Two Different Genetic Questions
A genetic association observed in a tissue can arise because a genotype is associated with which cell types are present, because it is associated with expression within a cell type, or because both patterns occur. These are different biological and statistical questions. A bulk-tissue expression association alone generally cannot distinguish them: the measured signal combines expression across the cell types contributing to the sample.
The distinction matters for interpretation. A variant associated with a higher fraction of one cell type may change the tissue-level abundance of a gene’s transcript even if no cell of that type changes its expression. Conversely, a variant can alter expression within a cell type while the relative abundance of that type remains stable. These associations should therefore be defined using separate outcomes and interpreted on their own scales.
In a donor-level analysis, let \(G_i\) denote donor \(i\)'s genotype dosage at a variant, coded as the number of copies of a specified allele, from 0 to 2. Let \(p_{ik}\) be the proportion of captured cells from donor \(i\) assigned to cell type \(k\). Let \(Y_{ik}\) be a donor-level expression measure for a gene in cell type \(k\), such as normalized pseudobulk expression. The units of \(p_{ik}\) are proportions (or percentage points if multiplied by 100); the units of \(Y_{ik}\) depend on the expression scale used.
Define the Outcome Before Fitting a Model
A simple donor-level model for cell abundance is
where \(\mathbf{C}_i\) contains specified donor-level covariates and \(\varepsilon_{ik}\) is the residual. Under this model, \(\beta_k\) is the expected change in the proportion of captured cells assigned to type \(k\) per additional allele, holding the included covariates fixed. If the outcome is expressed from 0 to 1, a coefficient of 0.02 means an increase of 0.02 in proportion, or 2 percentage points, per allele. It does not mean a 2% relative increase.
This linear model is a convenient association model, not a claim that proportions are unbounded. Its conditional mean should be a reasonable approximation over the observed genotype range, and its residual and variance behavior should be checked for the intended analysis. Alternative models can respect the bounded scale or the joint structure of proportions. In any case, the observational unit for this regression is the donor, not each individual cell: treating cells from the same donor as independent genotype observations would not create additional independent genotype information.
For expression within type \(k\), a corresponding donor-level model is
Here \(\theta_k\) is the expected change in the chosen expression measure per additional allele among the donor-level summaries for cells assigned to type \(k\), conditional on included covariates. If \(Y_{ik}\) is log-base-2 normalized expression, for example, \(\theta_k\) is in log-base-2 expression units per allele. It is not a change in cell proportion. The model requires that the donor-level outcome and its scale be defined consistently, along with a suitable conditional mean model and residual assumptions for the chosen estimator.
Worked Example: A Bulk Association Caused by Composition
Consider a hypothetical tissue with two cell types, A and B, and one gene. Suppose cell-type A has expression 10 units per cell and type B has expression 2 units per cell for every genotype. Thus, there is no within-cell expression association in either type. Assume, for this illustration, that bulk expression is the cell-proportion-weighted average of these per-cell expression values.
Among donors with genotype dosage 0, suppose the proportion of type A is 0.20 and type B is 0.80. The expected bulk expression is
Among donors with dosage 1, suppose the proportions are 0.60 for type A and 0.40 for type B, while the expression values within both types remain 10 and 2. Then
The difference between these two genotype-group means is \(6.80-3.60=3.20\) bulk expression units for one allele of dosage difference. With only these two group means, the fitted slope is
This bulk association is entirely due to the changed composition in this hypothetical example: expression within each cell type was held fixed. A cell-type-specific expression analysis would target a different outcome and would not report this compositional difference as a within-type expression effect.
Why Bulk Expression Is a Mixture
For a tissue represented by \(K\) cell types, let \(p_{ik}\) be the fraction of cells of type \(k\) in donor \(i\), and let \(\mu_{ik}\) be the mean expression of a gene within that type on a scale where averaging is appropriate. If the fractions sum to one and cells contribute comparably to the measured signal, the tissue-level mean can be represented as
This identity explains why a bulk genetic association does not by itself identify a within-cell expression effect. A difference in \(Y_i\) can occur because the \(p_{ik}\) values differ, because the \(\mu_{ik}\) values differ, or because both differ. In real assays, RNA contribution per cell can vary across types, so the effective mixture weights may be RNA-weighted rather than equal to cell proportions. The simple equation is an explanatory model; its weights must match the measurement process for a quantitative decomposition to be appropriate.
A two-group difference can be separated exactly using one reference convention. Write \(p_{0k}\) and \(\mu_{0k}\) for proportions and within-type expression in one genotype group, and \(p_{1k}\) and \(\mu_{1k}\) for the other. Add and subtract \(\sum_k p_{1k}\mu_{0k}\):
The first term is the composition contribution evaluated at the reference group's expression levels. The second is the within-type expression contribution evaluated using the other group's proportions. The equality follows by expanding the right-hand side: the two terms involving \(p_{1k}\mu_{0k}\) cancel, leaving \(\sum_k p_{1k}\mu_{1k}-\sum_k p_{0k}\mu_{0k}\). This is an exact accounting identity under the mixture representation, not a causal decomposition. Other reference choices can allocate the interaction between composition and expression differently, so the convention should be stated.
Worked Example: Both Composition and Expression Change
Suppose a hypothetical two-cell-type tissue has the following group means. Type A has proportions 0.20, 0.40, and 0.60 at genotype dosages 0, 1, and 2, respectively. Its mean expression is 5, 6, and 7 units. Type B has the remaining proportions and constant mean expression of 2 units. The mixture assumption is the same as in the preceding example.
The type-A proportion increases by 0.20 for each allele across these group means. The slope from dosage 0 to dosage 2 is
Within type A, expression increases by 2 units across the two-allele difference, giving
Type B's within-type expression slope is \((2-2)/(2-0)=0\). Thus both a cell-abundance association for A and a within-A expression association are present in these constructed means. They are distinct effects with distinct units.
