Two Results, Two Different Questions
A significant transcriptome-wide association study (TWAS) result can identify a gene whose genetically predicted expression is associated with a phenotype. It does not, by itself, establish that the same causal variant drives the expression association and the phenotype association. Nearby variants in linkage disequilibrium can produce an association pattern for both traits even when their underlying causal variants differ. Colocalization addresses this variant-sharing question directly.
The useful interpretation therefore depends on keeping two questions separate. First, is the TWAS association sufficiently strong under the chosen testing procedure? Second, does the locus provide evidence that the molecular trait and the phenotype share a causal variant? A strong answer to one question does not guarantee a strong answer to the other.
What Colocalization Adds
For the usual two-trait formulation, the hypotheses distinguish no association, association with only one trait, and association with both traits under either shared or distinct causal variants. \(H_0\) means neither trait is associated in the region; \(H_1\) means only the first trait is associated; \(H_2\) means only the second is associated; \(H_3\) means both are associated but with distinct causal variants; and \(H_4\) means both are associated and share a causal variant.
Colocalization methods use the variant-level evidence across a locus to compare these hypotheses. Their outputs are posterior probabilities, often written \(PP_0,\ldots,PP_4\), which sum to one under the specified model. In particular, \(PP_4\) is the posterior probability assigned to \(H_4\), conditional on the data, the model, and the prior probabilities used in the analysis. It is not a probability that a gene is causal in an unrestricted biological sense.
A useful comparison when the question is “shared or distinct, given that both traits are associated?” is the posterior probability of \(H_4\) conditional on \(H_3\) or \(H_4\):
This ratio focuses on the contest between a shared and a distinct causal variant. It does not replace inspection of the full posterior: if the evidence favors \(H_0\), \(H_1\), or \(H_2\), there may be little support for association with both traits at all. Nor does a high ratio guarantee a high \(PP_4\) when the combined probability \(PP_3+PP_4\) is small.
How to Read Agreement and Discordance
TWAS and colocalization results should be reported as complementary evidence, not combined into a single yes-or-no test. TWAS summarizes an association involving predicted expression, whereas colocalization assesses whether the molecular and phenotype signals are consistent with a shared causal variant. A nominally significant TWAS result can coexist with weak evidence for sharing; conversely, colocalization can favor a shared variant even when the TWAS statistic is not significant.
| TWAS evidence | Colocalization pattern | Interpretation |
|---|---|---|
| Strong under the stated testing threshold | High \(PP_4\), with little support for \(PP_3\) | Evidence for a TWAS association and for a shared variant; this is not proof of mediation. |
| Strong under the stated testing threshold | High \(PP_3\), low \(PP_4\) | The gene-level association is present, but the locus favors distinct causal variants rather than sharing. |
| Weak or not significant | High \(PP_4\) | The variant-level signals favor sharing, but the TWAS test does not show a strong gene-level association under its chosen model or threshold. |
| Weak or not significant | Low \(PP_4\), with little evidence for both traits being associated | Neither result provides persuasive support for a shared causal variant. |
“Strong” and “weak” must be judged using the study’s declared statistical procedure and threshold. A nominal \(p\)-value is not automatically sufficient when many genes, tissues, or phenotypes have been tested. That issue is separate from colocalization: a high \(PP_4\) does not turn a nominal TWAS \(p\)-value into a study-wide significant result.
Worked Interpretations
Worked Example: Strong TWAS and Strong Sharing Evidence
Suppose a hypothetical analysis estimates a TWAS effect of \(0.18\) phenotype standard deviations per one-unit increase in genetically predicted expression, with standard error \(0.045\). The standard normal TWAS statistic is:
Using a two-sided standard normal reference distribution gives \(p \approx 6.33 \times 10^{-5}\). For illustration, suppose the prespecified TWAS threshold for this example is \(0.001\); the association meets that threshold. The effect is in phenotype standard-deviation units per predicted-expression unit.
Suppose a compatible colocalization analysis reports \(PP_0=0.01\), \(PP_1=0.02\), \(PP_2=0.03\), \(PP_3=0.08\), and \(PP_4=0.86\). The probabilities sum to \(1.00\), and the conditional sharing probability is:
This example has both a TWAS association under the stated threshold and substantial colocalization support for a shared variant. The appropriate conclusion is that the results jointly support an association involving predicted expression and a shared causal variant at this locus, under the analysis assumptions. They do not establish that changing expression causes the phenotype.
Worked Example: Strong TWAS but Evidence for Distinct Variants
In a second hypothetical analysis, the TWAS effect is \(0.12\) phenotype standard deviations per predicted-expression unit, with standard error \(0.030\). Thus:
The association again meets the illustrative threshold \(p<0.001\). However, suppose the colocalization posterior probabilities are \(PP_0=0.01\), \(PP_1=0.03\), \(PP_2=0.06\), \(PP_3=0.82\), and \(PP_4=0.08\). Then:
Although the TWAS result is strong under the example threshold, the colocalization result favors \(H_3\), in which both traits are associated through distinct causal variants, over \(H_4\). The TWAS result alone should not be described as evidence that the molecular and phenotype associations share a causal variant. Linkage disequilibrium can help explain how association evidence at a gene can coexist with distinct causal variants.
