Allocating Cells Across Donors

Why Cell Allocation Is a Design Decision

A single-cell experiment can yield many thousands of measured cells without providing many independent biological replicates. For a condition comparison, cells from the same donor tend to resemble one another because they share biological and technical characteristics. Consequently, increasing the number of cells from a donor improves the estimate for that donor, but it does not create another independent donor. The design question is not simply how many cells to sequence: it is how to distribute them across donors while preserving enough independent replication to estimate condition differences.

The earlier material on intraclass correlation and effective sample size established why within-donor dependence reduces the information in a cell count. Here the focus is allocation: how donor-level and cell-level variation combine when donors contribute the same or different numbers of cells, and when additional donors can be more valuable than deeper sequencing.

A Donor-Level Variance Model

Consider one condition and one prespecified cell population. Let \(Y_{ij}\) be a continuous expression summary for cell \(j\) from donor \(i\), such as a suitably transformed expression measurement. A simple random-intercept model is

Here \(\mu\) is the condition mean, \(b_i\) is the donor-specific deviation, and \(\epsilon_{ij}\) is cell-level variation around that donor's value. Assume that donors are independent, cell residuals are independent conditional on their donor effects, and donor effects and residuals are mutually independent. For this basic calculation, also assume the same variances apply across donors and conditions, cell counts are fixed by design, and the outcome is measured comparably across donors. These are planning assumptions, not guarantees about real data.

The donor mean contains the donor effect \(b_i\) plus the average of \(m_i\) cell residuals. Under the model, its variance is \(\tau^2+\sigma^2/m_i\). Thus, more cells reduce the residual component, but the donor component remains. With the same number \(m\) of cells from each donor, the variance of the equal-donor-weighted condition mean is \((\tau^2+\sigma^2/m)/n\).

For two independent conditions with \(n\) donors in each, the estimated difference in condition means has variance \(2(\tau^2+\sigma^2/m)/n\), when both conditions have the same allocation and variance components. Its standard error is the square root of that variance. This formula makes the design tradeoff explicit: increasing \(m\) reduces only \(\sigma^2/m\); increasing \(n\) reduces both components by averaging over more independent donors.

Unequal Cell Counts Across Donors

If donors contribute different numbers of cells, an equal-donor-weighted condition mean has variance

Each donor contributes one donor mean to the condition mean, regardless of how many cells they supplied. This avoids allowing a high-yield donor to dominate the estimate, but a donor with few cells has a less precise donor mean. The formula accounts for that difference through \(1/m_i\).

For a fixed number of donors and a fixed total cell count \(M=\sum_i m_i\), with positive integer cell counts, \(\sum_i 1/m_i\) is minimized by an allocation whose counts differ by at most one. If \(M\) is divisible by \(n\), this is equal allocation. A lower bound follows from the Cauchy–Schwarz inequality:

Therefore \(\sum_i 1/m_i\geq n^2/M\), with equality when all \(m_i=M/n\), which is possible only when \(M\) is divisible by \(n\). If \(M\) is not divisible by \(n\), the integer minimum is attained by counts differing by at most one: if two counts \(a\) and \(b\) satisfy \(b\geq a+2\), moving one cell from the larger count to the smaller decreases their reciprocal sum, since \(\frac{1}{a}+\frac{1}{b}-\frac{1}{a+1}-\frac{1}{b-1}=\frac{1}{a(a+1)}-\frac{1}{b(b-1)}>0\). Thus, for a fixed total number of cells and fixed donor count, no other integer allocation can improve the variance of the equal-donor-weighted mean under this model. The donor variance term, \(\tau^2/n\), is unaffected by how those cells are distributed.

When More Donors Beat More Cells

A useful comparison holds the total cell count per condition fixed while changing its allocation. Suppose a hypothetical design can use either 12 donors with 20 cells per donor or 6 donors with 40 cells per donor. Each uses 240 cells per condition. Under the model, the first design has more independent biological replicates; the second estimates each sampled donor's mean more precisely. Which is better depends on the relative sizes of \(\tau^2\) and \(\sigma^2\), as well as the effect being studied.

Assumptions, Diagnostics, and Alternatives

The calculations are only as useful as their assumptions. They treat the analyzed population, outcome scale, donor variance, cell variance, and target effect as sufficiently stable for planning. They also presume the chosen donors represent the target population, conditions are not confounded with batch or other donor characteristics, and a donor contributes a meaningful estimate of the same outcome as other donors. If cell yields vary because of biological abundance or sample quality, the observed \(m_i\) may be informative rather than a design-only quantity.

Before relying on an allocation calculation, inspect a donor-by-condition table of usable cell counts for the target cell population, not just total cells captured. Check for donors with very low counts, large differences in cell-type composition, or cells concentrated in a small number of donors. Review whether condition and processing batch are aligned, and whether any donor has unusual quality metrics. These checks do not prove the variance model, but they can reveal allocation or measurement problems that make its assumptions implausible.

The equal-donor-weighted summary is one estimand and one analysis strategy. A cell-pooled mean weights donors in proportion to their cell counts, which may be appropriate for a different target but can make high-yield donors disproportionately influential. A donor-level analysis instead treats donor summaries as the replication units. A mixed-effects analysis can represent donor clustering directly while retaining cell-level observations, but it still needs a defensible model for donor variation and does not turn correlated cells into independent donors. Choice among these approaches should follow the scientific target and analysis model, not whichever one yields the smallest standard error.

The normal-approximation power values above are illustrative. With a small number of donors, estimating variance components adds uncertainty and a normal critical value can overstate power. Also, a single variance model may not capture gene-specific variability, cell-type-specific yield, or non-normal outcomes. When these features materially affect the design, a richer design-specific power analysis is needed rather than mechanically applying the simplified formula.

Common Allocation Mistakes

• Counting cells as independent biological replicates. A study with thousands of cells but few donors does not have thousands of independent donors. Account for within-donor dependence in the analysis and planning.
• Assuming deeper sequencing keeps reducing uncertainty at the same rate. The term \(\sigma^2/m\) shrinks as \(m\) grows, but the donor contribution \(\tau^2\) remains.
• Using only the average cell count when allocation is highly uneven. For an equal-donor-weighted mean, the cell-level contribution depends on \(\sum_i 1/m_i\), not only on the average.
• Treating balanced allocation as a universal optimum. It minimizes the stated sampling variance for fixed donors and cell total under this model; cost, cell-type yield, donor importance, and other scientific objectives may change the practical design.