Donor Count Versus Cell Count

Two Counts, Two Sources of Information

A single-cell study may measure thousands of cells while including only a small number of donors. These are not interchangeable forms of replication. Cells provide information about the sampled donors and can reduce uncertainty from measuring only a subset of their cells. Donors provide independent biological replication for learning about variation across the donor population. The distinction matters whenever a conclusion is intended to apply beyond the particular people whose cells were sequenced.

Let \(D\) be the number of independently sampled donors, and let \(m\) be the number of measured cells per donor in a balanced design. The total number of cells is \(N_{\text{cell}}=Dm\), but \(N_{\text{cell}}\) is not the number of independent biological replicates. A study with 4 donors and 100 cells per donor has 400 measured cells and 4 biological replicates.

The introductory material on biological replicates versus technical replicates distinguishes biological variation from repeated measurement. Here the focus is quantitative: how do the two counts enter uncertainty? To answer, first specify the population target and a model that represents both levels of variation.

A Two-Level Model for Donors and Cells

Suppose \(X_{ij}\) is a numerical measurement for cell \(j\) from donor \(i\), such as an expression measurement on a chosen scale. Consider the balanced random-intercept model

Here \(\mu\) is the population mean on the specified measurement scale, \(b_i\) is the deviation of donor \(i\) from that population mean, and \(e_{ij}\) is the cell-level deviation within that donor. Assume donors are independent draws from the target donor population, with \(E(b_i)=0\) and \(\operatorname{Var}(b_i)=\tau^2\). Conditional on the donor effects, assume the cell deviations have mean zero, variance \(\sigma^2\), are independent across cells, and are independent of the donor effects. For this simple model, assume the same \(m\), \(\tau^2\), and \(\sigma^2\) for all donors.

These assumptions are a working model, not a guarantee about real data. They exclude, for example, unmodelled batch structure that aligns with donor, systematic differences in cell sampling, and additional dependence among cells beyond their shared donor effect. They also presume that the donors represent the population to which the conclusion is intended to apply. A large number of cells cannot correct a donor sample that is systematically unrepresentative.

Why the Variance Has a Donor Component

The result follows by accounting for the covariance between cells from the same donor. Define the overall cell mean by \(\bar X_{\text{cell}}=(Dm)^{-1}\sum_{i=1}^{D}\sum_{j=1}^{m}X_{ij}\). Two cells from the same donor share \(b_i\), so their covariance is \(\tau^2\). Cells from different donors have covariance zero under the independence assumptions. A direct decomposition makes the contributions explicit.

The donor effects are independent across donors, so the variance of their average is \(\tau^2/D\). There are \(Dm\) independent cell deviations, each with variance \(\sigma^2\); their average therefore has variance \(\sigma^2/(Dm)\). The two terms are uncorrelated by assumption, so their variances add:

This derivation identifies exactly what each count can improve under the model. More cells per donor reduce the second term by estimating the sampled donors' cell distributions more precisely. They do not create additional independent draws of \(b_i\). Adding donors reduces the donor term and also adds cells if \(m\) is held fixed.

What the Counts Do—and Do Not—Tell You

The model gives a useful comparison, but it does not imply that donor count is the only relevant quantity in every analysis. If \(\tau^2=0\) under this model, there is no between-donor variation in the measured outcome, and the variance reduces to \(\sigma^2/(Dm)\). In that special case, cell measurements directly reduce the modeled sampling variance. In biological settings, however, assuming no donor-to-donor variation requires substantive justification; it should not be inferred merely from a large cell count.

Conversely, a small number of donors leaves population-level conclusions fragile even when each donor contributes many cells. Those cells can characterize the included donors in detail, but they cannot reveal how variable a wider population of donors would be as reliably as additional independent donors can. The target population also matters: donors selected from one clinical setting may not represent a broader population, regardless of the number of cells profiled.

A cell-independent calculation treats the \(Dm\) observations as if each were an independent draw from the donor population. Under the model, that is incorrect whenever \(\tau^2>0\), because within-donor cells share a donor effect. The earlier material on effective sample size and the cluster design effect addresses related consequences of this dependence. The practical lesson here is to report both \(D\) and the distribution of cells across donors, rather than presenting the total cell count as a proxy for biological replication.

Diagnostics and Common Pitfalls

Before interpreting a donor-versus-cell calculation, check whether the design and assumptions make it meaningful. Useful questions include:

• Are donors genuinely independent? Related donors, repeated samples from the same person, or repeated visits may create additional dependence that is not represented by the simple model.
• Are cells sampled comparably? Cell capture and quality filtering can differ by donor or cell type. The simple balanced model assumes comparable cell sampling and equal cell counts.
• Could processing be confounded with donor? If each donor is processed in a distinct batch, donor and batch differences may be difficult or impossible to separate.
• Is the target population represented? A large \(D\) is valuable only insofar as the donors are relevant to the population for which the conclusion is intended.
• Is there evidence of donor-level heterogeneity? Strong differences across donor measurements are a warning against interpreting the cells as independent population replicates. Estimated variance components also need cautious interpretation when \(D\) is small.

A common mistake is to reason, “There are 10,000 cells, so the study has 10,000 independent replicates and must have very small population uncertainty.” The correction is to identify the independent biological units first. If those cells come from 5 donors, the study has 5 independent donor replicates; the cells can improve measurement within those donors but do not become 10,000 independent donors.

The main alternatives answer different questions. A cell-independent calculation ignores within-donor dependence and can give unjustifiably small uncertainty for a donor-population target. A hierarchical model represents both donor and cell variation, as the variance decomposition here illustrates. Approaches based on donor-level data instead make the donor the unit of analysis; how to construct those summaries and carry out inference from them requires additional decisions beyond counting donors and cells. No approach can compensate for a mismatch between the chosen population target and the actual donor sampling process.