Worked Example: Colocalization Support Without a Significant TWAS Result
For a third hypothetical gene, let the TWAS effect be \(0.040\) phenotype standard deviations per predicted-expression unit, with standard error \(0.040\). The statistic and approximate two-sided \(p\)-value are:
This does not meet the illustrative threshold \(p<0.001\). Now suppose the colocalization results are \(PP_0=0.01\), \(PP_1=0.02\), \(PP_2=0.02\), \(PP_3=0.04\), and \(PP_4=0.91\). The conditional probability of sharing, given \(H_3\) or \(H_4\), is:
The colocalization posterior strongly favors a shared variant, while the TWAS statistic does not show a strong association under the example threshold. These results are not logically contradictory: the tests use different summaries and answer different questions. The careful conclusion is that variant-level evidence favors sharing, but the TWAS analysis does not provide a significant association for predicted expression under the stated threshold.
Worked Example: Neither Result Supports Sharing
Finally, suppose a hypothetical TWAS estimate is \(0.020\) phenotype standard deviations per predicted-expression unit, with standard error \(0.050\). Then:
The TWAS result is not significant at \(0.001\). Suppose the colocalization output is \(PP_0=0.78\), \(PP_1=0.05\), \(PP_2=0.05\), \(PP_3=0.08\), and \(PP_4=0.04\). These values sum to \(1.00\), and:
That conditional ratio alone is not compelling evidence for sharing, and the full posterior assigns most probability to \(H_0\). The TWAS result is also weak. In this example, neither analysis provides persuasive evidence for a shared causal variant. This is a lack of support in the analyzed data, not proof that the gene and phenotype are unrelated.
Why the Assumptions Matter
These interpretations are meaningful only if the analyses refer to comparable molecular and phenotype signals. Variant alleles and genomic positions must be harmonized, the locus must be defined consistently, and the linkage-disequilibrium information must be appropriate for the analyzed samples. Poor alignment or a mismatched LD reference can distort apparent sharing. The model must also be suitable for the locus: a single-causal-variant analysis can misrepresent a region with multiple signals, so a method that accounts for multiple signals may be needed.
Colocalization results also depend on the specified prior probabilities and on which variants were available to the analysis. A high \(PP_4\) is therefore conditional on those choices as well as on the observed summary statistics. When evidence is sensitive to reasonable changes in priors, variant coverage, or modeling assumptions, that sensitivity should temper the interpretation.
A Short Justification for the Shared-versus-Distinct Comparison
The ratio \(PP_4/(PP_3+PP_4)\) follows directly from conditioning on the two hypotheses in which both traits are associated. The definition of conditional probability gives:
Because \(H_4\) is one of the two alternatives in the condition, the numerator is \(PP_4\). Because \(H_3\) and \(H_4\) are mutually exclusive, the denominator is \(PP_3+PP_4\). Substitution yields:
This derivation also shows why the ratio must be read alongside the full posterior. It conditions away the possibility that one or both traits are not associated, so it cannot by itself establish that both signals are present.
Common Mistake and Practical Interpretation
- Wrong reasoning: “The TWAS \(p\)-value is small, so the expression and phenotype share a causal variant.” A small TWAS \(p\)-value supports an association under the TWAS model; it does not distinguish \(H_4\) from \(H_3\).
- Correction: Report the TWAS association and the colocalization evidence separately. To argue that a shared variant is supported, examine \(PP_4\) and its contrast with \(PP_3\), while checking the full posterior and the analysis assumptions.
- Wrong reasoning: “A high \(PP_4\) proves that altered expression mediates the phenotype.” Colocalization supports a shared genetic signal under its model; sharing alone does not establish a causal pathway from expression to phenotype.
- Correction: Describe shared-variant evidence as support for a locus-level relationship that warrants further investigation, not as proof of mediation or a causal gene mechanism.
Check Your Understanding
For each question, distinguish evidence for association from evidence for variant sharing.
- A gene has a strong TWAS association, while colocalization favors \(H_3\) over \(H_4\). What conclusion is supported, and what conclusion is not?
- Why should \(PP_4/(PP_3+PP_4)\) be interpreted together with the full set of colocalization posterior probabilities?
- A TWAS test is not significant, but colocalization assigns most posterior probability to \(H_4\). Describe the two findings without calling them contradictory.
- What does a high \(PP_4\) support, and what causal claim does it not establish by itself?
- Name two analysis conditions that should be checked before interpreting a colocalization result alongside a TWAS result.