Why Set Definition Is Part of the Hypothesis
A gene-level association analysis begins before a test statistic is calculated: the analyst must decide which variants count as belonging to the gene and which of those variants qualify for analysis. A set that includes coding variants only asks a different question from one that also includes splice-region or regulatory variants. Likewise, choosing one transcript rather than all transcripts can change both the number and identity of included variants.
The set is therefore not merely a convenient container for variants. It determines the collection of variant effects covered by the association hypothesis. A reproducible analysis must specify the genomic reference, gene boundaries, annotation source, transcript rule, and all inclusion and exclusion rules. The introductory material on rare-variant set tests and their effect targets establishes that set-based procedures can target different patterns of effects; here the focus is on defining which variants those targets refer to.
Write the Set Rule Explicitly
A useful general definition is an intersection of eligibility conditions. For example, a coding-variant set might include variants inside a gene interval, annotated as protein-altering in a specified transcript set, and passing specified quality and frequency filters. If the conditions are denoted by \(B_g(j)\) for boundary membership, \(F(j)\) for functional eligibility, and \(Q(j)\) for quality eligibility, then:
The notation does not prescribe which conditions are appropriate. It makes clear that changing any condition changes \(S_g\). In practice, the rule should also identify the genome build, annotation release, coordinate convention, and how variants are represented and matched to annotations. A variant described against one reference genome can have different coordinates on another, so a coordinate without its reference build is incomplete.
A gene boundary needs an operational definition. One common choice is a genomic interval from the gene’s start coordinate through its end coordinate, inclusive, on a named reference genome. The gene also has a strand, which determines transcriptional orientation but does not reverse the numerical order of genomic coordinates. If the analysis instead extends boundaries upstream or downstream, the extension length and direction must be stated. The interval used for association should not be assumed to be identical to a gene’s biological regulatory region.
Coordinate conventions matter at interval endpoints. In a 1-based, closed convention, an interval \([a,b]\) includes both coordinates \(a\) and \(b\). In a 0-based, half-open convention, \([a,b)\) includes \(a\) but excludes \(b\). A coordinate file and a gene annotation may use different conventions; converting one without care can add or omit variants at boundaries. Small endpoint discrepancies can be consequential when a set is sparse.
Worked Example: Applying a Gene Boundary
Suppose a hypothetical gene spans coordinates 10,000 through 10,500 on a specified reference genome, using 1-based, closed coordinates. Five candidate variants have positions 9,999, 10,000, 10,250, 10,500, and 10,501. For this example, location is the only membership condition.
The boundary rule is \(10{,}000\leq\text{position}\leq10{,}500\). The variant at 9,999 fails because \(9{,}999<10{,}000\). The variants at 10,000, 10,250, and 10,500 satisfy the rule, including both endpoints. The variant at 10,501 fails because \(10{,}501>10{,}500\). Thus the location-defined set contains 3 of the 5 candidates.
If the same interval were interpreted as 0-based, half-open, its endpoint behavior would differ. Applying a coordinate convention silently could therefore change the set even though the written numbers appear identical.
Functional Annotations and Transcript Rules
A genomic position alone does not establish a variant’s functional category. An annotation assigns consequences using a particular transcript reference and annotation procedure. One variant may be intronic in one transcript, exonic in another, and outside a third. Protein consequence categories can also differ among transcripts. The analyst must specify how multiple annotations are resolved.
Common transcript policies include using a designated canonical transcript, including a variant if it meets a criterion in any transcript, or defining separate sets for different transcript groups. These policies answer different questions. An “any transcript” rule is often more inclusive, while a single-transcript rule is narrower and depends on the selected transcript. Neither is universally correct; the choice should be biologically justified and set before looking at association results.
Functional rules also need precise category definitions. “Predicted damaging,” for example, is not a complete rule unless the prediction tool, version, threshold, and treatment of missing predictions are specified. A set may be limited to protein-altering consequences, or may add specified splice-region categories. The annotation source and version matter because annotations can change across releases.
Worked Example: Resolving Transcript-Level Annotations
Consider three hypothetical variants inside a gene boundary. The analysis rule is: include a variant if at least one transcript in a specified annotation release labels it as a protein-truncating consequence. Quality eligibility is assumed to have been checked separately.
Variant A is labeled “missense” in Transcript 1 and “synonymous” in Transcript 2. It does not satisfy the stated truncating-consequence rule in either transcript, so it is excluded. Variant B is labeled “intronic” in Transcript 1 and “stop-gained” in Transcript 2. Because at least one transcript meets the rule, B is included. Variant C is labeled “splice-region” in both transcripts, but the rule does not include splice-region consequences; C is excluded.
The resulting set contains only Variant B. If the rule were changed to include splice-region consequences, Variant C would also enter. If instead the analysis used Transcript 1 alone, Variant B would not enter under this example’s annotation. These are changes to the tested set, not merely changes in how the same set is described.
Set Membership Defines the Association Hypothesis
Let \(\beta_j\) denote the variant-specific effect parameter for variant \(j\), as defined by the association model being used. A general set-level global null for a specified set \(S_g\) is that every effect in the set is zero. Its alternative is that at least one included variant has a nonzero effect:
This formulation identifies a global null; it does not say that every set-based test has the same alternative or effect target. The earlier material on rare-variant set tests distinguishes tests that emphasize a shared directional effect from tests that can respond to heterogeneous effects. The present point is that each such target is defined over the chosen members. Excluding a variant excludes its effect from this set-level hypothesis; adding one expands the collection of effects covered by it.
