From a Locus Signal to a Gene-Level Assessment
A genetic association locus can contain several plausible genes. A TWAS may report association for one or more of them, while eQTL and colocalization analyses provide evidence about genetic regulation of expression in a particular tissue. The practical task is not to select whichever gene has the smallest p-value. It is to compare what each analysis supports, check whether the evidence concerns the same genetic signal, and state how much the combined evidence can justify.
The worked locus below is entirely hypothetical. It contains three candidate genes, GENE-A, GENE-B, and GENE-C, in one tissue. The GWAS association signal and each gene's expression association have been analyzed over the same region and for the same trait and tissue. Treat the reported colocalization results as having been calculated for the relevant conditioned signals, rather than from an analysis that assumes a complex multi-signal region is a single signal. That distinction matters: the usual single-signal colocalization model assumes at most one causal variant for each trait in the region.
For a standard two-sided TWAS test, the statistic \(Z_{\mathrm{TWAS}}\) is compared with a standard normal distribution under the null hypothesis of no association. Its p-value is \(2\{1-\Phi(|Z_{\mathrm{TWAS}}|)\}\), where \(\Phi\) is the standard normal cumulative distribution function. A small p-value is evidence of association under the test assumptions; it is not a probability that the gene is causal. The direction of the statistic refers to the association with predicted expression as encoded by the model's weights and alleles.
Why the TWAS Statistic Depends on LD
A brief justification helps explain why TWAS results are not independent evidence from SNP-level association. Suppose the vector of SNP association statistics is \(Z\), the vector of expression-prediction weights is \(w\), and \(R\) is the SNP correlation matrix in the analysis population. Under a calibrated null model, take \(\operatorname{Cov}(Z)=R\). The weighted numerator \(w^\mathsf{T}Z\) then has variance:
Standardizing by the square root of this variance gives the usual form of the TWAS statistic:
This argument requires that the association statistics and LD reference be compatible, that the weights and alleles be aligned, and that the null calibration be appropriate. If the LD matrix is mismatched or the weights are unstable, the statistic may be miscalibrated. The formula also makes clear that a strong TWAS result can arise because the weighted SNP pattern tracks a GWAS signal in LD; it does not, by itself, establish a shared causal variant or a causal role for expression.
Worked Example: Comparing Three TWAS Statistics
Suppose a hypothetical study reports \(Z_{\mathrm{TWAS}}\) values of 4.1 for GENE-A, 3.3 for GENE-B, and 2.1 for GENE-C in the same tissue. Assume the null reference is standard normal and these are unadjusted, two-sided p-values.
For GENE-A, \(p=2\{1-\Phi(4.1)\}\approx 0.0000413\). For GENE-B, \(p=2\{1-\Phi(3.3)\}\approx 0.000967\). For GENE-C, \(p=2\{1-\Phi(2.1)\}\approx 0.0357\). Thus, GENE-A has the largest absolute TWAS statistic and smallest unadjusted p-value, followed by GENE-B and GENE-C.
These calculations rank the strength of the three test results, but they do not establish that GENE-A is causal. Nor do the unadjusted p-values alone establish genome-wide significance: that conclusion depends on the testing scope and its multiplicity procedure. A candidate's predicted-expression association must be assessed alongside its eQTL and colocalization evidence.
Read the Evidence Gene by Gene
Colocalization is commonly summarized using posterior probabilities for five hypotheses: \(H_0\), neither trait is associated in the region; \(H_1\), only the GWAS trait is associated; \(H_2\), only expression is associated; \(H_3\), both are associated but with distinct causal variants; and \(H_4\), both are associated with a shared causal variant. The posterior probabilities sum to one for the specified model and data. A high \(PP.H4\) supports a shared-variant explanation relative to the alternatives included in that model. It does not prove that expression mediates the trait association or that the gene is causal.
The following hypothetical results concern the same tissue and region. The eQTL entry is the strongest conditional eQTL statistic for that gene's expression; its sign is included to show the estimated direction for the stated allele coding. Colocalization results are shown as posterior probabilities, not p-values.
| Candidate | TWAS Z (two-sided p) | Conditional eQTL Z | PP.H0 | PP.H1 | PP.H2 | PP.H3 | PP.H4 |
|---|---|---|---|---|---|---|---|
| GENE-A | 4.1 (0.0000413) | +4.0 | 0.01 | 0.02 | 0.03 | 0.08 | 0.86 |
| GENE-B | 3.3 (0.000967) | +3.0 | 0.02 | 0.03 | 0.04 | 0.67 | 0.24 |
| GENE-C | 2.1 (0.0357) | −2.0 | 0.05 | 0.06 | 0.04 | 0.20 | 0.65 |
Worked Example: Interpreting the Colocalization Posteriors
For GENE-A, the reported probabilities are 0.01, 0.02, 0.03, 0.08, and 0.86. They sum to \(0.01+0.02+0.03+0.08+0.86=1.00\). The shared-variant hypothesis has posterior probability 0.86, while the distinct-variant hypothesis has probability 0.08. Within this model and its assumptions, the evidence favors a shared variant for the GWAS and GENE-A expression associations.
For GENE-B, \(PP.H3=0.67\) exceeds \(PP.H4=0.24\). Although GENE-B has a stronger TWAS statistic than GENE-C, its colocalization results favor distinct causal variants over a shared one. This weakens the case that the same variant explains both its expression association and the GWAS association. It does not show that the TWAS finding is false; LD, multiple signals, or other model limitations may affect the comparison.
GENE-C has \(PP.H4=0.65\), but its TWAS statistic is weaker and its eQTL statistic is also less strong in this illustration. A posterior of 0.65 is support for \(H_4\) relative to the alternatives, not certainty. It is less compelling than GENE-A's 0.86 in this set of results, and interpretation should consider the posterior mass on \(H_3\) and the model's priors and assumptions.
