Why Molecular QTL Effects Need a Precise Target
A genetic association with gene expression, splicing, or protein abundance is an association with a measured molecular trait. Its estimated effect is therefore tied to how that trait was defined and recorded: for example, normalized expression on a log scale, the proportion of transcripts using a particular splice event, or a protein assay’s relative abundance measurement. The allele effect is not automatically an effect on disease, health, or another organism-level phenotype.
This distinction is consequential. A number such as 0.30 has no complete interpretation by itself. It could mean 0.30 units of log-transformed expression per allele, 0.30 percentage points of a splicing measure, or 0.30 units on an assay scale. The trait, units, transformation, allele coding, and comparison all belong in the interpretation.
Allele Dosage and the Per-Copy Estimand
Let \(G\) denote the number of copies of a specified effect allele, so \(G\) takes values 0, 1, or 2. Let \(T\) denote a defined molecular trait on its stated measurement scale. For a simple additive association model, write the conditional mean as
where \(C\) is a set of covariates, \(\alpha\) is an intercept, and \(\gamma\) describes the covariate terms. The model assumes that, conditional on \(C\), the mean of \(T\) changes linearly with allele dosage: each additional copy has the same mean contrast. The coefficient \(\beta_T\) is the conditional per-allele association in units of \(T\), holding \(C\) fixed. It is not automatically a causal effect.
The linear mean assumption makes the dosage interpretation precise. At a fixed covariate value \(c\), the expected-trait contrast between dosage \(g+1\) and dosage \(g\) is
Thus, under the stated model, \(\beta_T\) is the expected change per additional allele copy on the chosen scale. The expected contrast between \(G=2\) and \(G=0\) is \(2\beta_T\). If the observed genotype means do not follow an additive pattern, one slope may summarize a trend without equaling both adjacent genotype contrasts; genotype-specific contrasts would then be needed for a complete description.
The interpretation also depends on what \(T\) is. If \(T\) is measured in expression units, \(\beta_T\) is in those units. If \(T\) is log-transformed expression, the coefficient is a difference in mean log expression. If \(T\) is a splice proportion, the effect may be a proportion difference. A transformation changes the scale of the estimand; it does not merely change the way the same number is written.
Worked Example: Expression on a Log₂ Scale
Worked Example: Expression on a Log₂ Scale
Suppose a hypothetical study measures normalized expression for one gene and defines \(T\) as log₂ expression. At the same covariate values, the estimated mean log₂ expression is 5.00 for \(G=0\), 5.30 for \(G=1\), and 5.60 for \(G=2\). The successive differences are
These means follow an additive dosage pattern, so the estimated per-copy effect is \(\beta_T=0.30\) log₂ units per allele copy. The two-copy contrast is \(5.60-5.00=0.60\) log₂ units.
Back-transforming the mean log₂ values gives a ratio of back-transformed mean log expression of
Equivalently, the geometric mean expression is about 1.23 times as large per additional allele copy, or about 23.1% higher on that geometric-mean scale. This does not establish that arithmetic mean expression is 23.1% higher. A difference in mean log expression alone does not determine the arithmetic-mean ratio if the distributions, including their variances, may differ across genotype groups.
The conclusion is an estimated association with normalized expression in this hypothetical analysis. It does not, by itself, show that the allele causally changes expression or that the expression change affects a clinical phenotype.
Splicing and Protein Traits Have Their Own Scales
A splicing trait might measure the fraction of transcripts using a particular junction or isoform. One common type of measure is a proportion between 0 and 1; it can also be reported as a percentage between 0% and 100%. When a per-allele contrast is reported on the proportion scale, multiplying by 100 expresses the difference in percentage points. A change from 0.42 to 0.47, for instance, is an increase of 0.05, or 5 percentage points—not a 5% relative increase.
Some analyses instead model a transformed splicing measure, such as its logit. A coefficient on that transformed scale is not itself a fixed percentage-point change: the corresponding change in the original proportion depends on the starting value. The scale must therefore be named before the coefficient is interpreted.
Protein abundance is likewise defined by its measurement. An assay may report relative abundance, normalized signal, or a transformed value rather than an absolute concentration. An effect in assay units is not automatically an effect in a physical concentration unit. For a log₂ abundance measurement, exponentiating a mean difference yields a ratio of geometric means (or back-transformed mean log abundance); it does not, without additional assumptions, yield a ratio of arithmetic mean abundances.
