Why Interpretation Errors Matter
A differential-abundance result is a statement about a defined comparison, a defined set of samples, and a defined measure of abundance. Errors often arise when one of these is silently changed: thousands of cells are treated as thousands of independent biological replicates, a relative proportion is described as an absolute count, or a denominator or cell label is chosen because it makes the result look compelling. Such errors can make a precise-looking result answer a different question from the one the study can support.
For notation, let \(i\) index biological samples, such as donors, and \(k\) index cell types. Let \(Y_{ik}\) be the number of captured cells assigned to type \(k\) in sample \(i\), and let \(N_i=\sum_k Y_{ik}\) be the total number of captured cells in the analyzed set. The observed proportion is \(\hat{p}_{ik}=Y_{ik}/N_i\). It describes the composition of the captured cells for that sample; by itself, it is not an estimate of the number of cells of type \(k\) in the donor's tissue.
Error 1: Treating Cells as Independent Replicates
Suppose the condition is assigned to donors. The independent replication for comparing conditions is ordinarily at the donor level, not the individual-cell level. Cells from one donor share biological features, collection and processing conditions, and often other sources of variation. A test that treats every cell as an independent replicate acts as if each cell independently received the condition and can therefore greatly overstate the information available for generalizing across donors.
A useful distinction is between measurement quantity and replication. Sequencing more cells may reduce uncertainty about the composition of a particular sample. It does not necessarily reduce between-donor variability or compensate for having few donors. A donor-level analysis instead compares the sample-level abundances while accounting for the variation among biological replicates.
Worked Example: Cell Counts Do Not Replace Donor Replicates
Consider a hypothetical study with three control donors and three treated donors. Each contributes 1,000 captured cells. The numbers assigned to one cell type are 80, 100, and 120 in controls, and 120, 150, and 180 in treated samples. The corresponding donor-level proportions are \(0.08, 0.10, 0.12\) and \(0.12, 0.15, 0.18\).
The control mean proportion is \((0.08+0.10+0.12)/3=0.100\), and the treated mean is \((0.12+0.15+0.18)/3=0.150\). The estimated difference is \(0.150-0.100=0.050\), or 5 percentage points. The sample standard deviations are \(s_C=0.020\) and \(s_T=0.030\). For an illustrative independent-donor comparison, the estimated standard error of the difference is
This standard error reflects variation among the three donors in each group. By contrast, pooling the cells gives 300 of 3,000 control cells and 450 of 3,000 treated cells. A naive two-proportion calculation that treats all 6,000 cells as independent uses pooled \(\hat{p}=750/6000=0.125\), giving
The latter calculation is much smaller, but it is not a valid substitute for donor-level uncertainty here: it ignores the fact that cells are clustered within only six donors. The example does not establish that a donor-level test is well calibrated with just three donors per group; it shows why counting cells as replicates changes the uncertainty calculation. The donor count and between-donor variability must guide the strength of the conclusion.
Error 2: Testing Each Proportion as Though It Were Independent
When cell types form an exhaustive partition of the analyzed cells, their proportions within a sample add to one. Under a simple multinomial sampling model, conditional on \(N_i\), the count vector has probabilities \(p_{i1},\ldots,p_{iK}\), with \(\sum_k p_{ik}=1\). This model is a useful way to see the dependence; real donor-to-donor variation may require additional modeling, but it does not remove the fixed-sum constraint.
For two distinct cell types \(j\) and \(k\), the multinomial covariance of their sample proportions is
The covariance is negative: with a fixed total, a larger share for one type leaves a smaller share for the others. This can be derived by writing \(\hat{p}_{ij}=Y_{ij}/N_i\) and using the multinomial covariance \(\operatorname{Cov}(Y_{ij},Y_{ik}\mid N_i)=-N_i p_{ij}p_{ik}\); dividing by \(N_i^2\) gives the expression above. Consequently, separate tests of each cell type do not describe independent evidence, and a result for one type may partly reflect shifts in the composition of the rest.
This does not mean that a component-wise test is always invalid. It means that its sampling assumptions and interpretation must be appropriate, and that testing many components requires attention to the collection of tests. A set of uncoordinated tests that assumes independent proportions is not justified simply because each proportion can be calculated separately.
Worked Example: A Component Increase Implies Changes Elsewhere
In a hypothetical sample of 100 captured cells, suppose the proportions of types A, B, and C are \(0.40, 0.30, 0.30\). In another sample they are \(0.50, 0.25, 0.25\). The changes are \(+0.10,-0.05,-0.05\), which sum to zero, as they must when these three types exhaust the total.
Under the multinomial model for the first sample, the conditional covariance between the proportions of A and B is
Their conditional variances are \(0.40(0.60)/100=0.00240\) and \(0.30(0.70)/100=0.00210\), respectively. The negative covariance is a mathematical consequence of the fixed total, not evidence that the biological abundance of A directly suppresses B. The observed shifts say that A occupies a larger share of the captured composition while B and C occupy smaller shares. They do not, on their own, establish which absolute cell numbers changed.
Error 3: Calling a Relative Change an Absolute Gain
A proportion has a denominator. If the fraction of captured cells assigned to a type rises, that type has a larger share of the analyzed composition. The fraction can rise because that type increased, because other types decreased, or because both occurred. It can also be affected by which cells were captured and retained. Therefore, an observed relative increase is not, by itself, evidence that the tissue contains more cells of that type.
