Why Burden-Test Errors Matter
A burden test combines information across selected variants, usually by summing or weighting their allele dosages. That summary can be useful when effects tend to align, but it also means that seemingly small analysis choices can change what the burden measures. A coding inconsistency can make the sum biologically incoherent; an undocumented mask can make the analysis irreproducible; and an omitted covariate can make a burden appear associated because it tracks a source of variation in the outcome.
The central discipline is to keep three things aligned: the genetic quantity being tested, the model used to test it, and the claim supported by the result. A significant gene-level test concerns the specified aggregate under the specified model. It does not by itself establish that each included variant has an effect, or that any observed association is causal.
State the Burden and Model Before Testing
Let \(G_{ij}\) be the genotype dosage for individual \(i\) at variant \(j\), coded as the number of copies of a consistently defined allele, and let \(w_j\) be its weight. A mask determines which variants are included. Write its indicator as \(M_j\), equal to 1 for an included variant and 0 otherwise. The burden for individual \(i\) is
A burden test asks whether this constructed quantity is associated with an outcome in a stated model. For a quantitative trait, one common model is \(Y_i=\beta_0+\beta_B B_i+\boldsymbol{\gamma}^{T}\mathbf{C}_i+\epsilon_i\), where \(\mathbf{C}_i\) contains covariates and the null hypothesis for the burden is \(H_0:\beta_B=0\). For a binary trait, the corresponding logistic model specifies the log odds as a function of \(B_i\) and the covariates. The appropriate score-test procedure depends on the trait model and its assumptions; this tutorial focuses on avoiding errors in how the tested burden and its interpretation are handled.
Before using a score-test result, check that the model is appropriate for the outcome, that the genotype and phenotype data have been quality-controlled, and that relevant dependence or structure—such as relatedness, ancestry, or technical batch effects—has been handled as needed. Also check that the test's calibration is suitable for the carrier counts and design. A small p-value cannot compensate for a misspecified burden or an inadequately controlled model.
Error 1: Inconsistent Allele Coding
At a biallelic site, genotype dosage can count copies of either allele. If the dosage at variant \(j\) counts the intended rare allele, the values are usually 0, 1, or 2. But if one variant is coded as the rare-allele count and another as the count of the other allele, adding those dosages does not produce a consistent rare-allele burden. The problem may arise when reference and alternate alleles differ across sites, or when data sources use different conventions.
Worked Example: Finding a Mixed Allele-Coding Error
Suppose four hypothetical individuals have genotypes at two variants. At both sites the analysis intends to count copies of the rare allele. Variant 1 is already coded that way. Variant 2 is instead stored as the count of the other allele. With equal weights, calculate the correct and incorrectly assembled burdens.
| Individual | Variant 1: rare-allele dosage | Variant 2: stored dosage of other allele | Variant 2: rare-allele dosage |
|---|---|---|---|
| A | 0 | 1 | 1 |
| B | 1 | 2 | 0 |
| C | 0 | 1 | 1 |
| D | 1 | 2 | 0 |
For a diploid genotype, the two allele dosages sum to 2, so the rare-allele dosage at Variant 2 is \(2-G_{i2,\mathrm{stored}}\). The correctly coded burden is therefore
If the stored dosage is added without recoding, the apparent burden is \([0+1,\;1+2,\;0+1,\;1+2]=[1,3,1,3]\). It no longer represents a sum of rare-allele copies across the two variants. The correct procedure is to verify allele identities and dosage conventions at every site, then recode before computing weights and burdens. In real analyses, allele alignment must be checked against the reference and variant metadata rather than inferred from dosage values alone.
A useful audit reports, for each included variant, the allele being counted, allele frequency, genotype encoding, weight, and inclusion status. A sign or allele flip can have a simple algebraic effect for an individual single-variant model, but a burden combines multiple variants. Mixing definitions within that sum can change the individual ranking and meaning of the aggregate rather than merely changing its label.
Error 2: Leaving the Mask or Weights Undocumented
A mask is the rule that decides which variants contribute to the burden. It may use information such as allele frequency, predicted functional consequence, or a specified combination of annotations. Weights also affect each variant's contribution. “We tested the gene” is not enough to reproduce an analysis: different masks or weights for the same gene define different \(B_i\), and hence different hypotheses.