Calculate the bulk means directly. At dosage 0, \(Y_0=0.20(5)+0.80(2)=1.00+1.60=2.60\). At dosage 1, \(Y_1=0.40(6)+0.60(2)=2.40+1.20=3.60\). At dosage 2, \(Y_2=0.60(7)+0.40(2)=4.20+0.80=5.00\). The extreme-group difference is \(5.00-2.60=2.40\) bulk expression units.
Using the decomposition with dosage 0 as reference, the composition contribution is
The within-type expression contribution, evaluated at dosage-2 proportions, is
Their sum is \(1.20+1.20=2.40\), exactly the observed bulk difference. The bulk means are not evenly spaced: their successive differences are \(3.60-2.60=1.00\) and \(5.00-3.60=1.40\). If an ordinary least-squares line is fitted to these three equally represented dosage-group means, its slope is 1.20 bulk units per allele: the mean dosage is 1, the mean bulk value is \(11.20/3=3.733\), and the slope numerator is \((-1)(2.60-3.733)+0+(1)(5.00-3.733)=2.40\); the dosage sum of squares is \(2\), so the slope is \(2.40/2=1.20\). This fitted bulk slope is not either of the type-specific slopes.
Relative Proportions Are Not Absolute Cell Counts
Cell-type proportions are compositional: for a set of exhaustive, mutually exclusive types, they satisfy \(\sum_k p_{ik}=1\). Consequently, an increase in one proportion must be balanced by a decrease in at least one other proportion. The proportions are not independent outcomes. A negative association between two proportions can arise from this constraint and does not by itself establish that one cell type biologically suppresses the other.
Proportions also describe relative abundance in the sampled set, not necessarily the number of cells in the tissue. Consider the following hypothetical counts.
Worked Example: A Proportion Rises While Its Cell Count Does Not
Suppose a sample at genotype dosage 0 contains 20 cells of type A, 30 of type B, and 50 of type C, for a total of 100 captured cells. The proportions are \(20/100=0.20\), \(30/100=0.30\), and \(50/100=0.50\).
At dosage 1, suppose the sample contains 20 cells of type A, 30 of type B, and 25 of type C, for a total of 75 cells. The proportions are \(20/75=0.2667\), \(30/75=0.4000\), and \(25/75=0.3333\). The type-A proportion has risen by about \(0.2667-0.20=0.0667\), or 6.67 percentage points, although its count stayed at 20. The change in relative proportion is explained by the smaller total and fewer type-C cells in this example, not an increase in the number of type-A cells.
Accordingly, a genetic association with \(p_{ik}\) should be described as an association with the relative proportion of the captured cell population unless the study design provides an appropriate measure of absolute abundance. Cell recovery and sampling can also affect observed proportions, so a proportion is not automatically a direct census of the tissue.
Interpreting the Two Results Together
A careful report names the phenotype, the scale, and the analysis unit. For a cell-abundance association, state the cell type, whether abundance means a captured-cell proportion or another measure, and the estimated change per allele. For a within-cell expression QTL, state the cell type, the expression scale, the donor-level summary, and the estimated change per allele. Neither association alone establishes that genotype causally changes the biological process; the interpretation is an association conditional on the study design and model.
It can be useful to place abundance and expression estimates side by side, but they should not be treated as interchangeable evidence. A variant associated with both outcomes may have associations with both composition and within-type expression. A bulk association without a corresponding within-type association may be consistent with a composition-driven signal, but absence of evidence in a cell-type analysis is not proof that the within-type effect is exactly zero. Precision and the amount of cell-type-specific data matter.
| Analysis outcome | Question answered | Typical coefficient interpretation |
|---|---|---|
| Cell-type proportion | Is genotype associated with the relative abundance of a cell type? | Change in proportion, or percentage points, per allele |
| Expression within a cell type | Is genotype associated with expression summarized among cells assigned to that type? | Change in the specified expression units per allele |
| Bulk-tissue expression | Is genotype associated with the combined tissue-level expression signal? | Change in bulk expression units per allele; it may combine composition and within-type changes |
Common Mistakes
- Calling a bulk association an eQTL within a cell type. Bulk expression is a mixture. Without a cell-type-specific outcome or other supporting analysis, the association does not isolate within-type expression.
- Reading a higher proportion as more cells in absolute terms. A proportion can rise because another cell type or the total sampled population falls. State whether the measure is relative or absolute.
- Interpreting the proportion coefficient as a relative percent change. In a model with proportions from 0 to 1, a coefficient of 0.02 is a 2-percentage-point change per allele, not necessarily a 2% increase relative to baseline.
- Treating cell observations as independent genotype observations. Genotype varies across donors, so donor-level summaries or models that account for donor clustering are needed for valid uncertainty assessment.
- Assuming a composition-expression decomposition proves mechanism. The mixture identity accounts for a difference under stated measurement assumptions; it does not establish causal pathways.
Check Your Understanding
Answer each question using the distinction between relative abundance, within-cell expression, and bulk expression.
- A variant is associated with the fraction of captured cells assigned to a cell type. What is the outcome, and what are the units of a linear-model coefficient when the fraction is coded from 0 to 1?
- In a two-type mixture, within-type expression values remain fixed but the proportion of the higher-expressing type increases. Explain why bulk expression can still increase.
- A cell type's captured-cell proportion rises from 0.25 to 0.30. Does this establish that the absolute number of those cells increased? Explain.
- For a donor-level expression model, what does the genotype coefficient represent, and how does its interpretation differ from a coefficient in a cell-proportion model?
- Why must a bulk-tissue expression association not automatically be described as an expression QTL within a particular cell type?