Capture Bias and the Limits of Observed Proportions

Why Captured Proportions Need Not Match Source Proportions

A cell-type proportion calculated from a single-cell assay describes the cells that entered and remained in the analyzed data, not automatically the cells present in the source sample. Cell types can differ in dissociation sensitivity, viability, sorting, loading, or recovery. If some types are less likely to be captured, the observed composition is shifted even when the source composition is known and unchanged. Statistical adjustment for sampling variation does not, by itself, remove this measurement distortion.

The distinction matters for differential-abundance comparisons. A difference in the captured proportions between conditions may reflect a biological change in source composition, a condition-related change in capture or survival, or both. The data alone do not generally separate those explanations. The appropriate target and interpretation therefore depend on whether capture probabilities are known, stable, or plausibly different across conditions.

A Model for Capture-Weighted Proportions

This model assumes that each source cell has a type, that capture and retention can be represented by a type- and condition-specific probability, and that the analyzed labels correctly identify the captured types. It also treats the source composition and capture probabilities as fixed within each condition for the comparison. Conditional on the total number \(n_g\) of captured cells, a basic sampling model is \(Y_{g1},\ldots,Y_{gK}\sim\operatorname{Multinomial}(n_g;r_{g1},\ldots,r_{gK})\), where \(Y_{gk}\) is the captured count of type \(k\). This multinomial model describes sampling variation around the captured composition; it does not assert that \(r_{gk}=\pi_{gk}\).

The expression for \(r_{gk}\) follows by considering the probability that a randomly selected source cell is both type \(k\) and captured. That joint probability is \(\pi_{gk}q_{gk}\). The probability that a source cell is captured, regardless of type, is \(\sum_j\pi_{gj}q_{gj}\). Conditioning the joint probability on capture gives the observed proportion:

The denominator is essential: observed proportions sum to one, so a low capture probability for one type changes the observed proportions of the other types as well. Thus capture bias is compositional, not merely a type-specific downward correction.

What Can Be Identified Without Calibration?

Observed proportions do not generally identify source proportions and capture probabilities separately. For each type, the observed data depend on the product \(\pi_{gk}q_{gk}\), followed by normalization. Different combinations of source composition and capture probabilities can therefore yield the same captured composition. More cells can reduce uncertainty about \(r_{gk}\), but cannot resolve this structural ambiguity.

For two types, the relationship is especially clear in odds form:

The observed odds combine source odds with relative capture probability. Unless the relative capture probability is known or constrained, the source odds cannot be recovered from the observed odds alone.

The correction assumes that the calibration applies to the samples being analyzed, that the relevant cell types are represented in the calibration, and that capture probabilities are positive. If a type has zero probability of capture, its source proportion cannot be recovered from captured cells by inverse weighting. If the probabilities are estimated rather than known, uncertainty in those estimates should also be reflected in uncertainty about the corrected proportions.

Comparing Conditions: Stable and Changing Capture

Whether capture bias cancels in a comparison depends on the contrast and on how capture probabilities behave across conditions. If \(q_{gk}=q_k\) is the same in every condition, pairwise observed log-ratios have a useful property:

Comparing this log-ratio between two conditions cancels the fixed capture term. Therefore, the change in the pairwise log-ratio equals the change in the source pairwise log-ratio, under the model and stable relative capture. This does not mean that the observed percentages themselves equal the source percentages, or that every summary of them is unbiased. If capture probabilities vary by condition, an additional capture term remains in the contrast.

Diagnostics, Alternatives, and Limits

Capture bias is difficult to diagnose from the captured composition alone, because that composition is the quantity jointly shaped by source proportions and capture. Useful evidence must therefore come from design information or independent measurements. Relevant checks include whether sample handling, dissociation, viability, sorting, and loading procedures were comparable across conditions; whether cell-type recovery differs in technical controls; and whether calibration material provides type-specific capture estimates that apply to the study samples. These checks can reveal concerns, but a lack of visible imbalance does not prove equal capture.

There are three practical approaches, each answering a different question:

A differential-abundance test can quantify sampling uncertainty in observed proportions, but a small p-value does not establish that a difference is biological rather than induced by condition-specific capture. Similarly, a large number of captured cells cannot compensate for missing calibration when the target is the source composition. If capture probabilities are believed stable, that belief should be justified by the protocol and supporting evidence; it is an assumption, not a consequence of observing similar sample processing.

A common mistake is to reason, “Type A is rare among captured cells, so it must be rare in the tissue,” or, “Both conditions used the same assay, so capture bias cancels.” The first ignores type-specific capture. The second is too broad: stable capture can preserve certain pairwise log-ratio contrasts, but does not make observed proportions equal to source proportions; condition-specific differences in survival or recovery can also invalidate the cancellation. State the target explicitly and describe conclusions as applying to the captured assay composition when source-level calibration is unavailable.