Worked Example: Making a Mask Reproducible
Consider a hypothetical gene with three rare variants. An analysis intends to include variants with minor-allele frequency below 0.01 and a prespecified damaging annotation. Its records are as follows.
| Variant | Minor-allele frequency | Annotation | Included by stated rule? |
|---|---|---|---|
| V1 | 0.004 | Damaging | Yes |
| V2 | 0.008 | Not damaging | No |
| V3 | 0.015 | Damaging | No |
The mask is \(M_j=1\) only when both conditions hold. Thus \(M_1=1\), \(M_2=0\), and \(M_3=0\). With specified weights \(w_1,w_2,w_3\), the burden is \(B_i=w_1G_{i1}\); the other two genotype dosages do not enter. If the annotation source, consequence categories, frequency definition, or threshold is omitted, another analyst cannot know whether the same mask was applied. A reproducible report states each rule, the annotation and frequency sources, the handling of missing or conflicting annotations, and the resulting included variants.
An undocumented mask is not merely a reporting weakness. It prevents evaluation of whether the tested aggregate matches the scientific question, and it obscures whether the reported result was one among many tried. Record the mask and weights before testing where possible, and retain the variant list used in the analysis.
Error 3: Choosing a Threshold After Seeing the Outcome
A threshold may define which variants enter a mask, for example by allele frequency or annotation score. If the threshold is chosen because it produces the smallest p-value in the same data, the reported p-value does not account for that search. The issue is selection: the threshold was not a single fixed analysis choice but one of several candidates examined in relation to the outcome.
Worked Example: Correcting Outcome-Informed Threshold Selection
Suppose an analyst examines three allele-frequency thresholds for a hypothetical gene and obtains p-values 0.040, 0.12, and 0.30. The analyst reports only the first result because it is the smallest.
If these three tests had been specified and treated as independent, the chance of at least one p-value below 0.05 under the global null would be
The tests are generally correlated because their variant sets overlap, so this independence calculation is illustrative rather than the exact error rate for these thresholds. It nevertheless shows why the single-test interpretation of 0.040 is not justified after searching. A simple conservative Bonferroni threshold for three tested choices is \(0.05/3=0.0167\); the p-value 0.040 does not pass that threshold. A procedure that accounts for dependence may be less conservative, but it must still account for the selection. Better options include prespecifying the threshold, validating a chosen rule in independent data, or applying a suitable multiplicity procedure across the choices actually examined.
The same concern applies when trying multiple masks, weight schemes, genes, or combinations of these choices. It is not enough to disclose only the final choice; the analysis should describe the search and the inferential adjustment. Sensitivity analyses can be informative, but their results should be presented as a set of related analyses rather than as independent confirmation of whichever one looked strongest.
Error 4: Ignoring Relevant Covariates
A burden can correlate with covariates that also relate to the outcome. An unadjusted association may then partly reflect ancestry, age, sex, recruitment site, batch, or another relevant factor rather than an association conditional on that factor. Covariates should be selected based on the design and scientific model, not added mechanically or chosen only to make a result significant.
For a linear model, the role of adjustment can be seen by residualizing both the outcome and the burden with respect to the included covariates. The coefficient for the burden in the adjusted model is the slope relating those residuals. If covariates are omitted, the comparison is instead based on unadjusted values. Thus, when a covariate tracks both burden and outcome, the unadjusted slope can differ from the covariate-adjusted slope.
Worked Example: A Burden Associated With a Covariate
In a hypothetical quantitative-trait example, let \(C=0\) for four individuals in one ancestry group and \(C=1\) for four in another. Let \(B\) be a burden score and \(Y\) an outcome. The data follow the simple pattern below.
| Group | Burden values | Outcome values |
|---|---|---|
| \(C=0\) | 0, 1, 2, 3 | 0, 1, 2, 3 |
| \(C=1\) | 4, 5, 6, 7 | 14, 15, 16, 17 |
Within each group, the outcome increases by 1 unit per burden unit. A model including group gives \(Y=B+10C\), so the burden coefficient is 1 outcome unit per burden unit and the group coefficient is 10 outcome units. To see what happens when group is ignored, the pooled least-squares slope is \(\operatorname{Cov}(B,Y)/\operatorname{Var}(B)\), using either both sample quantities or both population quantities. Since \(Y=B+10C\),
Here \(\operatorname{Var}(B)=5.25\) for the eight listed values, and \(\operatorname{Cov}(B,C)=1\). The unadjusted slope is therefore about 2.905 outcome units per burden unit, not the within-group slope of 1. This constructed example shows how group differences can inflate an unadjusted association. In an actual analysis, adjustment and population-structure control must reflect the study design; this arithmetic alone does not establish which covariates are sufficient.
