Why Discordant Results Need Diagnosis
A transcriptome-wide association study (TWAS) tests whether genetically predicted expression is associated with a trait. Colocalization instead evaluates whether genetic association signals for the trait and gene expression are consistent with a shared causal variant. Since these are different questions, a significant TWAS result and weak colocalization evidence are not automatically contradictory. Nor does a significant result from both methods establish that expression causes the trait.
A useful diagnosis asks what generated each result: Is there a strong enough association signal in both traits? Could linkage disequilibrium (LD) make distinct causal variants look associated with the same markers? Does the gene have multiple causal variants? Is the expression predictor accurate in the relevant population and tissue? These questions help separate biological explanations from limitations of the analyses.
The basic, single-signal colocalization model assumes that at most one causal variant for each trait is being represented in the analyzed region. Under that model, strong posterior support for \(H_4\) is evidence for a shared variant; it is not proof of a causal effect of expression on the trait. Strong support for \(H_3\) favors distinct causal variants. If neither hypothesis receives substantial support, the result may be unresolved rather than evidence against sharing.
For summary-statistic TWAS, one common form of the test statistic is \(Z_{\text{TWAS}}=w^\mathsf{T}z/\sqrt{w^\mathsf{T}Rw}\), where \(w\) is the vector of expression-prediction weights, \(z\) is the vector of trait-association \(Z\)-statistics for the same variants, and \(R\) is their LD correlation matrix. This calculation relies on consistent variant order, allele alignment, and an LD matrix appropriate to the analyzed data. It tests a weighted association signal; it does not, by itself, identify which variant is causal.
LD Can Produce a Strong TWAS Without a Shared Causal Variant
When two variants are correlated, a trait-associated causal variant can make a nearby, noncausal variant appear associated with the trait. If the noncausal variant also predicts expression, a TWAS may detect an association. The predicted-expression association can therefore be strong even when the expression and trait signals have different causal variants. Colocalization is intended to distinguish this situation from a shared-variant pattern, provided its assumptions and available data are adequate.
Worked Example: A Strong TWAS and Distinct Signals in LD
Consider a hypothetical region with two standardized genotypes, \(G_1\) and \(G_2\), whose correlation is \(r=0.90\). Suppose the trait is generated by \(Y=\gamma G_1+\varepsilon\), while the expression-predicting component is \(G_2\). Assume the residual \(\varepsilon\) is uncorrelated with both genotypes. Thus, \(G_1\) is the trait’s causal variant and \(G_2\) predicts expression; they are not the same variant.
Because the genotypes are standardized, their variances are 1 and their covariance is \(0.90\). The trait’s covariance with the expression-predicting component is therefore \( \operatorname{Cov}(Y,G_2)=\operatorname{Cov}(\gamma G_1+\varepsilon,G_2)=\gamma(0.90)+0=0.90\gamma \). So \(G_2\) carries a substantial trait-association signal through LD with \(G_1\).
For illustration, suppose the trait-association \(Z\)-statistics are \(z=(6.0,5.4)\) for \((G_1,G_2)\), the expression model uses weights \(w=(0,1)\), and the LD matrix is \(R=\begin{pmatrix}1&0.90\\0.90&1\end{pmatrix}\). Then \( w^\mathsf{T}z=0(6.0)+1(5.4)=5.4 \), and \( \sqrt{w^\mathsf{T}Rw}=\sqrt{1}=1 \). The TWAS statistic is \(Z_{\text{TWAS}}=5.4/1=5.4\), a strong association under a standard normal calibration.
Now suppose the expression association peaks at \(G_2\), while the trait’s underlying causal variant is \(G_1\). A hypothetical single-signal colocalization analysis might return posterior probabilities \(P(H_3\mid\text{data})=0.86\) and \(P(H_4\mid\text{data})=0.10\), with the remaining \(0.04\) assigned to \(H_0,H_1,H_2\). In that example the TWAS detects association, but the colocalization evidence favors distinct variants. The numerical posterior probabilities are illustrative analysis outputs, not values implied by the TWAS statistic alone.
This diagnosis is only as reliable as the LD and variant data: the example assumes correct allele alignment, both variants are measured or well imputed, and the colocalization model represents the signals adequately. If LD is misspecified or a causal variant is absent from the analyzed set, the apparent distinction may be less clear.
