Two Different Questions at a Locus
A gene can have a significant transcriptome-wide association study (TWAS) result without strong evidence that its expression association and a trait association arise from the same causal variant. Conversely, colocalization can support a shared variant even when the TWAS test for that gene is not significant. This is not a contradiction: the methods ask different statistical questions.
A TWAS tests whether genetically predicted expression of a gene is associated with a trait. Colocalization evaluates whether the genetic association patterns for expression and the trait are better explained by a shared causal variant or by distinct causal variants. Neither test, by itself, establishes that changing the gene's expression would change the trait. The distinction is especially important when several variants in a locus are correlated through linkage disequilibrium (LD).
For that single-signal formulation, the other hypotheses are \(H_0\), neither trait is associated in the region; \(H_1\), only the trait is associated; and \(H_2\), only expression is associated. Colocalization reports posterior probabilities for these hypotheses under specified prior probabilities and the model. In regions with multiple causal signals, a suitable multi-signal analysis is needed; the five-hypothesis interpretation should not be applied as if it resolved every signal in such a region.
What a TWAS Statistic Measures
Let \(m\) SNP genotypes in a region be standardized, let \(w\) be a fixed vector of prediction weights for a gene, and let \(R\) be the LD correlation matrix for those SNPs in the relevant ancestry and allele alignment. The predicted expression is a weighted combination of genotypes. In a summary-statistic implementation, let \(z\) be the vector of SNP association statistics for the trait. Under the usual approximation that these statistics have covariance matrix \(R\) under the null, a common TWAS statistic is
This formula assumes that the weights and LD matrix are appropriate for the tested sample, that SNP alleles are aligned consistently, and that the relevant null distribution is adequately approximated by a standard normal distribution. In individual-level analyses, the corresponding idea is to test the association between the phenotype and expression predicted from genotype. In either form, the test is about the weighted predicted-expression score, not a direct measurement of the causal effect of expression.
The denominator in the summary-statistic formula accounts for correlation among the SNPs. If the weights and LD are correctly specified, then under the null \(z\) has mean zero and covariance \(R\). The numerator therefore has mean zero and variance \(w^{\mathsf T}Rw\), which gives the standardization:
A two-sided TWAS p-value is then approximately \(2\{1-\Phi(|Z_{\mathrm{TWAS}}|)\}\), where \(\Phi\) is the standard normal cumulative distribution function. Statistical significance depends on the chosen threshold, including any adjustment for the number of genes and tissues tested. A small p-value indicates that the predicted-expression score is associated with the trait under this test; it does not identify which variant is causal or show that expression mediates the association.
Worked Example: A Significant TWAS With Distinct Signals
Suppose two standardized SNPs have LD correlation \(0.60\). A gene's prediction model assigns all its weight to SNP 2, so \(w=(0,1)^{\mathsf T}\). In a hypothetical trait analysis, the SNP association statistics are \(z=(8.0,4.8)^{\mathsf T}\). The SNP 2 statistic is consistent with LD tagging a trait signal centered on SNP 1. Suppose the expression association pattern is centered on SNP 2, and a suitably specified colocalization analysis of the full regional data gives posterior probabilities \(P(H_3\mid D)=0.94\) and \(P(H_4\mid D)=0.03\), where \(D\) denotes the association data.
The TWAS numerator is \(w^{\mathsf T}z=0(8.0)+1(4.8)=4.8\). Since the weight is only on SNP 2, \(w^{\mathsf T}Rw=1\), so
The two-sided normal p-value is approximately \(1.59\times10^{-6}\), which is below an illustrative threshold of \(0.001\). Thus the gene has a significant TWAS association at that threshold. Yet the stated colocalization output favors distinct causal variants (\(H_3\)) over a shared one (\(H_4\)). The TWAS can be significant because the expression-prediction SNP tags the trait-associated SNP through LD. It does not follow that the expression and trait signals share a causal variant.
What Colocalization Adds
Colocalization uses the regional association patterns for expression and the trait to compare hypotheses about their causal variants. In the single-signal setting, posterior probabilities are calculated by combining the data's relative support for each hypothesis with the prior probabilities assigned to those hypotheses. In schematic form,
The posterior is conditional on the data, the model, and the priors. A high \(P(H_4\mid D)\) supports a shared causal variant under that analysis; it is not the probability that expression causally mediates the trait. A high \(P(H_3\mid D)\) supports association of both traits with distinct causal variants. When neither is high, the data may be insufficient to distinguish hypotheses, or may not fit the model well.
The distinction between \(H_3\) and \(H_4\) depends on the patterns across variants, not merely on whether both traits have small association p-values somewhere in the region. If variants are in strong LD, their association patterns can look similar even when different variants drive the two traits. If expression evidence is weak, colocalization may not have enough information to distinguish a shared signal from a trait-only signal. Prior sensitivity and posterior diagnostics are therefore relevant to interpretation.
Worked Example: Colocalization Supports Sharing but TWAS Is Not Significant
Consider a hypothetical gene for which regional expression and trait association patterns support a shared variant. A colocalization analysis reports \(P(H_4\mid D)=0.96\) and \(P(H_3\mid D)=0.02\). However, a prediction model trained in an external sample transfers poorly to the target sample, and the summary-statistic TWAS result is \(Z_{\mathrm{TWAS}}=1.20\).
