Donor Recruitment and Population Coverage

Why recruitment determines what a study can speak about

Single-cell assays may produce many cells and measurements, but the biological replicates for a donor-level comparison are the donors. Recruiting more cells from a narrow set of donors does not make that set representative of a broader population. Recruitment therefore affects both the precision of a comparison and the population to which its results can reasonably apply.

The first decision is not how many donors to sequence. It is which people the study is intended to describe, what makes someone eligible, and how those people can be reached. These choices should be consistent with the target comparison and estimand. If eligibility rules exclude a group, then the resulting inference does not automatically apply to that excluded group.

Definition: The target population is the set of people to which the study aims to apply its conclusions. Eligibility criteria specify which members can participate. A sampling frame is the operational list or system from which potential participants can be identified and approached. Coverage describes how much of the target population is represented in that frame; it is not the same as the number of people enrolled.

A frame may be incomplete, out of date, or include people outside the target population. Thus, a frame count divided by an estimated population count is not automatically a coverage rate. The numerator must be the number of unique target-population members actually present in the frame, and the denominator must refer to the same target population and time period. If overlap is unknown, coverage is unknown; counts alone do not establish it.

Define the target and eligibility before recruitment

A useful recruitment plan states the target population in concrete terms: geography, age range, clinical definition, relevant time period, and any other feature that determines membership. Eligibility rules should be justified by the scientific question or practical and ethical constraints, not added casually because one group is harder to recruit. If the question concerns adults with a condition in a defined region, for example, excluding older adults for convenience narrows the population the study can represent.

In a condition comparison, describe the population for each condition group and the source of potential donors in each group. Recruitment should not produce condition groups that differ sharply in characteristics such as age or site merely because one group was easier to find in a particular recruitment channel. This does not mean forcing identical samples in every study; it means identifying important dimensions in advance and ensuring that the recruitment process does not silently redefine the comparison.

Worked Example: Calculating Coverage From Known Overlap

Suppose the target population is 1,000 adults with a specified diagnosis who live in a region during a defined year. A registry contains 720 people. A record linkage and eligibility review establish that 600 registry members are unique members of this target population; the other 120 are out of region or do not meet the diagnosis definition. What is the registry's coverage of the target?

The coverage numerator is 600, not the registry count of 720, because only 600 are confirmed members of the target population. With the target count of 1,000 defined for the same region and year, the coverage is

\text{Coverage}=\frac{600}{1{,}000}=0.60=60\%.

Thus, 60% of the defined target population is known to appear in the registry. The remaining 400 target members are not represented there, although they might be reachable through another source. This calculation does not show that the 600 are a random or representative subset: the people missing from the registry may differ systematically from those listed. If the overlap had not been established, dividing 720 by 1,000 would only compare two counts, not estimate coverage.

Stratify recruitment to expose gaps

A recruitment stratum is a prespecified category used to organize the approach to sampling—for example, age group, geographic area, or recruitment site. Stratification can make gaps visible and support recruitment targets for groups that would otherwise be scarce. It does not, by itself, make participants representative. The method used to select or invite people within each stratum still matters, and the chosen strata should reflect the target population and scientific comparison.

For a population divided into \(H\) mutually exclusive and exhaustive strata, let \(N_h\) be the number of target-population members in stratum \(h\), and let \(N=\sum_{h=1}^H N_h\). The target proportion in stratum \(h\) is \(W_h=N_h/N\). If the study enrolls \(n_h\) donors in that stratum, the sample proportion is \(n_h/n\), where \(n=\sum_h n_h\). When sample and target proportions differ, an unweighted donor average generally describes the recruited sample, not the target population.

Stratified target mean: If \(Y\) is a donor-level quantity and the target mean in stratum \(h\) is \(\mu_h\), then the target-population mean is \(\mu=\sum_{h=1}^H W_h\mu_h\). If donors are sampled representatively within each stratum, a corresponding estimator is \(\hat{\mu}_{\mathrm{str}}=\sum_{h=1}^H W_h\bar{y}_h\), where \(\bar{y}_h\) is the sample mean in stratum \(h\). This requires known or defensibly estimated target stratum proportions and observations from every stratum with positive target weight.

The reason for weighting is direct. Under representative sampling within each stratum, the expected sample mean \(\bar{y}_h\) is \(\mu_h\). Therefore,

E(\hat{\mu}_{\mathrm{str}}) =E\left(\sum_{h=1}^H W_h\bar{y}_h\right) =\sum_{h=1}^H W_hE(\bar{y}_h) =\sum_{h=1}^H W_h\mu_h =\mu.

This justifies the estimator under its stated conditions; it does not guarantee those conditions hold in a real recruitment process. In particular, weighting cannot reconstruct outcomes for a target stratum that has no enrolled donors, and it cannot correct selection within a stratum when the chance of participation is related to the outcome in an unmeasured way.

Worked Example: Correcting an Oversampled Stratum

A hypothetical target population is 70% urban and 30% rural. To ensure rural donors are included, a study recruits 20 urban and 20 rural donors. For a donor-level cell-type proportion, the urban sample mean is 0.12 and the rural sample mean is 0.20. Assume the target proportions are known and recruitment is representative within each stratum. What target mean is estimated?

The sample gives equal weight to the two strata, but the target does not. The unweighted sample mean is

\bar{y}=\frac{20(0.12)+20(0.20)}{40} =\frac{2.4+4.0}{40}=0.16.

This is the recruited-sample mean. The target-weighted estimate is

\hat{\mu}_{\mathrm{str}}=0.70(0.12)+0.30(0.20) =0.084+0.060=0.144.

