What Does a Significant Burden Test Tell Us?
A burden test combines information across selected variants in a region, often using a mask and weights chosen before testing. A small p-value can provide evidence that this particular aggregate is associated with a specified phenotype. It does not, by itself, tell us which variant is responsible, whether every included variant matters, or whether the annotations used to select or weight variants are correct.
The right interpretation starts with the test that was actually performed. The tested region, included variants, weights, phenotype, covariates, and statistical model together define the question. A result is evidence about that specified aggregate under the assumptions and calibration of the analysis—not an unrestricted conclusion about a gene or its biological function.
For a quantitative phenotype, a typical model is \(Y_i=\beta_0+\beta_BB_i+\boldsymbol{\gamma}^{T}\mathbf{C}_i+\varepsilon_i\), where \(\mathbf{C}_i\) contains covariates. For a binary phenotype, a logistic model may specify \(\operatorname{logit}\{P(Y_i=1\mid B_i,\mathbf{C}_i)\}=\beta_0+\beta_BB_i+\boldsymbol{\gamma}^{T}\mathbf{C}_i\). The tested parameter is the coefficient of the burden, not a separate coefficient for every variant.
A valid p-value requires a suitable model and appropriate calibration. Depending on the analysis, assumptions include correctly specified covariate adjustment, adequate treatment of relatedness or population structure, and a null distribution appropriate for the sample size and number of carriers. The phenotype and burden must also be defined as intended. A significant p-value is evidence against the specified null under those conditions; it is not the probability that the null is true, nor the probability that the region has a causal effect.
Scope of the Evidence
The phrase “gene-level result” is convenient, but the actual tested object is the burden formed from the variants admitted by a particular mask and weighting rule. A mask may cover only selected functional categories or frequency ranges within a region. Thus the precise conclusion is about the tested regional burden and phenotype, conditional on the study design and model. It need not apply to every variant in the gene, other masks, other phenotypes, or other populations.
Statistical significance should also be interpreted in light of the testing plan. If many genes, masks, thresholds, or phenotypes were examined, the relevant claim should reflect the multiplicity procedure used for that family of tests. A nominal p-value below a conventional cutoff is not necessarily significant after adjustment. Even when the result passes an appropriate adjusted threshold, the adjustment supports the stated statistical evidence; it does not expand what the burden coefficient represents.
Worked Example: A Quantitative-Trait Burden Association
Suppose a hypothetical study tests a pre-specified burden in one region against a quantitative biomarker measured in mmol/L. The burden is a weighted sum of allele counts, and a linear regression adjusts for age and sex. Assume the model’s residual and sampling assumptions are adequate for the reported t-test. The fitted burden coefficient is \(0.40\) mmol/L per burden unit, with \(SE=0.12\) mmol/L per burden unit, in \(n=100\) unrelated participants. With four fitted parameters (intercept, burden, age, and sex), the residual degrees of freedom are \(96\).
The test statistic for \(H_0:\beta_B=0\) is:
For a two-sided t-test with \(96\) degrees of freedom, the p-value is approximately \(0.0012\). If this test belongs to a multiplicity family with an adjusted significance threshold of \(0.0025\), it passes that threshold. In this hypothetical analysis, the data provide evidence of an association between the specified regional burden and the biomarker, conditional on age and sex.
The coefficient estimates a \(0.40\) mmol/L difference in the modeled mean biomarker per one-unit increase in this weighted burden, conditional on the covariates. It does not say that each included allele raises the biomarker by \(0.40\) mmol/L. Nor does the significant test identify which variant contributes to the association or establish that changing the burden would change the biomarker.
Why an Aggregate Result Does Not Identify a Variant
A burden test compresses several genotype measurements into one number per individual. That compression is useful when the variant effects follow a pattern the burden can represent, but it limits what can be inferred from the test. A rejection of the burden null is not a collection of separate rejections of variant-specific null hypotheses. The burden test does not report which variant has an effect, whether effects are equal, or whether all effects have the same direction.
One way to see the distinction is to compare a model with separate variant effects to a burden model. Let \(X\) be the \(n\times m\) matrix of observed variant genotypes, let \(\boldsymbol{\beta}\) be the vector of variant coefficients, and let \(\mathbf{w}\) be the weight vector. The genotype contribution in a variant-specific model is \(X\boldsymbol{\beta}\). The burden model’s contribution is \(\beta_BX\mathbf{w}\). These expressions agree for all possible genotype configurations when \(\beta_j=\beta_Bw_j\) for every \(j\). On an observed genotype design, however, equality can also hold when the coefficient difference lies in the null space of the genotype matrix.