Covariate omission and inadequate control of relatedness or population structure can affect calibration as well as the estimated association. Conversely, indiscriminate adjustment can also be problematic if a variable is downstream of the genetic effect or otherwise inappropriate to condition on. State the model and justify its covariates in context. For binary traits, use the appropriate covariate-adjusted logistic model and a score-test procedure calibrated for the design, rather than assuming that a quantitative-trait calculation transfers unchanged.
Error 5: Turning a Gene-Level Result Into a Variant-Level or Causal Claim
A burden test assesses the aggregate defined by its mask and weights. A significant result is evidence against the null for that aggregate under the stated model and testing procedure. It does not identify which included variant contributes to the result. Depending on the burden and effect pattern, a signal may be driven by a subset of variants; it may also be affected by coding, annotation, confounding, or other design features.
Worked Example: Interpreting a Significant Gene-Level Test
Suppose a hypothetical, appropriately calibrated two-sided burden score test yields \(Z=2.58\), with the burden direction defined in advance. Its p-value is
The p-value is the probability, under the specified null model, of a test statistic at least as extreme in either direction as the observed value. If this gene-level test was prespecified and its p-value is judged against an appropriate significance criterion after accounting for the analysis plan, the result supports an association between the tested burden and the outcome under that model. It does not show that every included variant is associated, identify a causal variant, or establish that changing the burden would change the outcome. Those conclusions require evidence beyond this aggregate test.
A complete report therefore names the gene, mask, weights, burden direction or coefficient where applicable, model, covariates, test statistic, p-value, and multiplicity handling. If the analysis uses a coefficient, state its units and the scale of the outcome and burden. Keep the conclusion at the level supported: an association for this specified gene-level burden, not a causal claim about the gene or a definitive claim about each constituent variant.
A Practical Error-Checking Sequence
Before accepting a burden-test result, work through a short audit. Each step addresses a different way that the intended analysis can diverge from the one actually tested.
Confirm that each dosage counts the intended allele, that strand and reference-allele alignment are resolved, and that allele frequencies and weights correspond to that coding.
Write down the mask, weights, missing-genotype handling, and included-variant list. Confirm that the computed \(B_i\) matches this specification.
Determine whether masks, thresholds, weights, and genes were prespecified or searched, and whether the reported inference accounts for the search.
Confirm that the trait model, covariates, dependence structure, and small-carrier calibration are appropriate to the data and study design.
Describe the association for the tested aggregate and model. Do not infer that all variants are implicated or that the result proves causation.
Common Mistakes
- “The dosage is 0, 1, or 2, so the coding must be consistent.” Those values alone do not reveal which allele is counted. Check allele identity at each site and recode before summing.
- “A threshold is only a tuning choice, so the smallest p-value is the natural result to report.” Choosing it after viewing outcomes is a search. Prespecify the rule, validate it independently, or account for the tested alternatives.
- “The gene-level p-value is small, so every variant in the gene is associated.” The test evaluates a weighted aggregate; it does not supply separate evidence for every included variant.
- “Adding covariates is optional because the score test is robust.” A score test does not automatically remove confounding or structure. Specify a suitable model and address relevant covariates and dependence.
- “A significant association shows that the gene causes the trait.” Association under a model is not proof of causality. Interpret the result at the level of the tested burden.
Check Your Understanding
Use the burden definition and error checks above to answer these questions.
- At a biallelic diploid site, one file records the count of the intended rare allele and another records the count of the other allele. What transformation aligns the second dosage with the first?
- Why is it not sufficient to report only that a burden test was performed “for a gene”?
- An analyst tests five thresholds and reports only the smallest p-value. What inferential issue does this create, and name one way to address it.
- In what circumstances can omitting a covariate change a burden coefficient? Explain using the relationship between burden, covariate, and outcome.
- What does a significant gene-level burden test establish, and what does it not establish about the included variants?