected associations. A concerning result is a reason to investigate, not by itself proof that the variant is artifactual.
Compare Call Rates Across Phenotype Groups
For a case-control phenotype, compare the proportion of cases with a callable genotype to the corresponding proportion of controls. A substantial difference matters because the association analysis may then compare different subsets of samples in the two phenotype groups. If callability depends on phenotype group, observed genotype distributions can be distorted, especially when missingness is handled as if it were unrelated to genotype or phenotype.
A simple diagnostic treats each sample's callability as a binary outcome: callable or not callable. Let \(n_1\) and \(n_0\) be the numbers of cases and controls, and let \(x_1\) and \(x_0\) be their callable counts. The observed call rates are \(\hat{p}_1=x_1/n_1\) and \(\hat{p}_0=x_0/n_0\). To test the null hypothesis of equal call rates, use the pooled estimate under that null and a two-sided two-proportion score test, provided the observations are independent and expected counts are adequate.
Under the null and the large-sample conditions, \(z\) is approximately standard normal. The two-sided p-value is \(2P(Z\geq |z|)\), where \(Z\sim N(0,1)\). The test detects a difference in callability; it does not identify its cause. Differences could arise from a technical artifact, but they could also reflect study design or another feature correlated with phenotype.
Worked Example: Case-Control Difference in Call Rate
In a hypothetical study, 285 of 300 cases and 270 of 300 controls have callable genotypes at one structural variant. Compare the call rates using the pooled two-proportion test. Assume the samples are independent and that the genotype-calling criteria were set before examining these group-specific rates.
The case call rate is \(285/300=0.950\), and the control call rate is \(270/300=0.900\). Thus the observed difference is \(0.950-0.900=0.0500\), or 5.00 percentage points. Under the null hypothesis of equal rates, the pooled call rate is
The null standard error and test statistic are
Equivalently, the one-degree-of-freedom chi-square statistic is \(z^2\approx 5.4054\), or \(\chi^2_1\approx 5.41\). The two-sided p-value is approximately 0.0201. At \(\alpha=0.05\), this is evidence against equal case and control call rates. It is a diagnostic flag: investigate why case callability is higher, and assess how missing calls were handled. The result alone does not establish that the genotype association is false.
The test assumes independent samples and sufficiently large expected numbers of callable and noncallable observations in both groups. Here, under the null, each group has an expected \(300(0.925)=277.5\) callable samples and \(300(0.075)=22.5\) noncallable samples, so the large-sample approximation is reasonable. If expected counts are sparse, use an appropriate exact procedure rather than relying on the normal approximation. In matched, related, or otherwise dependent samples, the independent two-proportion test is not appropriate without accounting for that dependence.
Look for Batch-Related Callability
Sequencing batch, laboratory, platform, or calling pipeline can affect whether a variant is detected. Compare call rates across these groups, and check whether phenotype groups are unevenly distributed across them. A batch difference can be harmless if it is unrelated to phenotype and handled appropriately, but it becomes a serious concern when batch and phenotype are entangled: the analysis may then have difficulty separating a biological association from a technical one.
For a table with \(r\) batches and two callability outcomes, the Pearson chi-square test compares observed cell counts \(O_{ij}\) with counts \(E_{ij}\) expected if callability and batch are independent. The statistic is \(\sum_{i,j}(O_{ij}-E_{ij})^2/E_{ij}\), with \((r-1)(2-1)\) degrees of freedom when the usual large-sample approximation applies. This is an omnibus test: evidence of heterogeneity says that not all batch call rates are alike, but does not say which batch differs or why.
Worked Example: Heterogeneous Call Rates Across Batches
Suppose a hypothetical cohort has 200 samples in each of three sequencing batches. The numbers callable at a structural variant are 190, 180, and 170, respectively. Assume samples are independent and that all expected cell counts are adequate. The observed call rates are 95%, 90%, and 85%.
There are 540 callable and 60 noncallable samples among 600 total. If callability is independent of batch, each batch is expected to have \(200(540/600)=180\) callable and \(200(60/600)=20\) noncallable samples. The Pearson statistic includes both callable and noncallable cells:
The degrees of freedom are \((3-1)(2-1)=2\), and the p-value is approximately \(0.00387\). This gives evidence that callability differs among batches. The counts are sufficiently large for the approximation: the expected counts are 180 callable and 20 noncallable in each batch. The diagnostic does not establish that batch caused an association, but it warrants checking batch composition, phenotype balance, and calling procedures before interpreting the variant result.
A useful follow-up is to tabulate phenotype by batch as well as callability by batch. If most cases were processed in one batch and most controls in another, an association can be difficult to distinguish from a batch effect. A regression adjustment for recorded batch may help when there is adequate overlap, but adjustment cannot reliably separate effects when phenotype and batch are nearly or completely confounded. Recalling samples, restricting to comparable batches, or seeking independent replication may be needed.
