Defining Donor-Population Estimands

Why the Target Must Be Named

A single-cell data set contains measurements from cells, but the scientific question often concerns people. An average computed by pooling every cell answers a different question from an average that first summarizes each donor and then gives every donor equal weight. Neither is universally correct. The choice depends on the population and sampling process the analysis is intended to describe.

An estimand is the precisely defined quantity a study aims to learn about. For donor-level single-cell studies, its definition should name the outcome and scale, the target cell population, the donor population, and the way donors or cells are weighted. It should also distinguish a population average from a prediction about one future donor.

The outcome might be expression on a specified transformed scale, a gene-detection indicator, or another cell-level quantity. The meaning of a mean depends on that choice: a mean on a log scale is not generally the log of a mean on the original scale. The target cell population matters too. For example, a mean among cells classified as one cell type is not automatically a mean among all cells in a tissue.

Three Targets, Three Questions

Suppose donors are drawn from a target donor population with distribution \(F_D\). For each donor \(D\), let \(\theta_D\) be the mean outcome for that donor’s target cells. The following targets separate the average donor, an average cell under a sampling design, and a new donor.

This target asks, “What is the mean donor-specific outcome for a donor selected uniformly from the population?” Equal donor weighting is appropriate when the scientific unit is the donor and the intended population is people, even if the number of captured cells differs across people.

A cell-weighted target instead starts from a rule for selecting a cell. If donor \(j\) contributes \(n_j\) sampled cells, the mean among those sampled cells is \(\sum_j n_j\bar{Y}_j/\sum_j n_j\), where \(\bar{Y}_j\) is the mean of the sampled outcomes for donor \(j\). This describes the observed cell collection, not necessarily a broader biological population. Donors with more sampled cells contribute more weight.

Here \(q_D\) represents the donor’s expected contribution under the stated design; it could reflect capture and sampling, not just the number of cells biologically present. If the scientific question is instead about a cell selected uniformly from the biological cell population, the weighting must reflect the number of eligible cells in each donor, not merely the number sequenced. Those weights can differ when cell abundance, tissue processing, or capture efficiency varies.

Finally, a new-donor target concerns the outcome for a donor not yet observed. Let \(\theta_{\mathrm{new}}\) be the donor-specific mean for a new donor drawn from the target population. Its distribution describes donor-to-donor variation; the outcome or mean for that particular new donor is not the same quantity as the population average.

Thus the expected value for a new donor equals the average-donor estimand when the new donor is drawn from the same population. The targets remain distinct: one is a population mean; the other asks what to expect for a particular unobserved donor, including the uncertainty that donor-to-donor variation creates. A prediction for one donor should not be described as though it were only an estimate of the population mean.

How Weighting Changes the Target

The distinction follows directly from the selection rule. Selecting a donor uniformly and then selecting one of that donor’s eligible cells gives each donor equal weight before the cell is chosen. Selecting one cell from a pooled collection gives a donor more chance of selection when that donor contributes more cells. The latter is a size-weighted selection.

For fixed donors and weights, the second expression is a weighted average of donor means. If all \(q_j\) are equal, it reduces to the equal-weight donor average. If they differ, the cell-weighted target generally differs. At the population level, the same argument gives \(E_D(q_D\theta_D)/E_D(q_D)\): donors with larger \(q_D\) have greater probability of supplying the selected cell.

This identity assumes that the weights describe the selection rule and that \(\theta_j\) is the mean outcome for cells selected from donor \(j\) under that rule. If capture is outcome-dependent within donors, the sampled-cell mean may not represent the intended cell population even after accounting for donor weights. The sampling mechanism therefore belongs in the estimand’s definition, not just in a later technical note.

Average Effects and the New-Donor Question

The same distinctions apply to comparisons. For a two-condition question, let \(\theta_j(1)\) and \(\theta_j(0)\) be the target-cell means for donor \(j\) under conditions 1 and 0, on the same outcome scale. Define the donor-specific contrast as \(\tau_j=\theta_j(1)-\theta_j(0)\). An average-donor contrast is \(E_D(\tau_D)\). It gives equal weight to donors in the target population and, where both conditions are defined for the same donor, averages within-donor contrasts.

A contrast between pooled cell means may use different cell weights in the two conditions. It therefore need not equal the average of donor-specific contrasts. The two quantities can answer different questions, even if both are calculated correctly. Before interpreting a contrast, specify whether the population is donors or sampled cells and whether the weighting rule is the same across conditions.

Assumptions, Diagnostics, and Limitations

An estimand is defined by the target, but estimating it from data requires that the observations and sampling process support that target. A donor-population average is most directly interpreted for a specified population of donors, not automatically for every patient group or setting. A new-donor prediction requires that the future donor be comparable to the population from which the study donors were drawn. These are substantive assumptions about the target population and transportability.

For cell-level observations to represent a donor’s target-cell mean, the cells must be sampled or modeled in a way appropriate to the stated cell population. If certain cells are more likely to be captured because of their state or outcome, the observed mean can be shifted. If donor cell counts vary, inspect whether the variation is part of the intended target (for example, abundance-weighted sampling) or a feature of collection and capture. A cell count should not silently determine donor weights.

• Check the denominator and weights. Record the number of donors and the number of cells contributed by each donor. Recalculate the stated target using its intended weights.
• Check the sampling interpretation. Ask whether a donor was selected uniformly, a cell was selected from a pooled collection, or a source-population cell was selected. These are different selection rules.
• Check the target population. State which donors, tissue, condition, cell type, and measurement scale the estimand concerns. A change in any of these can change the target.
• Check donor coverage. A sample with many cells but few donors may describe its observed cells in detail while providing limited coverage of the donor population.

No one weighting rule is always preferable. Equal donor weighting is natural for a typical-donor question; weighting by sampled cells is appropriate for a sampled-cell question; weighting by biological cell abundance is relevant to a source-population cell question when abundance is known or appropriately estimated. A new-donor prediction additionally concerns between-donor variation, not merely the average outcome. These choices define the scientific question; they do not by themselves guarantee that a particular estimator or uncertainty calculation is valid.

A Practical Specification

A concise estimand statement can prevent ambiguity before analysis begins. For example: “The target is the mean log-scale expression among a specified cell type for a donor selected from the stated patient population, with donors equally weighted.” For a cell-level target, replace the donor selection rule with an explicit description of how the cell is selected and how donor contribution is determined.

Common Mistake

Wrong reasoning: “There are many more cells from donor B, so the pooled mean is the best estimate of the average donor.” This confuses the number of observed cells with the intended donor weights. More cells from B may improve information about B’s mean, but that fact does not mean B should count as more than one donor for an average-donor target.

Correction: Write down the target first. For an equal-weight average-donor target, each donor’s mean receives equal weight. For a sampled-cell target, sampled cells determine the weights. For a new-donor prediction, describe the donor-specific distribution as well as its mean. Then check whether the study’s donor selection and cell-sampling process support that target.