Build a Qualified Locus-Level Conclusion
The evidence for GENE-A is the most coherent in this hypothetical comparison: it has the largest absolute TWAS statistic, a clear eQTL association, and the largest \(PP.H4\), with relatively little posterior mass on \(H_3\). GENE-B has a substantial TWAS statistic and eQTL evidence, but its colocalization posterior favors distinct variants. GENE-C has some support for colocalization but weaker TWAS and eQTL statistics. A defensible conclusion is therefore: GENE-A is the leading candidate for follow-up in this tissue, because the TWAS, eQTL, and colocalization results converge more strongly for it than for the other candidates; these results do not establish that GENE-A causes the trait association.
The evidence should not be treated as three independent votes. TWAS and eQTL association are based on genetic association patterns in the same region, and colocalization also uses regional association evidence. Multiplying p-values, or informally adding a TWAS result to a colocalization posterior as if they were independent, would not be justified. Instead, ask whether the analyses answer complementary questions and whether their assumptions and inputs are compatible.
Confirm that GWAS trait, tissue, region, allele coding, and relevant conditioned signals match across the evidence being compared.
Review TWAS statistics and eQTL results, noting their directions and the scale of each test. Do not interpret a ranking of p-values as a causal ranking.
Compare \(PP.H4\) with \(PP.H3\), and inspect the other posterior mass. Check whether the colocalization model's signal assumptions are reasonable for the locus.
Rank candidates for follow-up, describe the converging and discordant evidence, and distinguish prioritization from proof of mediation or causation.
Diagnostics, Alternatives, and Limits
The apparent ranking can be misleading when inputs or assumptions fail. Check that SNP alleles and effect directions are aligned; that the LD reference is suitable for the GWAS population; and that the expression weights are applicable to the tissue and samples being analyzed. For colocalization, inspect whether multiple independent signals exist and whether the analysis has conditioned or fine-mapped them appropriately. If posterior support is split between \(H_3\) and \(H_4\), or spread broadly across hypotheses, report that ambiguity rather than selecting the largest number without qualification.
Alternative approaches answer related but distinct questions. Fine-mapping can identify variants with high posterior support for association, but a credible variant alone does not identify the effector gene. Conditional colocalization can compare expression and trait signals after accounting for multiple signals, but still relies on its model and data. Comparing tissues can reveal whether support is tissue-specific or shared, while functional experiments can test mechanisms more directly. These approaches can strengthen or refine prioritization; none turns a statistical association alone into proof of causal mediation.
| Evidence | What it contributes | What it does not establish alone |
|---|---|---|
| TWAS | Association of predicted expression with the trait | A shared causal variant or causal effect of expression |
| eQTL | Evidence that genetic variation is associated with expression | That the expression-associated variant drives the GWAS signal |
| Colocalization | Relative support for shared versus distinct causal variants under a specified model | That expression mediates the trait effect or the gene is the causal effector |
A common mistake is to say, “GENE-A has the smallest TWAS p-value, so it is the causal gene.” This reasoning confuses association strength with causal identification and ignores whether the expression and trait signals share a variant. The correction is to compare each gene's association evidence with its colocalization result, examine model adequacy, and conclude only that the combined pattern prioritizes a gene for follow-up. Even a strong \(PP.H4\) is conditional on the analyzed variants, priors, and signal model; unmeasured tissues, regulatory mechanisms, or additional variants may change the interpretation.
Worked Example: Writing the Locus Conclusion
Suppose the three rows in the table are the complete results available for this hypothetical locus. GENE-A has \(Z_{\mathrm{TWAS}}=4.1\), eQTL \(Z=+4.0\), and \(PP.H4=0.86\) versus \(PP.H3=0.08\). GENE-B has a smaller but still notable TWAS statistic, \(Z=3.3\), while \(PP.H3=0.67\) exceeds \(PP.H4=0.24\). GENE-C has \(Z=2.1\) and \(PP.H4=0.65\).
A suitable report is: “In this tissue, GENE-A is the strongest candidate for follow-up because it combines the largest TWAS statistic with eQTL evidence and the strongest posterior support for a shared GWAS–expression variant among the three candidates. GENE-B has TWAS association but its colocalization results favor distinct variants; GENE-C has more limited association evidence and intermediate shared-variant support. These analyses prioritize GENE-A but do not demonstrate that its expression mediates the trait association.”
This conclusion follows the relative evidence without turning a posterior probability into certainty or calling the selected gene causal. If the signal model, tissue match, or LD assumptions were doubtful, the report should say so and treat the ranking as more tentative.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- At a locus, a candidate has a strong TWAS statistic but \(PP.H3=0.72\) and \(PP.H4=0.18\). What does this pattern suggest, and what does it not prove?
- Why is a high \(PP.H4\) not equivalent to a probability that a gene is causal?
- For a second gene, \(PP.H3=0.12\) and \(PP.H4=0.81\). Which hypothesis is better supported within the specified model?
- Name two checks that should be made before interpreting a TWAS and colocalization comparison at a multi-signal locus.
Solutions. (1) The TWAS supports association with predicted expression, but the colocalization posterior favors distinct causal variants over a shared one. This does not prove the TWAS finding is false or identify the mechanism. (2) \(PP.H4\) is posterior support for a shared-variant hypothesis under a particular model, data set, and prior specification; it does not establish mediation or causality of the gene. (3) \(H_4\), the shared-variant hypothesis, is better supported than \(H_3\) in that model. (4) Check that alleles, region, tissue, and relevant signals are aligned, and assess whether multiple signals have been handled with suitable conditioning or fine-mapping; also check LD-reference compatibility for TWAS calibration.