Assess Null Association Patterns
A null association analysis uses a phenotype or variant for which no association is expected under the diagnostic design. Under a correctly specified null model and suitable calibration, p-values are approximately uniform between 0 and 1. In particular, among many valid null tests, the expected proportion below a prespecified threshold \(\alpha\) is \(\alpha\). This expectation applies across repeated tests; it does not mean that every individual p-value should be large.
An excess of small p-values across null tests can indicate systematic problems, such as population structure, unmodeled relatedness, phenotype or batch imbalance, or technical artifacts. A single small p-value may occur by chance. Conversely, an apparently uniform set of p-values does not prove that every variant is well called: a localized artifact affecting one variant may not create a broad pattern. Inspect results by batch, phenotype group, call rate, and other relevant technical strata rather than relying on one summary.
Worked Example: Interpreting Small P-Values Under the Null
Consider 100 hypothetical independent tests that are all truly null and correctly calibrated. At a threshold of 0.01, each test has probability 0.01 of producing a p-value below the threshold. The expected number below 0.01 is
The probability of seeing at least one p-value below 0.01 is
Thus, at least one small p-value is not surprising in this set of null tests. If many more than one test is small, that pattern may merit investigation, but the exact assessment should account for dependence among tests and the analysis design. A cluster of small p-values among variants with poor call rates or one processing batch is more specifically concerning than an isolated small p-value, though it still does not identify a cause by itself.
Use Negative Controls
A negative control is an outcome, exposure, or genetic feature chosen because the study design gives no plausible causal or biological reason for the association being tested, while preserving relevant sources of bias. A negative-control outcome can reveal whether the variant appears associated with an unrelated phenotype measured through similar procedures. A negative-control variant or region can probe whether the same technical pipeline produces unexpected signals. The control is most informative when it shares the technical vulnerabilities of the target analysis.
Negative controls require justification. A supposedly unrelated phenotype may share causes with the primary phenotype, and a control region may have different mapping or calling properties from the structural variant of interest. A positive association with a negative control is therefore a warning that may reflect residual confounding, a technical problem, chance, or an invalid control choice. It should prompt investigation rather than automatic deletion of the target result.
Worked Example: An Unexpected Negative-Control Association
In a hypothetical analysis, investigators test a structural-variant dosage against a negative-control binary outcome selected in advance because no direct biological association is expected. A covariate-adjusted logistic regression reports a dosage coefficient of 0.420 on the log-odds scale, with standard error 0.150. Assume the model and standard-error calculation are appropriate for this diagnostic.
The Wald statistic is
The two-sided normal-approximation p-value is approximately 0.00511. The estimated odds ratio per one-unit increase in dosage is \(\exp(0.420)\approx 1.52\). In context, the fitted model estimates about 1.52 times the odds of the negative-control outcome per dosage unit, conditional on the included covariates. Because the outcome was chosen as a negative control, this unexpected association raises concern about chance, residual confounding, or technical structure shared by the analysis. It does not prove which explanation is correct, and it does not by itself prove that the primary association is artifactual.
A Practical Diagnostic Sequence
The checks work best as a connected review. First establish how callability was defined and whether the criteria were applied consistently. Then compare call rates across phenotype groups and technical strata. Next examine whether cases and controls are balanced across batches, and whether the association pattern is stable within comparable strata. Finally, evaluate null analyses and negative controls whose assumptions are explicit.
Report callable and noncallable counts, not only percentages, for cases, controls, and relevant technical groups.
Use a suitable comparison for the design, and examine which groups contribute to any heterogeneity. Statistical significance should be considered alongside the size and direction of the call-rate difference.
Determine whether phenotype groups are represented across batches and whether null tests show a broader excess of small p-values or a localized technical pattern.
Use controls with defensible assumptions, and compare results under reasonable alternative calling, filtering, or sample-restriction choices.
Common Pitfall: Treating a Diagnostic as a Verdict
A low p-value for a call-rate comparison does not mean that a variant association is definitely false; it means the observed callability pattern is difficult to reconcile with equal rates under the test assumptions. Likewise, a nonsignificant comparison does not prove equal call rates, particularly when sample sizes are small or missingness is substantial. Report the rates and counts so that practical differences remain visible even when a test lacks power.
Another mistake is to count missing genotypes as reference genotypes or noncarriers. A sample without a callable genotype does not provide evidence that the variant is absent. Keep callability distinct from dosage, and explain how missing calls enter each association analysis. Finally, do not regard adjustment for batch as a universal repair: when batch and phenotype have little overlap, the data may not identify their separate contributions.
Check Your Understanding
Use the definitions and diagnostic logic in this tutorial to answer the following.
- Why is a call rate different from a carrier proportion?
- In a case-control study, a call-rate test has a small p-value. What does that establish, and what does it not establish?
- For three batches and two callability outcomes, what are the degrees of freedom for the Pearson independence test, and what does a significant omnibus result tell you?
- Why can one p-value below 0.01 be unsurprising among many null tests?
- What properties make a negative-control outcome or variant informative, and why can an unexpected negative-control association have more than one explanation?
- Why may adjustment for sequencing batch be insufficient when cases and controls were processed in nearly separate batches?