A short justification follows directly from the definition. The set-level null is a conjunction of variant-level null statements, one for each member. If \(S_g=\{2,5,8\}\), for example, then the null is \(\beta_2=0,\ \beta_5=0,\ \beta_8=0\). The alternative is the negation of that conjunction, so at least one of those three effects is nonzero. A variant outside \(S_g\) does not appear in either statement. Changing membership therefore changes the hypothesis itself.
Worked Example: How an Inclusion Rule Changes the Null
Suppose a hypothetical gene has four candidate variants, numbered 1 through 4. A coding-only rule includes Variants 1 and 2, so \(S_g=\{1,2\}\). For the global-null formulation above, the null is \(H_0:\beta_1=0\) and \(\beta_2=0\); the alternative is that \(\beta_1\neq0\) or \(\beta_2\neq0\).
Now suppose the rule is expanded to include a specified splice category, and Variant 3 meets that category. The new set is \(S_g=\{1,2,3\}\). The null becomes \(H_0:\beta_1=0,\ \beta_2=0,\ \beta_3=0\). Variant 4 remains outside both sets, so its effect is not part of either set-level hypothesis.
This comparison does not imply that the expanded set is preferable or that one test must produce a smaller p-value. It shows that the two analyses address different null hypotheses, even if they use the same phenotype and participants.
Prespecification, Diagnostics, and Alternatives
Set definitions should be fixed independently of the association results whenever possible. Selecting annotation categories, transcript rules, or boundary extensions because they produce the smallest p-value makes the tested hypothesis data-adaptive. If several sets are explored, the analysis must account for the multiplicity or selection involved; simply reporting the most favorable set as though it had been the only planned analysis overstates evidence.
Useful diagnostics include checking the number of variants at each construction stage, confirming that all variants and annotations use compatible reference builds, inspecting variants near interval endpoints, and reviewing how many annotations are missing or ambiguous. The membership list should be exportable, so the exact variants included in the analysis can be audited and reproduced. A set unexpectedly empty or much larger than anticipated can indicate mismatched coordinates, inconsistent variant representation, or an overly broad annotation rule.
Population context also matters. A frequency-based inclusion rule, if used, should specify the frequency source, ancestry definition, threshold, and handling of unavailable frequencies. Frequencies can differ across populations, so a rule using one reference population may include a different set than a rule using another. This changes the variants represented in the hypothesis and can affect comparisons across studies. The threshold’s statistical consequences are a separate issue; here it is essential to make the membership rule explicit.
There are several defensible alternatives, each with a distinct interpretation. A canonical-transcript set is more tightly tied to one transcript; an any-transcript set is more inclusive. A coding-only set restricts membership to specified coding consequences; a set that also includes splice or regulatory annotations represents a broader functional scope. A fixed gene interval is straightforward to reproduce, whereas a flanking interval includes additional nearby variants but requires explicit extension rules. A pathway set can pool variants across multiple genes, but it is no longer the same gene-specific set. These alternatives are not interchangeable analyses of an unchanged hypothesis.
Set construction has limitations. Functional annotations are predictions or consequence labels, not proof that an included variant changes the phenotype. Conversely, a strict annotation rule can omit functional variants that are poorly annotated. Gene boundaries are operational genomic intervals and do not capture all long-range regulatory relationships. Thus a gene-level result supports an association with the specified set under the chosen model; it does not establish that the gene is causal or that every included variant contributes to the association.
Common Mistakes
- Using a gene name as the entire definition. A gene name does not identify the genome build, boundaries, transcript rule, or qualifying annotations. State each operational choice.
- Treating all annotations as unambiguous. A variant can receive different consequences across transcripts. Specify whether one transcript, a designated transcript set, or an any-transcript rule controls membership.
- Assuming the same gene set across analyses. Different annotation releases, coordinate conventions, frequency references, or quality filters can produce different member lists. Compare the actual variants, not only the gene label.
- Interpreting a broader set as the same test with extra data. Adding eligible variants changes the global null and can change the alternative emphasized by the procedure. Describe the revised set and hypothesis.
- Calling an associated set a causal gene. Association concerns the specified variants and phenotype under the model. It does not by itself prove a causal mechanism or establish which member is responsible.
Check Your Understanding
Answer each question, then compare with the brief solutions below.
- Under a 1-based, closed interval from 2,000 through 2,100, is a variant at 2,100 inside the gene interval? What changes under a 0-based, half-open interval written with the same endpoints?
- A rule includes a variant if any specified transcript labels it stop-gained. One transcript labels the variant intronic and another labels it stop-gained. Is it included?
- If \(S_g=\{4,7\}\), write the global null and alternative for the set.
- Why can two studies using the same gene name still test different hypotheses?
- Name two checks that could reveal a problem in set construction before association results are interpreted.
Solutions. (1) Yes: 2,100 is included because both endpoints are included. In a 0-based, half-open interval \([2{,}000,2{,}100)\), 2,100 is excluded. (2) Yes, because the stated any-transcript rule is satisfied by the stop-gained annotation. (3) \(H_0:\beta_4=0\) and \(\beta_7=0\); \(H_a:\beta_4\neq0\) or \(\beta_7\neq0\). (4) They may use different genome builds, boundaries, annotation releases, transcript policies, or filters, leading to different members and therefore different null hypotheses. (5) Examples include checking coordinate-build compatibility, inspecting boundary variants, counting members after each filter, and reviewing missing or conflicting annotations.