For example, if type A accounts for 20% of 1,000 cells in one condition, its count in that hypothetical total is 200. If it accounts for 30% of 500 cells in another, the corresponding count is 150. The proportion rose by 10 percentage points, while the count in these totals fell. In single-cell data, totals of captured cells are not automatically comparable measures of total tissue cell number, so even this arithmetic does not recover absolute abundance without an appropriate sampling basis or external measurement.
Worked Example: A Larger Share Can Accompany Fewer Cells
Suppose, hypothetically, that a tissue contains 1,000 cells in condition 1 and 500 in condition 2. Type A makes up 20% and 30%, respectively. Its implied counts under these stated totals are
The relative change is \(0.30-0.20=0.10\), or 10 percentage points, but the absolute count changes by \(150-200=-50\) cells. Thus “type A increased in relative abundance” matches the proportions, whereas “type A increased in number” does not match these hypothetical totals. For captured single-cell data, a count of sequenced cells is not necessarily the total number in the tissue; an absolute-number conclusion requires measurements that support that scale.
Error 4: Choosing the Denominator or Cell Labels After Seeing Results
A log-ratio compares the abundance of one component with another, so the reference cell type is part of the question being asked. Choosing a reference after inspecting which one produces the largest contrast can make a nominal result misleading: the reported contrast was selected from several possibilities, and ordinary uncertainty calculations for a single prespecified contrast do not account for that search. The same concern applies to trying multiple groupings or cell labels and reporting only the one with the clearest difference.
Cell labels also define the components being compared. If annotation rules, resolution, or inclusion decisions are altered in response to the observed condition difference, the apparent discovery may reflect selective analysis rather than a stable biological contrast. A defensible confirmatory analysis specifies the cell categories and contrast before examining the condition effect. If a choice is made during exploration, report it as exploratory, show the relevant alternatives, and seek confirmation using a prespecified analysis or independent data.
Worked Example: A Log-Ratio Depends on Its Reference
Suppose hypothetical group-level compositions are control \((A,B,C)=(0.20,0.30,0.50)\) and treated \((A,B,C)=(0.30,0.30,0.40)\). The change in the log-ratio of A to B is
The change in the log-ratio of A to C is different:
Both calculations use the same compositions, but they answer different relative questions. The A-to-B ratio changed because A's share rose while B's remained at 0.30; the A-to-C ratio also reflects C's decline. Neither ratio is an absolute count change. If the reference was chosen only after comparing these values, the larger contrast cannot be presented as if it were the sole prespecified analysis.
Practical Checks and Better Interpretations
Before interpreting a differential-abundance result, verify what the analysis treated as the replicate, what population of cells formed the denominator, and how the cell categories were defined. Then describe the result at the scale actually measured. A statement such as “the estimated proportion of type A among captured cells was higher in the treated group” is narrower, and usually more accurate, than “treatment increased the number of type A cells.”
Identify the independently sampled biological units. Do not use the number of cells as the number of independent donors.
Confirm which categories sum to the denominator and remember that proportions in a fixed total are dependent.
State whether the result concerns a proportion, a log-ratio, or an absolute number. These are not interchangeable.
Determine whether labels, denominators, and contrasts were specified before inspecting results. Treat result-guided choices as exploratory.
The main alternatives address different problems. Donor-level analyses use biological replication to represent between-donor variation; they are preferable to treating cells as independent when the condition comparison is across donors. Compositional or log-ratio approaches make relative comparisons while respecting the shared total, but their contrasts still require clear interpretation. External counts or other measurements tied to a known tissue quantity are needed to support absolute-abundance claims. No adjustment can make a post hoc choice equivalent to a prespecified one, although transparent reporting and independent confirmation can help assess its stability.
These checks do not replace model diagnostics or careful study design. For example, a donor-level analysis can still be unstable with few donors, and captured proportions can still be affected by sampling and capture biases. Earlier material on relative abundance versus absolute cell number and on log-ratio effects provides the relevant distinctions; the central safeguard here is to keep the wording aligned with the data and the analysis choices.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A study has two donors per condition and 20,000 cells per donor. What is the biological replicate count per condition, and why is it not 40,000?
- Three exhaustive cell-type proportions change by \(+0.08,-0.03,-0.05\). What constraint does this satisfy, and what does it not establish?
- A cell type's captured proportion rises from 0.10 to 0.15. Can this alone show that its absolute number increased? State why or why not.
- An analyst tries four reference cell types and reports only the contrast with the largest estimated effect. What is the interpretation problem, and how should the analysis be described?
Solutions. (1) There are two biological replicates per condition: the two donors. The 20,000 cells within each donor are nested observations, not independently assigned condition replicates. (2) The changes sum to zero, as required for exhaustive proportions with a common total. They describe relative composition and do not establish which absolute cell numbers changed. (3) No. The proportion is relative to the captured-cell denominator; other types may have changed, and captured totals do not automatically measure tissue cell totals. (4) The reported contrast was selected after examining alternatives, so it should not be presented as a single prespecified test with ordinary single-contrast interpretation. Report the selection as exploratory, disclose the alternatives considered, and confirm a prespecified contrast independently.