The two-sided p-value is approximately \(2\{1-\Phi(1.20)\}=0.230\). It is not below the illustrative threshold \(0.001\). Thus, the TWAS test does not provide significant evidence of association for this gene under that prediction model. The colocalization result, by contrast, supports a shared causal variant under its model and priors.
These results can coexist because colocalization uses the measured expression and trait association patterns, whereas TWAS tests the particular genetically predicted-expression score. A model that predicts expression poorly, uses weights that do not capture the relevant variant's effect, or does not transfer well can yield a weak TWAS statistic even when the measured expression and trait signals colocalize. The posterior does not turn the nonsignificant TWAS result into a significant one; each result answers its own question.
Why Significance Can Differ
The methods use related genetic data but respond to different features of it. A TWAS compresses SNP-level trait evidence using gene-specific prediction weights. Colocalization compares the regional patterns of evidence for expression and trait association. Consequently, their significance outcomes are not required to match.
| Result pattern | One possible explanation | What it does not establish |
|---|---|---|
| TWAS significant; little support for \(H_4\) | The prediction score tags a trait signal through LD, while the expression and trait signals arise from distinct variants. | That the same causal variant affects both traits, or that expression mediates the trait. |
| Colocalization supports \(H_4\); TWAS not significant | The measured expression and trait signals share a variant, but the prediction weights produce a weak or poorly transferred score. | That a particular TWAS model has detected an association, or that expression is causal. |
| Both are significant or strongly supported | The gene-level score is associated and the regional patterns support a shared variant. | That the shared variant acts on the trait through this gene's expression rather than another pathway. |
Worked Example: Both Methods Support Their Respective Signals
In a hypothetical analysis, suppose a gene has \(Z_{\mathrm{TWAS}}=4.2\), and colocalization reports \(P(H_4\mid D)=0.93\), with low posterior probability for \(H_3\). The TWAS p-value is approximately \(2.67\times10^{-5}\), below the illustrative threshold \(0.001\). The colocalization posterior favors a shared variant under the stated model.
The joint interpretation is that the predicted-expression score is associated with the trait and that the regional expression and trait association patterns support a shared causal variant. These are complementary pieces of evidence, not duplicate versions of one test. They still do not prove that expression mediates the trait: a shared variant could affect the trait through another molecular mechanism or a different gene. Neither the TWAS p-value nor the colocalization posterior is a direct estimate of a causal effect of expression.
Assumptions, Diagnostics, and Limitations
Before interpreting either result, check that the analysis matches the data and question. For a TWAS, the SNP set, allele coding, prediction weights, and LD reference must be compatible. Poor prediction accuracy, ancestry differences between training and testing samples, or an LD mismatch can distort the statistic or reduce its power. If weights are estimated with uncertainty, treating them as fixed can also understate uncertainty. A significant result should be interpreted in light of the multiple-testing threshold for the genes and tissues actually tested.
For colocalization, check whether the assumed number of causal signals is appropriate, whether the expression and trait data cover comparable variants, and whether the result is sensitive to prior choices. Weak or missing expression evidence can leave the shared-versus-distinct comparison unresolved. A high posterior for \(H_4\) is conditional on the model and priors; it is not a universal measure of causal certainty.
The main alternative to a TWAS question is not another calculation of the same statistic, but a different question about genetic evidence. Colocalization asks about sharing of causal variants, while fine-mapping addresses which variants are plausible causal candidates within a signal. An ordinary SNP association test asks whether a particular variant is associated with a trait. These analyses can inform interpretation, but none alone establishes that gene expression causes the trait. The appropriate analysis depends on whether the target is a gene-level predicted-expression association, shared-variant support, or variant prioritization.
A Common Interpretive Mistake
A common mistake is to treat a significant TWAS result as proof that the gene's expression mediates the trait, or to treat a high \(P(H_4\mid D)\) as proof that the same variant acts through expression. The correction is to name the tested quantity precisely: TWAS tests association of a weighted predicted-expression score with the trait; colocalization evaluates shared versus distinct causal-variant hypotheses. Strong results can prioritize a gene or support a shared signal, but causal mediation requires additional evidence and assumptions.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A TWAS result is significant, but colocalization favors \(H_3\) over \(H_4\). What does each result support?
- Suppose \(w=(1,1)^{\mathsf T}\), \(z=(2,3)^{\mathsf T}\), and \(R\) has diagonal entries 1 and off-diagonal entries 0.5. Calculate \(Z_{\mathrm{TWAS}}\).
- Colocalization gives \(P(H_4\mid D)=0.90\), while the TWAS p-value is 0.18. Is this necessarily contradictory? Explain.
- Why does a high posterior probability for \(H_4\) not prove that expression mediates a trait association?
Solutions. (1) TWAS supports association of the gene's predicted-expression score with the trait. \(H_3\) support favors distinct causal variants for expression and trait, rather than a shared variant; the TWAS result does not override that comparison. (2) The numerator is \(w^{\mathsf T}z=1(2)+1(3)=5\). The denominator squared is \(w^{\mathsf T}Rw=1+0.5+0.5+1=3\), so \(Z_{\mathrm{TWAS}}=5/\sqrt{3}=2.887\). (3) No. Colocalization supports a shared variant under its model, while the TWAS test of the specified prediction score is not significant at conventional thresholds; the tests use different information and answer different questions. (4) \(H_4\) concerns a shared variant, not the pathway through which that variant affects the trait. The variant could influence the trait through another gene or mechanism, so mediation is not established.