Why Model Choice Starts With the Study Design
A cell-type QTL study can contain thousands of measured cells but only a small number of genotyped donors. The choice of model should therefore begin with the question being asked and the structure of the sampling, not with the raw number of expression measurements. A model that treats every cell as an independent genetic replicate can report far more apparent information than the study actually contains.
Three common approaches address different analysis needs. Pseudobulk regression summarizes expression for each donor and cell type before relating expression to genotype. Cell-level mixed models retain cell-level measurements while accounting for donor clustering. Genotype-by-cell-type analysis asks whether genetic effects differ between cell types; it can be implemented using pseudobulk values or a suitable cell-level model. These approaches are not interchangeable labels for the same question.
What Each Analysis Targets
For one gene and one cell type, a pseudobulk analysis aggregates that gene’s measurements across the cells of the type for each donor, producing one response per donor. It then models the donor-level response as a function of genotype and relevant covariates. The response may be an appropriately normalized expression summary or counts analyzed with a model suited to counts. Aggregation reduces the cell-level data to donor-by-cell-type units; it does not create additional donors.
A cell-level mixed model retains the measurements from individual cells. A generic continuous-response form is:
Here \(Y_{ij}\) is expression for cell \(j\) from donor \(i\), \(G_i\) is that donor’s genotype dosage, and \(\mathbf{C}_i\) denotes included covariates. The donor effect \(u_i\) accounts for correlation among cells from the same donor. This equation illustrates a continuous-response model; for count outcomes, the response distribution and link must instead be chosen to suit the counts. In either case, the model requires a defensible mean structure, a suitable within-donor dependence structure, and enough independent donors to estimate the genetic association reliably.
An interaction analysis targets heterogeneity of genetic effects. For two cell types, one possible donor-level model includes genotype, cell type, and their product. The interaction coefficient represents a difference between cell-type-specific genetic effects, under the model’s coding and other assumptions. Because cell types from the same donor are repeated observations, their dependence must be accommodated. That may be handled in a joint pseudobulk model with donor-level dependence or in an appropriate cell-level mixed model.
A Short Justification: Why Cells Are Not Genetic Replicates
Suppose, for illustration, that the continuous expression measurement in one cell is \(Y_{ij}=\mu+u_i+\varepsilon_{ij}\), where the donor component has variance \(\tau^2\), the cell-specific component has variance \(\sigma^2\), and the two components are independent. For \(m\) cells from one donor, the donor mean is \(\bar{Y}_i=\mu+u_i+\bar{\varepsilon}_i\). Since averaging \(m\) independent cell-specific errors divides their variance by \(m\), the variance of this mean is:
As \(m\) grows, the second term shrinks, but the donor-level component remains. Thus additional cells can sharpen a donor’s expression summary, while the number of independent genotype observations remains the number of donors. Treating all cells as independent would omit the shared \(u_i\) and generally understate uncertainty when \(\tau^2>0\).
Worked Example: A Donor-Level Pseudobulk Association
Worked Example: A Donor-Level Pseudobulk Association
Consider a hypothetical study of one cell type in six donors. Expression is a normalized pseudobulk value in arbitrary expression units, and genotype is allele dosage \(G_i\), coded 0, 1, or 2. For a simple unadjusted linear regression, calculate the estimated expression change per additional allele.
| Donor | \(G_i\) (allele dosage) | \(Y_i\) (expression units) |
|---|---|---|
| 1 | 0 | 4 |
| 2 | 0 | 5 |
| 3 | 2 | 7 |
| 4 | 2 | 8 |
| 5 | 1 | 5 |
| 6 | 1 | 6 |
The model is \(Y_i=\beta_0+\beta_GG_i+\varepsilon_i\). It assumes a linear mean relationship between dosage and expression, independent donor-level errors with constant variance for the usual linear-regression standard errors, and no unaccounted confounding of genotype and expression. With only six donors, this is a numerical illustration, not a claim that the study has adequate power or that its assumptions have been checked empirically.
The means are \(\bar{G}=1\) and \(\bar{Y}=35/6\). The ordinary least-squares slope is:
For the numerator, the centered genotype values are \((-1,-1,1,1,0,0)\). The first four contributions sum to \((-1)(4-35/6)+(-1)(5-35/6)+(1)(7-35/6)+(1)(8-35/6)=6\); the final two contributions are zero. The denominator is \((-1)^2+(-1)^2+1^2+1^2=4\). The fitted association is therefore 1.5 normalized expression units per additional allele. This is an estimated association, not evidence by itself of a causal effect.
For this one-cell-type question, pseudobulk regression is a transparent choice: the response and the genotype are both represented at donor level. The six donors, rather than the number of cells contributing to their summaries, determine the amount of independent genetic replication.
Worked Example: Many Cells but Few Donors
Worked Example: Many Cells but Few Donors
Suppose a hypothetical study has 12 donors and measures 500 cells of a cell type per donor. The research question is the association between genotype and expression in that cell type. A rough illustration of the information loss from within-donor dependence uses the equal-cluster-size design effect \(1+(m-1)\rho\), where \(m\) is cells per donor and \(\rho\) is the within-donor correlation. This approximation is not a replacement for fitting a model.
If \(\rho=0.20\), then:
The calculation shows why 6,000 cells should not be interpreted as 6,000 independent genotype observations. The approximate effective cell count is still not an effective donor count: genotype varies across the 12 donors, so there are only 12 independent genotype-bearing units. For the stated primary question, a donor-level pseudobulk regression is a reasonable and interpretable starting analysis if aggregation and the response model suit the data. A cell-level mixed model may be useful if cell-level variation is itself important or aggregation loses relevant information, but it must account for donor clustering and cannot manufacture donor replication. With 12 donors, the central design limitation is the small donor count; collecting more cells alone does not resolve it.
