Why Expression Weights May Not Travel
A TWAS uses genetic variants to predict gene expression and tests whether that predicted expression is associated with a trait. The prediction weights are learned in a reference sample, often for a particular ancestry, tissue, and expression assay. Applying those weights elsewhere assumes that the same variants predict the same expression quantity in the target setting. That assumption can fail even when the gene name and variant list appear to match.
A weak transfer can reduce power: the target prediction may contain little information about target expression. More subtly, a transferred model can represent a different genetic component of expression, so a gene-level association may be weakened, redirected, or difficult to interpret. These issues concern the model being tested; they do not, by themselves, establish whether a gene causes a trait.
The subscript \(A\) identifies the setting in which the weights were estimated; it does not guarantee that they predict expression in \(T\). A useful model for understanding transfer is \(E_T=w_T^T S+\epsilon_T\), where \(w_T\) describes the target setting's genetic component of expression and \(\epsilon_T\) is residual expression variation. This representation assumes a linear genetic predictor, finite variances, and residual variation uncorrelated with \(S\). It is a working model, not a claim that all expression regulation is linear or genetic.
How Transfer Accuracy Depends on Covariance
Write \(\Sigma_T=\operatorname{Var}(S)\) for the target genotype covariance matrix. Under the model above, and assuming the reference weights are fixed rather than estimated from the target outcomes,
If \(\epsilon_T\) is also uncorrelated with \(\hat E_A\), the target-population coefficient of determination from the best linear prediction with an intercept is
This is squared correlation between the transferred prediction and target expression; it is not the fraction of expression variation explained in the reference sample. It can be estimated by evaluating the fixed predictor in an independent target sample, using the same allele coding and expression definition intended for analysis. Cross-validation within the reference sample estimates performance in that reference setting, not automatically in the target.
Worked Example: Ancestry-Related Changes in Genetic Alignment
Suppose two centered, standardized genotypes in a target ancestry have covariance matrix \(\Sigma_T=\begin{pmatrix}1&0.5\\0.5&1\end{pmatrix}\). Reference weights are \(w_A=(0.8,0.6)^T\), while target expression follows \(E_T=w_T^T S+\epsilon_T\), with \(w_T=(0.8,-0.6)^T\) and independent residual variance \(\operatorname{Var}(\epsilon_T)=0.48\). These are hypothetical values.
The variance of the transferred prediction is \(0.8^2+0.6^2+2(0.5)(0.8)(0.6)=1.48\). The target genetic component has variance \(0.8^2+(-0.6)^2+2(0.5)(0.8)(-0.6)=0.52\), so \(\operatorname{Var}(E_T)=0.52+0.48=1.00\).
Their covariance is \(w_A^T\Sigma_Tw_T\). The two diagonal contributions sum to \(0.8(0.8)+0.6(-0.6)=0.28\); the off-diagonal contributions cancel: \(0.5[0.8(-0.6)+0.6(0.8)]=0\). Thus the target prediction accuracy is \(R_T^2=0.28^2/(1.48\times1.00)=0.0530\), or about 5.3%.
The reference and target weights use the same two variants, but their contributions to expression differ in sign for the second variant. The transferred score therefore captures little of target expression. This example illustrates a possible change in genetic effects or tagging relationships; it does not show that ancestry labels alone determine transfer accuracy.
Ancestry differences can matter through allele frequencies, linkage disequilibrium (LD), or genuine differences in variant effects. If a causal variant is not included in the model, a nearby variant may predict expression because it is correlated with that causal variant in the reference sample. A different LD pattern in the target can weaken or change that proxy relationship. Allele-frequency changes also alter genotype variances and hence the covariance matrix used by the predictor. Correct allele alignment is essential: a dosage coded for the opposite allele changes a weight's sign unless the coding is harmonized.
The target LD structure also matters when calculating the variance of a TWAS score or its standard error from summary statistics. Using LD from a mismatched reference can misrepresent covariance among weighted variants. A poor weight-transfer model and a poor LD reference are distinct problems, though both can affect the result. Where possible, validate prediction and score calibration using target-compatible genotype data.