The estimate is 0.144, or 14.4% of the relevant cells on the stated donor-level scale, for the target population under the assumptions above. The rural group was intentionally oversampled, which can be useful for obtaining information about it; weighting returns the overall estimate to the target's 70:30 urban-rural composition. If urban and rural recruitment within their strata was itself selective, this calculation would not remove that bias.

Condition-related selection can distort a comparison

Recruitment is especially consequential when the scientific comparison is between conditions. Suppose condition and age are both related to the donor-level outcome. If the condition group is recruited mostly from older adults and the comparison group mostly from younger adults, the observed difference combines condition differences with age-composition differences. This is a selection and comparability problem; merely having many donors does not resolve it.

A practical plan lists the important strata and tracks, by condition, the number eligible, approached, consenting, and enrolled. These counts help distinguish a gap in the target population or frame from a gap introduced during contact or consent. Recruitment targets can be set to ensure that each relevant condition-by-stratum group is represented. Targets should be based on the intended population and comparison, rather than set after observing which groups happen to be easiest to enroll.

Worked Example: A Condition Difference With Unequal Age Composition

Consider a hypothetical target divided equally between younger and older adults. Within each age group, the donor-level outcome mean is 0.10 for condition A and 0.14 for condition B. Assume, for illustration, that these age-specific means are the same in the target and that recruitment is representative within each condition-by-age group. A convenience sample contains 80% younger adults in A but only 20% younger adults in B. Calculate the unadjusted sample difference and the age-standardized difference using the target's 50:50 age distribution.

For condition A, the unadjusted mean is

$$ 0.80(0.10)+0.20(0.10)=0.10. $$

For condition B, it is

$$ 0.20(0.14)+0.80(0.14)=0.14. $$

Here the within-age means happen to be constant across age, so the sample difference is \(0.14-0.10=0.04\). To see why recruitment composition must still be checked, consider a more realistic set of age-specific means: A has 0.08 among younger and 0.12 among older donors; B has 0.12 among younger and 0.16 among older donors. The target-standardized means are

\hat{\mu}_{A,\mathrm{std}}=0.50(0.08)+0.50(0.12)=0.10, \qquad \hat{\mu}_{B,\mathrm{std}}=0.50(0.12)+0.50(0.16)=0.14.

The target-standardized difference is \(0.14-0.10=0.04\). Under the stated convenience-sample compositions, the unadjusted means instead are

\bar{y}_A=0.80(0.08)+0.20(0.12)=0.088, \qquad \bar{y}_B=0.20(0.12)+0.80(0.16)=0.152,

giving an unadjusted difference of \(0.152-0.088=0.064\). The difference is larger because condition B has more older donors and older donors have higher outcomes in this hypothetical setup. Standardization addresses the specified age-composition difference; it does not establish a causal condition effect or correct unmeasured selection.

Diagnostics, alternatives, and limitations

Recruitment should be monitored against the plan, not assessed only after sequencing. Useful diagnostics include the proportion of the target population covered by each frame source, the condition and stratum counts at each recruitment stage, the distribution of key characteristics among enrollees compared with the best available target data, and the number of target strata with no donors. A large discrepancy between target and enrolled composition is a warning that an unweighted result may describe the enrolled group rather than the intended population.

Possible responses depend on the problem. A broader frame or additional recruitment source may improve coverage. Stratified recruitment can ensure inclusion of groups likely to be missed. If the target stratum proportions are known and each stratum is adequately represented, standardization or weighting can address intentional oversampling. These options have different requirements: broader recruitment improves reach; stratification organizes enrollment; weighting changes how observed strata contribute to a summary. None is a substitute for clear eligibility definitions and reliable information about who could have been recruited.

When participation probabilities are unknown, outcome-related nonparticipation can leave selection bias unidentified from the enrolled sample alone. Large weights for very small or sparsely recruited strata can also make estimates unstable. If a target group has no enrolled donors, a weighted overall estimate requires assumptions or information beyond the observed sample. Report that limitation rather than implying that a numerical correction has restored representation.

Common mistake: “The frame lists 8,000 people and the target population is estimated at 10,000, so coverage is 80%.” This is not justified unless all 8,000 are confirmed unique members of that same target population. A frame can include ineligible people, omit eligible people, or overlap the target in an unknown way. Establish the overlap and definitions first; otherwise report the counts and state that coverage cannot be calculated from them.

A further pitfall is treating equal numbers in each condition as proof of representative recruitment. Equal condition counts may help the planned comparison, but they say nothing by themselves about whether each condition group represents its target population or whether relevant strata have been included. The recruitment report should state the target, frame sources, eligibility rules, observed recruitment by condition and stratum, and any standardization assumptions.

Check Your Understanding

Answer each question, then compare with the solutions below.

A target population has 2,000 people. A registry lists 1,500, but overlap with the target has not been checked. Can coverage be reported as 75%? What additional fact is needed?
A target population is 80% urban and 20% rural. A study recruits 30 donors from each group. What weights should be used for an overall stratified mean?
Why can recruiting the same number of donors in two conditions fail to prevent a misleading comparison?
A target stratum has positive population weight but no enrolled donors. Can ordinary post-stratification calculate its contribution from the observed data alone?

Solutions. (1) No. The count of registry members who are unique members of the defined target population is needed; if it is unknown, the overlap and therefore coverage are unknown. (2) Use weights 0.80 for the urban mean and 0.20 for the rural mean, so the estimate is \(0.80\bar{y}_{urban}+0.20\bar{y}_{rural}\). Equal recruitment counts do not change the target proportions. (3) The condition groups may still have different age, site, or other relevant compositions, and recruitment may select different kinds of donors within each condition. Equal totals do not ensure comparable or representative composition. (4) No. The stratum's outcome mean is unobserved, so its weighted contribution cannot be estimated by ordinary post-stratification without additional data or assumptions.