Cell Composition As A Confounder In Bulk QTL Studies

Why Cell Composition Matters in Bulk QTL Mapping

A bulk-tissue molecular measurement combines signal from many cells. If two samples differ in their cell-type proportions, their measured expression can differ even when expression within each cell type is unchanged. Consequently, a genotype associated with cell composition can appear to be associated with a bulk molecular phenotype, or a genuine within-cell effect can be diluted or amplified by the mixture.

The central question is not simply whether to “adjust for cell type.” It is what the observed association represents. Composition can be a pre-existing confounder, a pathway through which genotype affects the bulk phenotype, or a modifier of a cell-specific genetic effect. These possibilities lead to different interpretations of an adjusted QTL coefficient.

A Mixture Model and the Source of Confounding

Let \(G\) denote genotype dosage, \(C\) the proportion of cell type A, and \(Y\) the bulk expression measurement. With two cell types, A and B, suppose the mean expression per unit contribution is \(\mu_A\) and \(\mu_B\), and suppose initially that genotype has the same within-cell effect \(\beta\) in both types. A simple model is

Here \(\varepsilon\) represents variation not captured by the displayed terms. This model assumes that the mixture is well represented by the cell proportions, expression combines linearly on the measurement scale used, and the same \(\beta\) applies in both cell types. Those assumptions are simplifying: if the genetic effects differ by cell type, a genotype-by-composition term is needed.

If genotype and composition are associated, omitting \(C\) can make the genotype coefficient reflect both \(\beta\) and the composition difference. In this model, if \(E(\varepsilon\mid G)=0\), the population slope from regressing \(Y\) on \(G\) alone is

The second term is the composition contribution to the unadjusted slope. It is zero if the cell types have the same mean expression or if genotype and composition are uncorrelated. Otherwise, an apparent QTL association can arise even when the within-cell genetic effect is zero. This is omitted-variable bias in a mixture setting.

Adjustment With Measured Composition

If composition is measured for each sample, a regression can include it alongside genotype. In the simple model above, fitting \(Y\) on \(G\) and \(C\) separates the genotype coefficient from the composition contribution, provided the model is correctly specified and there is enough independent variation in genotype and composition. The adjusted genotype coefficient is a comparison of samples with the same modeled composition; it is not automatically a cell-type-specific estimate.

In practice, composition is represented by proportions that sum to one. With \(K\) cell types, \(\sum_{k=1}^{K}C_k=1\). A regression with an intercept must therefore omit one proportion or use another nonredundant representation; including all \(K\) proportions and an intercept creates exact linear dependence. The coefficient for a particular proportion is also relative to the omitted type or chosen representation, not an effect of increasing that proportion while every other proportion stays fixed.

Composition as a Confounder or a Mediator

The word “confounder” requires care. If composition is associated with genotype because of ancestry, sampling, or another shared cause, and composition also affects bulk expression, adjustment can help isolate a genotype association conditional on composition. But genotype may itself alter cell abundance or survival. In that case, composition is on a possible pathway from genotype to the bulk phenotype. Adjusting for it removes that pathway from the genotype coefficient.

A simple mediation model makes this distinction explicit. Let composition follow \(C=a+\gamma G+u\), and let expression follow \(Y=\beta G+\delta C+\varepsilon\). Assume the errors have mean zero conditional on \(G\), and that the displayed linear relations are appropriate. Substituting the first relation into the second gives

Under these assumptions, \(\beta\) is the genotype effect conditional on composition, while \(\delta\gamma\) is the composition-mediated contribution to the total genotype association. The marginal slope is \(\beta+\delta\gamma\). Calling the adjusted coefficient the “true effect” without naming the estimand is therefore misleading: it is a conditional or direct-effect parameter in this model, not the total effect through all pathways.

A composition-mediated interpretation needs stronger causal assumptions than a regression decomposition. For example, unmeasured causes of composition and expression can distort \(\delta\), and conditioning on a variable influenced by genotype can introduce bias if that variable also acts as a collider. In an observational QTL analysis, adjusted and unadjusted estimates should first be described as statistical associations under their respective models; a causal interpretation requires additional design and assumptions.

Measured and Inferred Proportions

Composition can be measured directly, estimated from cell counts, or inferred from bulk molecular data using reference profiles or other methods. Inferred proportions are not error-free observations of the true \(C\). If an estimate \(\widehat{C}\) contains error, adjusting for it may not remove the composition association fully. The remaining genotype coefficient can still contain composition-driven signal.

A classical measurement-error calculation illustrates the issue. Let \(C\) be the true centered proportion, and suppose \(\widehat{C}=C+v\), where the error \(v\) is independent of \(G\), \(C\), and the outcome error. Even when this simple error model is plausible, regression on \(\widehat{C}\) does not generally have the same adjustment as regression on \(C\). Error in inferred composition can also be more complicated: it may depend on expression levels, reference-panel similarity, or the cell types represented in the sample.

Practical Interpretation and Common Pitfalls

Composition adjustment is most informative when reported as a comparison of clearly defined models: an unadjusted bulk association and an association conditional on measured or inferred composition. If the result changes materially, that change is evidence that composition matters to the fitted association, but it does not by itself distinguish confounding from mediation. If effects differ across cell types, a single adjusted genotype coefficient may also conceal heterogeneity; the bulk effect can depend on each sample’s mixture.

Interpret effect units precisely. A coefficient for genotype dosage is the expected change in the modeled molecular phenotype for a one-unit increase in dosage, holding included covariates fixed. A coefficient for a proportion is typically scaled to a full 1.0 change in the fraction, so a change of 0.01 corresponds to one hundredth of that coefficient under a linear model. Neither coefficient should be described as a cell-specific effect unless the analysis actually estimates effects within cell types.

• Mistake: “The adjusted coefficient is the true genetic effect.” This ignores that adjustment changes the estimand and may remove a genotype-mediated composition pathway. State whether the target is the total bulk association or the conditional association at fixed composition.
• Mistake: “Including estimated cell fractions removes all cell-composition bias.” Inferred proportions may be noisy or systematically inaccurate. Describe how composition was obtained and recognize that residual bias can remain.
• Mistake: “A significant bulk QTL must act within the measured cell type.” Bulk signal can reflect genotype-associated shifts in cell proportions, as well as within-cell regulation. The bulk result alone does not locate the effect to a cell type.
• Mistake: putting every cell proportion in a regression with an intercept. Since proportions sum to one, this creates exact collinearity. Use a nonredundant representation and interpret proportion coefficients relative to it.