Worked Example: A Splicing QTL in Percentage Points
Suppose a hypothetical splicing analysis defines \(T\) as the proportion of transcripts using a specified splice junction. At fixed covariates, the mean proportions are 0.42 for \(G=0\), 0.47 for \(G=1\), and 0.52 for \(G=2\). The adjacent contrasts are
The estimated additive effect is therefore 0.05 proportion units per copy. In percentage-point units, the calculation is \(0.05\times100=5\) percentage points per copy. The \(G=2\) versus \(G=0\) contrast is 0.10, or 10 percentage points.
This is not a 5% relative increase. For example, relative to the \(G=0\) mean of 0.42, a change of 0.05 is \(0.05/0.42\approx0.119\), or about 11.9% of that starting mean. The percentage-point contrast and the relative change answer different questions. The interpretation here concerns the measured splice-use proportion, not total gene expression or an organism-level phenotype.
Worked Example: A Protein QTL on a Log₂ Abundance Scale
Suppose a hypothetical protein assay reports log₂-transformed normalized abundance, and the estimated per-copy coefficient for a variant is \(-0.20\) log₂ units. The corresponding ratio of geometric mean abundance per allele copy is
Thus, the geometric mean abundance, or back-transformed mean log abundance, is estimated to be about 0.871 times as large per additional copy. The relative difference on this scale is \((0.8706-1)\times100\approx-12.94\%\), or about 12.9% lower geometric mean abundance per copy.
The coefficient does not alone imply a 12.9% lower arithmetic mean abundance. That conclusion would require further distributional assumptions—for example, assumptions that justify the same variance structure across genotype groups in an appropriate log-scale model. The result is also in the assay’s normalized abundance context; it should not be described as a change in a specific concentration unit unless the measurement and model support that interpretation.
Molecular Effects Are Not Organism-Level Effects
Let \(Y\) denote an organism-level phenotype, such as a clinical measurement or disease status. An association coefficient for \(Y\), if estimated, is a separate estimand from \(\beta_T\). Its units and scale depend on the definition of \(Y\) and the model used: a continuous phenotype might have a difference in its measurement units, while a binary phenotype might be summarized by a risk difference, risk ratio, or log odds contrast. A molecular effect cannot be substituted for any of these.
For example, an eQTL estimate of 0.30 log₂ units per copy describes an expression association. It does not say that disease risk changes by 0.30 units, that disease odds are multiplied by \(2^{0.30}\), or that expression mediates a genetic association with disease. Establishing a causal effect on a molecular trait requires appropriate causal assumptions; establishing a causal effect on an organism-level outcome, or a pathway between the two, requires additional evidence and assumptions. Association with both traits is not sufficient by itself.
Worked Example: Reporting Molecular and Organism-Level Associations Separately
Suppose, hypothetically, the same allele is associated with a 0.30-unit increase per copy in a gene’s mean log₂ expression and with a one-percentage-point increase per copy in the observed risk of a binary clinical outcome. The first estimate has units of log₂ expression; the second is a risk difference of 0.01 per copy.
A clear report keeps them separate: “Each additional allele copy was associated with 0.30 higher mean log₂ expression and with a 0.01 higher observed outcome risk.” The expression estimate does not convert into the risk difference, and these two associations alone do not establish that expression lies on a causal pathway to the outcome. The wording describes associations, not effects proven to be causal.
Common Mistake: Treating Every Allele Coefficient as the Same Kind of Effect
Incorrect reasoning: “The allele increases expression by 0.30, so it increases average expression by 23%, and it should increase disease risk by the same amount.”
This statement changes the estimand twice without justification. If 0.30 is a difference in mean log₂ expression, exponentiating it gives a ratio of geometric means, not necessarily arithmetic means. And an expression effect has neither the units nor the outcome definition of a disease-risk effect. Even evidence for associations with both traits would not, on its own, establish mediation or causation.
Correction: Name the measured trait and scale, state the per-copy contrast on that scale, and only transform it when the transformation has a valid interpretation. Report an organism-level association separately, in its own units and with appropriate causal qualifications.
Check Your Understanding
For each question, identify the relevant estimand and state what can—and cannot—be concluded.
- A gene-expression model estimates 0.18 per copy on a log₂ scale. What is the interpretation of \(2^{0.18}\), and why does it not necessarily describe an arithmetic-mean ratio?
- A splice-use proportion differs by 0.04 per copy. Express this contrast in percentage points and explain why it is not automatically a 4% relative change.
- What trait does a pQTL concern, and why should an assay-scale effect not automatically be reported as a concentration change?
- Under an additive dosage mean model, what is the expected contrast between \(G=2\) and \(G=0\) if the per-copy coefficient is \(\beta_T\)?
- A variant is associated with both expression and a clinical outcome. Why do those associations alone not establish that expression mediates a causal effect on the outcome?