From Biological Hypothesis to Burden Definition
A rare-variant burden is not a fixed summary of all variation in a gene. It is a summary defined by choices: which variants are eligible, how rare they must be, and how much each eligible variant contributes. Those choices determine what genetic signal the test represents. A useful analysis therefore starts with a biological hypothesis, not with whichever set of variants produces the strongest association in the observed data.
Suppose the hypothesis is that reduced function of a gene increases a disease risk. A burden designed for this hypothesis might include variants likely to impair the encoded protein, exclude variants unlikely to affect protein function, and give greater weight to variants with stronger evidence of functional impact. The particular rules need to be specified clearly enough that another analyst could reproduce the same burden.
The mask and threshold determine membership in \(\mathcal{S}\); the weights determine the contribution of each member. A variant can be biologically relevant but fail the frequency rule, or pass the frequency rule but fail the functional mask. Keeping these decisions distinct makes the resulting burden easier to interpret.
A Worked Gene Example: Establishing the Candidate Set
Consider a hypothetical gene and a hypothetical case-control study of a disease. The proposed mechanism is that variants that disrupt protein function increase disease risk in the same direction. Assume that genotypes are accurately called, functional annotations and frequency estimates are available, and the annotation and frequency rules are chosen before examining the association results. The following reference frequency estimates are supplied for illustration; they are not estimated from the four people shown later.
| Variant | Annotation | Reference MAF |
|---|---|---|
| v1 | Stop-gain | 0.0005 |
| v2 | Damaging missense | 0.0040 |
| v3 | Damaging missense | 0.0150 |
| v4 | Synonymous | 0.0020 |
| v5 | Canonical splice-site | 0.0080 |
| v6 | Damaging missense | 0.0002 |
A defensible functional mask for this hypothesis could include stop-gain, canonical splice-site, and missense variants meeting a prespecified damaging-annotation rule. It would exclude synonymous variants because the stated hypothesis concerns protein disruption, not because synonymous variants can never have biological effects. With this mask, v1, v2, v3, v5, and v6 pass the functional criterion; v4 does not.
Now choose a MAF threshold of 1%, or 0.01. The threshold is applied in addition to the functional mask. Variants with MAF at or below 0.01 pass; v3, with MAF 0.015, does not. The final set is therefore v1, v2, v5, and v6. Stating the inequality matters: under a rule of MAF at or below 1%, a variant exactly at 1% is included.
Worked Example: Turning the Mechanism Into a Mask
The biological hypothesis is that reduced gene function increases disease risk. Use the supplied annotations to select a functional mask, then apply a MAF threshold of 1%.
Functional decision. Include stop-gain and canonical splice-site variants, and include missense variants only when they meet the stated damaging-annotation criterion. This selects v1, v2, v3, v5, and v6. Exclude v4 because it is synonymous and does not meet this mask’s functional rule.
Frequency decision. Compare each selected variant’s MAF with 0.01. Variants v1, v2, v5, and v6 have MAFs 0.0005, 0.0040, 0.0080, and 0.0002, respectively, so each is at or below 0.01. Variant v3 has MAF 0.0150, which is greater than 0.01, so it is excluded.
Result. The analysis set is \(\mathcal{S}=\{v1,v2,v5,v6\}\). The functional rule excluded v4; the frequency rule excluded v3. This distinction records why each variant is absent.
How the Choices Change Individual Burdens
To see the practical effect, consider these hypothetical alternate-allele dosages for four people. Each entry is 0 or 1 in this example, so no person carries two alternate copies at any listed variant. The table is illustrative and is not a real study.
| Person | v1 | v2 | v3 | v4 | v5 | v6 |
|---|---|---|---|---|---|---|
| A | 1 | 1 | 1 | 0 | 0 | 1 |
| B | 0 | 0 | 0 | 0 | 1 | 0 |
| C | 1 | 0 | 0 | 1 | 0 | 0 |
| D | 0 | 1 | 0 | 0 | 1 | 1 |
With the selected set \(\{v1,v2,v5,v6\}\) and unit weights, the burden is the sum of those four dosage entries. Person A has \(1+1+0+1=3\); B has \(0+0+1+0=1\); C has \(1+0+0+0=1\); and D has \(0+1+1+1=3\). The excluded variants do not contribute, even when a person carries them.
Worked Example: Changing the Frequency Threshold
Keep the same functional mask, but compare thresholds of 0.5% and 1%, using unit weights. Since 0.5% is 0.005, v2 at 0.0040 passes, but v5 at 0.0080 does not. Variants v1 and v6 also pass. The 0.5% set is \(\{v1,v2,v6\}\); the 1% set is \(\{v1,v2,v5,v6\}\).
For person B, the 0.5% burden is \(G_{B1}+G_{B2}+G_{B6}=0+0+0=0\). At the 1% threshold, v5 is added, so the burden becomes \(0+0+1+0=1\). For person D, the 0.5% burden is \(0+1+1=2\); at 1%, the v5 dosage adds 1, giving \(0+1+1+1=3\).