Tissue and Assay Are Part of the Prediction Target
Expression is not a single interchangeable quantity. A model trained in one tissue may emphasize regulatory effects that are absent, weaker, or reversed in another tissue. Cell composition, stimulation, developmental stage, and disease state can change which cells contribute RNA and which regulatory mechanisms are active. Tissue labels alone may conceal substantial differences in sample composition or experimental conditions.
Assay context matters as well. Different technologies, normalization procedures, transcript definitions, or probes can measure different expression quantities. A pure change of units need not destroy the genetic ranking: if target measurements are an affine transformation of the same underlying quantity, a recalibration may suffice. If the assay changes which transcript or biological component is measured, a scale correction cannot recover the missing correspondence.
Worked Example: A Scale Change Versus a Biology Change
Suppose a standardized genotype \(S\) has variance 1. A reference model predicts \(\hat E_A=S\). In a hypothetical target assay, measured expression is \(E_B=2+3S+\epsilon\), where \(\epsilon\) is independent of \(S\), has mean 0, and variance 4. The target expression variance is \(3^2(1)+4=13\).
The prediction covariance is \(\operatorname{Cov}(\hat E_A,E_B)=3\), and its variance is 1. Therefore, \(R_B^2=3^2/(1\times13)=9/13=0.692\). The best linear calibration is \(E_B=2+3\hat E_A+\epsilon\): the intercept and slope correct the scale, and the prediction still captures about 69.2% of target variance in this example.
Now suppose the assay measures a different transcript whose genetic component is not proportional to \(S\). The affine calibration above would no longer be justified, even if the gene label were unchanged. One must evaluate prediction against the actual target assay and expression definition; a good calibration for one measurement does not establish transfer to another.
What Low Accuracy Does to Gene-Level Inference
For a simple illustration, suppose target expression is \(E_T=w_T^T S+\epsilon_T\) and the trait satisfies \(Y=\beta E_T+u\), where \(u\) is uncorrelated with \(S\) and \(\epsilon_T\). Then
The equality follows by substituting \(Y\), using covariance linearity, and setting \(\operatorname{Cov}(\hat E_A,u)=0\). If the transferred predictor is poorly aligned with target expression, this covariance can be small even when \(\beta\) is not. The resulting TWAS may have low power for the target expression component. If the transferred score is aligned with a different component of expression, the gene-level signal may not represent the intended tissue or assay.
This simple model requires more than a high or low \(R_T^2\): it assumes no correlation between the score and \(u\), among other conditions. In real data, horizontal pleiotropy, population structure, sample overlap, or other dependence can complicate interpretation. A low prediction \(R_T^2\) alone does not prove that a TWAS p-value is inflated. With fixed weights, suitable LD, and a correctly calibrated test under its null assumptions, low accuracy can chiefly reduce power. Incorrect covariance modeling, confounding, or a misspecified test can threaten calibration separately.
Worked Example: Weak Tissue Transfer and an Attenuated Association
Let \(S\) have variance 1, and suppose the target-tissue expression is \(E_T=0.1S+\epsilon_T\), where \(\operatorname{Var}(\epsilon_T)=0.99\) and the residual is independent of \(S\). Thus \(\operatorname{Var}(E_T)=1\). A transferred model predicts \(\hat E_A=0.5S\), so \(\operatorname{Var}(\hat E_A)=0.25\) and \(\operatorname{Cov}(\hat E_A,E_T)=0.05\).
The target accuracy is \(R_T^2=0.05^2/(0.25\times1)=0.0100\), or 1.00%. Suppose the unstandardized trait follows \(Y=0.3E_T+u\), with \(u\) independent of \(S\) and \(\epsilon_T\), and \(\operatorname{Var}(u)=1\). Then \(\operatorname{Var}(Y)=0.3^2(1)+1=1.09\), and \(\operatorname{Cov}(\hat E_A,Y)=0.3(0.05)=0.0150\).
