Unequal Cell Numbers Across Pseudobulk Samples

Why Unequal Cell Numbers Matter

A pseudobulk sample is formed by summing the counts for a chosen cell type across cells belonging to a biological sample, such as a donor-condition combination. If one pseudobulk contains 80 cells and another contains 800, their raw gene counts will often differ even when their per-cell expression is similar. That difference can reflect a larger cell pool, greater sequencing depth, or both; it is not automatically a biological expression change.

Unequal cell numbers also affect how precisely a sample represents its underlying cell population. More cells can reduce the noise from sampling cells within a sample, but they do not create additional independent donors or biological samples. Correct interpretation therefore requires separating two sources of information: cells contribute to the quality of each pseudobulk measurement, while biological replicates provide information about variability between biological samples.

How Cell Number Can Affect Precision

A simple model shows the within-sample effect. Suppose the count for gene \(g\) in each of \(m_i\) sampled cells is independent, with per-cell mean \(\lambda_g\) and variance \(\tau_g^2\). The pseudobulk sum is the sum of those cell counts. Its expected value and variance are

Dividing the sum by the number of cells gives a per-cell average with variance \(\tau_g^2/m_i\). Under these assumptions, increasing the cell count improves the precision of that sample's estimated per-cell expression. This is a within-sample sampling result: it does not say that cells are independent biological replicates, nor that real cells from the same donor are necessarily independent.

In practice, cells from one biological sample share conditions and biological influences. A useful illustrative decomposition for a per-cell sample summary is

Here, \(\sigma^2_{\mathrm{within},g}\) represents cell-level sampling variation, while \(\sigma^2_{\mathrm{between},g}\) represents variation between biological samples. This decomposition is an idealization, not a universal pseudobulk variance model. Its important implication is that adding cells can reduce the second term but cannot remove the between-sample term. Once within-sample uncertainty is small relative to between-sample variation, collecting still more cells has diminishing returns.

Library Size, Cell Count, and the Pseudobulk Model

Let \(L_i\) denote the library size used for pseudobulk sample \(i\), such as its total retained read or count total under the analysis pipeline. In a common negative binomial pseudobulk model, the gene count has mean \(\mu_{gi}\), and

Here \(\phi_g\) is the gene-specific dispersion. The model typically relates the mean to biological condition and other sample-level design variables, while a library-size offset accounts for differences in sequencing exposure. In a log-link formulation, this is written

The offset is a known exposure term; \(\mathbf{x}_i\) contains the modeled sample-level predictors, and \(\boldsymbol{\beta}_g\) contains their gene-specific coefficients. In practice, normalization may use an effective library size that combines the observed library size with a normalization factor. The point is to compare expression after accounting for sequencing exposure and compositional effects, rather than to compare raw sums alone.

Cell number and library size are related but not interchangeable. If sequencing depth per cell is broadly similar, a sample with more cells may have a larger library. But library size also depends on sequencing allocation, capture efficiency, RNA content, filtering, and the mixture of cell states. Conversely, libraries may be sequenced to similar depths despite very different numbers of cells. Therefore, adding \(m_i\) as an offset in addition to a library-size offset is not automatically justified: it can adjust for the same exposure twice or impose an inappropriate per-cell interpretation.

Derivation: Why More Cells Do Not Replace More Replicates

Suppose there are \(n\) independent biological samples in a group. For each sample, imagine a per-cell summary \(Z_i\) with between-sample variance \(\sigma^2_{\mathrm{between}}\) and within-sample variance contribution \(\sigma^2_{\mathrm{within}}/m_i\). If the sample summaries are independent across biological samples, the variance of their group average is the variance of a sum of independent terms divided by \(n^2\):

Increasing \(m_i\) reduces the within-sample contribution, the second term. Increasing \(n\) reduces the between-sample contribution, the first term, as well as the within-sample contribution to the group average. This derivation relies on independent biological samples and the stated variance model. It makes precise why a very large cell count in a small number of samples cannot generally substitute for more independent biological samples.

Practical Checks and Alternative Choices

Unequal cell numbers are not automatically a defect. They become concerning when small pseudobulks poorly represent the target population, when cell recovery is related to condition or sample quality, or when the resulting library sizes and precision differ substantially. Review cell counts alongside library sizes, sequencing depth, sample identities, and the distribution of cells across relevant conditions. If low cell counts occur mostly in one condition, cell count may be entangled with condition, and a simple adjustment cannot guarantee unbiased inference.

The main options address different issues:

A cell-count offset is appropriate only when the scientific model specifies that expected counts are proportional to cell number, the proportionality is meaningful for the target quantity, and relevant sequencing exposure is handled consistently. For ordinary pseudobulk differential expression, library-size normalization is central; cell count should not be inserted as an additional offset by reflex. If the target is expression per cell and cell count is a meaningful exposure, that modeling choice needs to be explicit and compatible with how counts were generated and normalized.

Cell number can also signal a change in cell composition or capture. A pseudobulk sum combines the cells assigned to that sample and cell type; if the mix of subtypes changes, a shift in the aggregate may reflect that mixture as well as within-subtype expression. More cells can estimate the mixture more stably, but cannot make different mixtures equivalent. The interpretation must match the analyzed population and the pseudobulk construction.

Common Mistakes and Limitations

• Counting cells as independent biological replicates. This treats cells from the same donor as independent evidence about donor-to-donor variability. The correction is to identify the biological sample as the replicate unit for the pseudobulk comparison.
• Assuming twice as many cells means twice the precision. Under independent cell sampling, the variance of a mean scales as \(1/m_i\), so standard error scales as \(1/\sqrt{m_i}\); real data may have additional shared variation.
• Using cell count as an offset automatically. This imposes a proportional relationship and can double-adjust exposure when library size is already used. Justify the estimand and offset rather than inferring the choice from unequal counts alone.
• Interpreting a larger raw count as higher expression. Raw pseudobulk counts depend on library size and cell number. Interpret modeled effects after appropriate normalization and in light of composition.
• Assuming equal cell subsampling solves imbalance. Equalizing cell counts may help assess sensitivity to representation, but it loses observations and does not create additional donors or remove confounding.

These principles are most useful when planning collection and interpreting uneven data. The precision gained from additional cells is finite and depends on how representative those cells are; biological replication remains necessary to assess how effects vary across the population of interest.