The threshold changes which people receive a contribution from v5. It does not merely change a label attached to the test. A more permissive threshold can add variants and alter the distribution of burdens across the sample; the added variants are not guaranteed to strengthen an association.
Weights Encode Relative Contributions
After defining the eligible set, choose weights to reflect the hypothesis. Unit weights treat each alternate allele in the set as making the same contribution to the burden. This is simple and transparent, but it does not express a belief that some eligible variants are more damaging or rarer than others.
A prespecified functional weighting rule could assign weight 2 to stop-gain and canonical splice-site variants and weight 1 to damaging missense variants. These numbers are illustrative relative weights, not calibrated estimates of clinical risk. In the selected set, this gives \(w_1=2\), \(w_2=1\), \(w_5=2\), and \(w_6=1\). The burden is calculated by multiplying each dosage by its weight before summing.
Worked Example: Applying Functional Weights
Use the 1% set and the functional weights just specified: 2 for v1 and v5, and 1 for v2 and v6. For person A, the weighted burden is
For person B, only v5 is present among the selected variants, so
For C, only v1 is present, giving \(B_C=2(1)+1(0)+2(0)+1(0)=2\). For D, v2, v5, and v6 are present, giving \(B_D=2(0)+1(1)+2(1)+1(1)=4\). Under unit weights the burdens were 3, 1, 1, and 3; the functional weighting changes them to 4, 2, 2, and 4. The larger values reflect the chosen scale and rules, not a measured increase in disease risk.
Frequency weights can instead give greater weight to rarer eligible variants. For example, one prespecified rule uses a frequency factor proportional to the beta density with parameters 1 and 25 evaluated at MAF \(f_j\). Omitting its common normalizing constant gives \(r_j=(1-f_j)^{24}\). This factor is larger for smaller MAFs in the range considered. A combined weight could multiply this factor by a functional weight, but such a combination should be stated in advance and interpreted as a modeling choice, not as a fact about each variant’s effect.
Why a Burden Is a Scientific Assumption
A burden analysis typically relates the trait to one summary per person rather than estimating a separate effect for every variant. In a simple linear predictor, the burden enters as \(\beta B_i\), where \(\beta\) is the burden coefficient. Since \(B_i=\sum_{j\in\mathcal{S}}w_jG_{ij}\), this contribution can be written as
Thus, using a single burden coefficient implies that variant-specific contributions are proportional to the selected weights and have a common direction. For a binary trait, the corresponding burden term is used in the linear predictor of a logistic model; the same restriction on relative contributions applies. A mask asserts which variants are relevant to the hypothesis, while weights assert their relative contributions. Neither choice proves that the included variants are causal.
This restriction is most plausible when the biological hypothesis predicts effects aligned in direction, as in a loss-of-function mechanism expected to increase risk. If effects differ in direction, summing dosages can obscure them: positive and negative contributions can cancel in the association with the burden. A burden’s interpretation is therefore conditional on its variant set and weights. A reported association is evidence about that specified summary, not evidence that every included variant has the same effect or is individually associated.
A Practical Selection Sequence
Specify the proposed functional consequence and the expected direction of trait effects. For example, the hypothesis may be that protein-disrupting variants increase disease risk.
Name the annotation categories and prediction criteria included, and identify categories excluded. Make the rule reproducible rather than relying on an informal label such as “damaging.”
Record the population frequency reference, the MAF cutoff, and whether the boundary is included. Frequency estimates can depend on the reference population, so this information is part of the rule.
State whether weights are uniform, functional, frequency-based, or a prespecified combination. Give enough detail to reproduce the value assigned to each eligible variant.
For each person, sum the weighted dosages of eligible variants. Describe the resulting unit as a weighted alternate-allele burden, not as a direct measure of disease risk.
Common Pitfall
- Wrong reasoning: “The stricter mask produced the smaller p-value, so it must be the biologically correct mask.” This treats the observed association as if it established the functional rule.
- Correction: Select masks, thresholds, and weights to represent a stated hypothesis and available functional evidence. The association result evaluates that specified burden; by itself, it does not validate the biological choices or show that every included variant acts as assumed.
- Wrong reasoning: “A variant passes the frequency threshold, so it belongs in the burden.” Frequency eligibility alone does not establish functional relevance.
- Correction: Apply the functional mask and frequency rule separately. A variant must meet both criteria to contribute, and its weight applies only after it is included.
Check Your Understanding
Use the hypothetical gene example and the definitions above to answer these questions.
- With the stated functional mask and a 1% threshold, why is v3 excluded while v4 is excluded for a different reason?
- Using unit weights and a 0.5% threshold, calculate person D’s burden from v1, v2, and v6.
- If v5 is added by raising the threshold from 0.5% to 1%, which people in the table have their unit-weight burdens increased?
- What assumption about relative variant contributions is represented by assigning weight 2 to v1 and weight 1 to v2 in a single-coefficient burden model?
- Why does an association with a weighted burden not establish that each included variant increases disease risk?