Signal Strength and Prediction Accuracy
Colocalization needs informative association patterns for both traits. If either the trait association or the expression association is weak, the data may not distinguish a shared variant from distinct variants. A low posterior for \(H_4\) is not, on its own, evidence for \(H_3\); check how much posterior support actually goes to \(H_3\), and how much remains on hypotheses representing no or limited association.
TWAS power also depends on the expression predictor. A model can be technically valid yet explain little of the relevant genetic variation in expression. In an idealized setting where prediction error is independent of the outcome given true genetically regulated expression, the predictor is calibrated, and its correlation with the target genetic expression component is \(c\), the expected TWAS signal is attenuated by approximately \(c\). Since prediction accuracy \(R^2=c^2\) in this setting, a true-expression signal of size \(Z_E\) gives an approximate predicted-expression signal of \(\sqrt{R^2}\,Z_E\). This is a useful approximation, not a general identity for every TWAS procedure.
Worked Example: Colocalization Support With a Weak TWAS
Suppose, hypothetically, strong trait and expression association data support a shared variant, with colocalization posterior \(P(H_4\mid\text{data})=0.92\). In a separate prediction exercise, assume the idealized true-expression signal would be \(Z_E=5.0\), but the expression predictor has accuracy \(R^2=0.09\) in the relevant target setting. The predictor correlation is \(c=\sqrt{0.09}=0.30\). Under the attenuation approximation, the expected TWAS signal is \( \sqrt{R^2}\,Z_E=0.30(5.0)=1.5 \).
A \(Z\)-statistic of 1.5 is not conventionally significant in a two-sided test at level \(0.05\), whose normal-reference cutoff is about 1.96. Thus, strong colocalization support can coexist with a weak TWAS if the predictor captures little of the relevant expression component. The conclusion depends on the approximation’s assumptions; it does not mean that every low-accuracy predictor must produce this particular statistic.
The example also assumes the colocalization analysis has adequate power and its variant set and priors are suitable. A high \(H_4\) posterior addresses shared-variant evidence under that model; it does not establish that altered expression mediates the trait association.
Multiple Causal Variants and Tissue Choice
A single-signal colocalization analysis can be misleading when either trait has multiple causal variants in the region. A mixture of signals can blur the association patterns that the model uses to compare \(H_3\) and \(H_4\). For example, one expression signal could share a variant with the trait while another expression signal is distinct. A single regional summary may then be ambiguous even though a signal-by-signal analysis is informative. Methods that allow multiple causal variants, or analyses that first separate signals and then compare them, are alternatives when their assumptions and data requirements are met.
Tissue choice adds another source of disagreement. Expression prediction weights are tissue-specific, and the genetic regulation of expression can differ across tissues. A TWAS signal in one tissue does not guarantee that the same expression-associated variant is present in another tissue. Conversely, a weak result in the selected tissue cannot rule out a shared signal in an unmeasured or poorly powered tissue. Comparing tissues should account for prediction accuracy, sample size, and the degree to which their expression signals are distinguishable, rather than treating the smallest \(P\)-value as proof that one tissue is causal.
Worked Example: Separating Signals Before Comparing Tissues
Consider a hypothetical two-variant region with trait-association statistics \(z=(2.0,4.5)\), LD correlation \(r=0.40\), and therefore \(R=\begin{pmatrix}1&0.40\\0.40&1\end{pmatrix}\). In tissue A, suppose the TWAS weights are \(w_A=(1,1)\). The numerator is \(w_A^\mathsf{T}z=2.0+4.5=6.5\). The denominator is \( \sqrt{w_A^\mathsf{T}Rw_A}=\sqrt{1+0.40+0.40+1}=\sqrt{2.8}=1.673 \). Hence \(Z_{\text{TWAS},A}=6.5/1.673=3.89\), a nominal two-sided association.
Suppose tissue A’s expression has two distinct association signals, one at each variant, while the trait signal is concentrated at the second variant. A single-signal colocalization analysis might give \(P(H_3\mid\text{data})=0.54\), \(P(H_4\mid\text{data})=0.42\), and \(0.04\) across the other hypotheses. This is not decisive support for either hypothesis. If a signal-separated analysis shows that the second expression signal and the trait signal share a variant, a hypothetical component-level result of \(P(H_4\mid\text{data})=0.93\) would support sharing for that pair of signals. The first expression signal remains a separate signal; the component-level result does not make every expression signal colocalize.