Worked Example: The Same Burden Fit From Different Variant Effects
Consider two hypothetical variants with weights \(w_1=w_2=1\). Suppose every analyzed individual has the same genotype at both variants: \(G_{i1}=G_{i2}=G_i\). The burden is then \(B_i=G_{i1}+G_{i2}=2G_i\). Imagine the outcome’s genotype contribution is \(G_i\), which could arise from variant-specific coefficients \(\beta_1=1\) and \(\beta_2=0\).
The burden model with \(\beta_B=0.5\) gives the same contribution:
For a hypothetical fitted analysis, suppose the burden coefficient estimate is \(0.50\) outcome units per burden unit and its standard error is \(0.15\) outcome units per burden unit. Then \(t=0.50/0.15=3.33\); with a sufficiently large residual degrees of freedom, the two-sided p-value is about \(0.001\). The aggregate association can therefore be statistically clear, yet the displayed genotype pattern and burden fit do not show that both variants contribute. The burden contribution is identical to a model in which only the first variant contributes.
In matrix terms, the two genotype columns are identical, so \(X(\boldsymbol{\beta}-\beta_B\mathbf{w})=\mathbf{0}\) even though \(\boldsymbol{\beta}\ne\beta_B\mathbf{w}\). This example is an identifiability point, not a claim that the first variant is causal. The association could also reflect other explanations, including an unmeasured linked factor or bias not handled by the model.
A Significant Burden Does Not Validate Its Annotations
Functional annotations may be used to decide which variants enter a mask or to assign their weights. Those choices define the aggregate being tested. If the burden is associated with a phenotype, the result supports evidence for association of that constructed aggregate; it does not independently establish that every included variant has the annotated function, that excluded variants are unimportant, or that the chosen annotation system correctly ranks functional impact.
For example, a burden may include variants predicted to disrupt a particular protein feature. A significant result does not prove that each variant disrupts that feature in the relevant tissue. The observed association could be driven by one variant, by another variant correlated with the included ones, by a feature of the mask’s selection, or by an issue in measurement or analysis. Functional evidence requires evidence appropriate to the functional claim; an association p-value answers a different question.
This distinction matters in interpretation and follow-up. A gene or region can be a useful candidate for further study without being established as a causal gene. Variant-level analyses, replication, functional assays, and other evidence may help distinguish explanations, but they are not conclusions supplied by the burden test itself.
Worked Example: What an Annotation-Based Mask Result Supports
Suppose researchers define a hypothetical mask to include rare variants labeled “predicted damaging” by a chosen annotation pipeline, assign those variants specified weights, and test the resulting burden against a binary disease phenotype. The logistic regression adjusts for age, sex, and ancestry covariates. Assume the test is well calibrated and the analysis accounts for the planned set of tests. The estimated burden coefficient is \(0.70\) with \(SE=0.22\), giving:
where \(Z\) has a standard normal null distribution for this Wald test. If the adjusted threshold for this hypothetical family of tests is \(0.005\), the result is significant. The odds ratio for a one-unit increase in the weighted burden is \(\exp(0.70)\approx2.01\), conditional on the covariates. This is an association in the modeled odds, not a causal effect.
The supported statement is that the specified annotation-based burden is associated with disease status in this analysis. The result does not demonstrate that the annotation is correct for every included variant, or that the annotation caused the association. It also does not establish that every variant in the mask has the same effect or that the region causes disease. Those conclusions go beyond the statistic and model that were tested.
Common Mistake: Turning an Aggregate Finding Into a Causal Claim
Incorrect reasoning: “The gene-level burden test is significant, so the gene is causal, and the predicted-damaging variants in the mask are confirmed functional variants.”
Correction: The test provides evidence against a null of no association for the specified burden and phenotype, under the model and its assumptions. It neither localizes the signal to an individual variant nor validates the functional labels that formed the mask. State the region, mask, phenotype, effect estimate, uncertainty, and adjustment context; describe causal or functional conclusions as questions requiring additional evidence.
Check Your Understanding
Answer each question by distinguishing the tested aggregate from claims about its component variants.
- A burden test is significant after the planned multiplicity adjustment. What is the most precise statement the result supports?
- Why does rejecting \(H_0:\beta_B=0\) not amount to rejecting a separate null hypothesis for every included variant?
- In the two-variant example, why can different variant coefficients give the same fitted genotype contribution on the observed data?
- A mask contains variants annotated as damaging, and its burden is associated with disease. Which conclusion about the annotations is not justified by that association alone?
- In a logistic burden model, what does \(\exp(\hat{\beta}_B)\) describe, and why is it not automatically a causal odds ratio?