When Cell-Type Coverage Makes an Interaction Analysis Necessary
An interaction analysis requires more than a wish to report separate results by cell type. The study must have enough donors with usable measurements in the cell types being compared, genotype variation among those donors, and a model that accounts for the fact that multiple cell types can come from the same donor. Uneven coverage can make the comparison depend on a small and potentially unrepresentative subset of donors. If a cell type is absent or too sparsely measured for many donors, its genetic effect—and especially a contrast with another type—may be weakly identified or imprecise.
The interaction coefficient is a contrast on the model’s specified scale. For example, a difference between slopes in a linear model is measured in expression units per allele. A contrast from a nonlinear model may instead be on its link scale unless converted to another scale. The interpretation must name the scale and cell types being compared. A cell-type-specific association in one group and a non-significant association in another does not, by itself, establish that the effects differ; the interaction contrast is the direct test of that difference.
Worked Example: Comparing Effects Across Two Cell Types
A hypothetical study has 30 donors, with both cell types measured in each donor and 10 donors at each genotype dosage \(G=0,1,2\). Assume for this illustration that the group means below are the fitted linear-model means and that the model includes donor-level dependence for the paired cell types. The target is the difference in genetic slopes, not merely two separate associations.
| Genotype dosage | Cell type A mean (expression units) | Cell type B mean (expression units) |
|---|---|---|
| 0 | 5.0 | 4.0 |
| 1 | 6.2 | 4.3 |
| 2 | 7.4 | 4.6 |
The estimated slope for type A is \((7.4-5.0)/(2-0)=1.2\) expression units per allele. For type B it is \((4.6-4.0)/(2-0)=0.3\) expression units per allele. The estimated difference, type B minus type A, is:
Thus the fitted genetic slope is 0.9 expression units per allele lower in type B than in type A. In a model with type A as the reference, this is the genotype-by-type interaction coefficient for type B. These means demonstrate how to calculate and interpret the contrast; without the donor-level residual data and a fitted model, they do not provide a standard error or a significance test. Because both types are observed in the same donors, an analysis that ignores within-donor correlation would fail to represent the design.
A Practical Model-Selection Sequence
The following sequence connects the scientific target to the data structure. It is a design guide, not an automatic rule that one model is always best.
Decide whether the target is an association within one cell type, a genetic effect using cell-level information, or a difference in genetic effects between cell types.
Determine how many independent donors contribute and whether their genotypes span enough variation to estimate the target. Do not substitute cell count for donor count.
Check how many cells contribute to each donor-by-type measurement, how uneven yields are, and which donors have data for each type. A summary based on very few cells may be noisy; a missing type cannot be recovered by model complexity.
Use pseudobulk when donor-by-type summaries match the target and the aggregation and outcome model are appropriate. Retain cell-level data when that granularity is needed, using a model that represents within-donor dependence.
When asking whether effects differ by type, fit the relevant genotype-by-type contrast and account for repeated types within donors. Check whether coverage and donor numbers can support that contrast.
| Design feature | Model implication | What it does not solve |
|---|---|---|
| One target cell type, reasonable donor summaries | Pseudobulk regression is often a clear primary analysis. | Aggregation does not correct confounding or create more donors. |
| Cell-level distribution or heterogeneity is central | Consider a cell-level mixed model with donor dependence represented. | A random effect does not compensate for very few genotype-bearing donors. |
| Target is a difference in effects across types | Fit a genotype-by-cell-type contrast, using a suitable joint model. | Separate type-specific results are not a formal test of their difference. |
| Low or highly uneven coverage in a type | Assess whether the target is estimable and whether the study needs improved sampling. | A more elaborate model cannot supply unobserved donor-by-type data. |
Common Mistake: Letting Cell Count Decide the Model
- Wrong reasoning: “There are thousands of cells, so the genetic association has thousands of independent observations.” Cells from one donor share genotype and donor-level factors; independence does not follow from having many cells.
- Correction: Identify the donor as the genotype-bearing unit. Use aggregation or a model that accounts for donor clustering, and evaluate precision in light of the number of donors and their genotype variation.
- Wrong reasoning: “The association is significant in one type but not another, so the effects differ.” Different significance results do not establish a difference in effects.
- Correction: If the scientific target is heterogeneity, estimate and test the genotype-by-cell-type contrast directly, with appropriate dependence handling and sufficient coverage.
Model selection matters because each approach makes the estimand and the information structure visible in a different way. Pseudobulk offers a direct donor-level analysis when donor-by-type summaries are suitable. Mixed models preserve cell-level information while representing clustering, but require adequate donor-level replication and a defensible dependence model. Interaction models address a distinct question and require usable coverage across the compared types. The best choice is the simplest model that matches the target and the observed design, with limitations reported rather than hidden by a large cell count.
Check Your Understanding
Use the study target and sampling structure to answer each question.
- A study has 20 donors and 400 cells per donor for one cell type. What is the independent genotype-bearing unit, and why is the cell count not the genetic sample size?
- For an association in one well-covered cell type, what is one reason to choose pseudobulk regression over a cell-level model?
- What feature must a cell-level mixed model represent when many cells come from each donor?
- A genetic association has a small p-value in type A and a large p-value in type B. What analysis directly evaluates whether the effects differ?
- Why can poor coverage of one cell type among donors weaken an interaction analysis even when the total number of cells is large?