For comparison, suppose tissue B has weights \(w_B=(1,0)\). Its numerator is \(2.0\), its denominator is \(\sqrt{1}=1\), and \(Z_{\text{TWAS},B}=2.0/1=2.0\). Its weaker TWAS does not by itself show that tissue A is the causal tissue: the tissues use different predictors, and their prediction accuracies may differ. The example assumes both variants are correctly aligned, the stated LD applies, and the weights are used on the same variant scale as the \(Z\)-statistics.
A Practical Diagnostic Sequence
A disciplined comparison begins by checking that the analyses refer to the same gene, genomic region, variant set, alleles, and tissue. Then inspect the trait and expression association strength separately, not just their final TWAS or colocalization summaries. The following steps help identify what a disagreement does—and does not—say.
Confirm variant identity, allele orientation, genome build, and the source of the LD matrix. Misalignment or mismatched LD can distort the TWAS statistic and the colocalization comparison.
Review expression and trait association strengths and the uncertainty in each signal. Weak evidence for either can leave colocalization unresolved even when a TWAS test is suggestive.
Separate posterior support for \(H_3\) and \(H_4\) from posterior mass on \(H_0,H_1,H_2\). Interpret the result in light of the model and prior probabilities.
Check prediction accuracy in the relevant setting, consider tissue choice, and ask whether multiple causal variants could invalidate a single-signal comparison.
Alternatives, Limitations, and a Common Mistake
TWAS and colocalization answer complementary questions, not interchangeable ones. A TWAS combines trait-association statistics using expression-prediction weights; a colocalization analysis compares evidence for shared versus distinct causal variants under a specified model. Signal-separated or multiple-causal-variant approaches can be more appropriate when a locus contains several signals, but they require adequate data and their own modeling assumptions. None of these analyses alone proves a causal pathway from gene expression to phenotype.
Several practical failure modes deserve attention. An LD reference that poorly represents the study population can make a weighted TWAS statistic unreliable. Incomplete variant coverage can hide the causal variant. Weak eQTL evidence may make a colocalization result inconclusive, and poor prediction accuracy can reduce TWAS power. Finally, analyzing many genes and tissues raises the need to interpret statistical evidence in light of the multiple-testing strategy used.
Common mistake: “The TWAS is significant, so the gene and trait must share a causal variant; a low \(H_4\) posterior therefore means the colocalization analysis is wrong.” The reasoning confuses association with shared-variant evidence. LD can generate a strong TWAS from distinct causal variants, while low \(H_4\) may reflect support for \(H_3\), weak evidence, or model misspecification. The correction is to examine the competing posterior probabilities, signal strength, LD, predictor performance, and number of signals before drawing a conclusion.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- In the two-variant example with \(r=0.90\), why can the TWAS be strong even though the expression and trait causal variants differ?
- What does strong support for \(H_3\) mean, and how does it differ from weak support for \(H_4\) when most posterior probability remains elsewhere?
- If \(R^2=0.25\) and the idealized true-expression signal is \(Z_E=4.0\), what signal does the attenuation approximation predict?
- Why can a single-signal colocalization result be inconclusive when expression has two causal variants?
- Does a stronger TWAS in one tissue establish that the tissue mediates the trait association? Explain.
Solutions. (1) LD makes the trait-associated genotype correlated with the expression-predicting genotype, so the latter can carry a trait-association signal even when it is not the trait’s causal variant. (2) \(H_3\) represents association with both traits but distinct causal variants. Weak \(H_4\) alone is not evidence for \(H_3\): posterior probability may instead reflect no association, association with only one trait, or uncertainty. (3) \(\sqrt{0.25}(4.0)=0.50(4.0)=2.0\). This is an approximation under the stated idealized assumptions. (4) A single-signal model cannot represent both expression signals at once, so the combined pattern may blur evidence about which expression signal, if any, shares a variant with the trait. (5) No. Tissue-specific prediction accuracy and power can differ, and a stronger association does not establish mediation or causation.