The regression slope of \(Y\) on \(\hat E_A\) is \(0.0150/0.25=0.0600\) trait units per prediction unit. In contrast, the slope of \(Y\) on the true \(E_T\) in the stated model is \(0.3\) trait units per expression unit. The numerical slopes have different predictors and should not be compared as if they were the same estimand; the small covariance demonstrates weak alignment and a potentially weak TWAS signal. No p-value can be calculated from these variances and covariances alone without sample size and the test's sampling assumptions.
Diagnostics and Practical Alternatives
A transfer assessment should match the intended analysis as closely as possible. Check the exact variants, genome build, effect alleles, dosage coding, and weight scaling before interpreting prediction performance. Then evaluate fixed weights in independent target samples, reporting \(R_T^2\), sample size, uncertainty where available, and the target's ancestry, tissue, assay, and expression definition. Check whether performance is driven by a small number of variants or changes materially across target subgroups. Very low or unstable accuracy is a warning that the score may not be a useful proxy for the intended expression phenotype.
Compare the main options according to what information they require and what they can repair:
| Approach | Useful when | Limitation |
|---|---|---|
| Apply reference weights unchanged | Weights have been validated in a sufficiently similar target setting | Reference performance does not establish target performance |
| Retrain or rebuild weights in the target setting | Target expression and genotype data are available in adequate quantity | Training may be underpowered, and the resulting model still needs independent validation |
| Recalibrate the prediction | The target measurement is demonstrably the same signal on a shifted or rescaled assay scale | Cannot repair changed biology, poor genetic alignment, or a different transcript target |
| Use a validated tissue- or context-specific model | The question concerns that specific tissue or experimental context | May have limited coverage or low prediction accuracy in the target population |
These are alternatives for addressing prediction transportability, not interchangeable fixes. Recalibration is appropriate only when the relationship between measurements supports it. Retraining can improve match to a target setting, but does not remove confounding or make a TWAS association causal. If target validation is unavailable, the uncertainty should be reported rather than treating transfer as established.
Common Pitfalls
- “The variants overlap, so the weights transfer.” Variant overlap is not enough; allele coding, LD, effect alignment, and target expression accuracy all matter.
- “A reference cross-validation \(R^2\) is the target \(R^2\).” It estimates performance under the reference validation conditions. Test in a target-relevant sample to assess transfer.
- “Low prediction accuracy proves the TWAS p-value is false.” Low accuracy can reduce power and weaken interpretation, but does not by itself determine type I error. Calibration depends on the full testing assumptions, including covariance modeling and confounding control.
- “A scale conversion fixes any assay mismatch.” An intercept and slope can correct a scale difference only when both assays measure a sufficiently corresponding quantity. They cannot make different biological targets equivalent.
- “A gene-level association identifies the causal tissue.” A transferred score may reflect the reference model rather than target-tissue regulation. Association alone does not settle tissue specificity or causality.
Check Your Understanding
Answer each question, then compare with the brief solutions.
- A target predictor has variance 2, target expression has variance 1, and their covariance is 0.4. What is the target \(R^2\)?
- Why can a change in LD weaken transferred weights even if the same causal variant affects expression in both populations?
- If an assay change is a known affine rescaling of the same expression quantity, what can recalibration address, and what can it not establish?
- Does low target prediction accuracy automatically imply an inflated TWAS type I error rate? State the more precise interpretation.
Solutions. (1) \(R_T^2=0.4^2/(2\times1)=0.0800\), or 8.00%. (2) A reference variant may predict the causal variant through LD; changed target correlations alter how well the weighted genotype score tracks the genetic component of expression. (3) Recalibration can correct a justified intercept or scale difference, but it cannot establish equivalence if the assays measure different biological quantities or repair poor genetic alignment. (4) No. Low accuracy can lower power and weaken interpretation; type I error depends on whether the test is calibrated under its assumptions, including appropriate covariance modeling and control of confounding.