Why Transparent Replication Reporting Matters
A single-cell dataset may contain thousands of cells but only a small number of donors. Those two counts describe different things: the number of measured cells and the number of biological units contributing independent information about variation between people. Reporting only a large cell total can therefore make the evidence seem more replicated than it is. A reader should be able to tell which units support the scientific comparison, how many cells came from each unit, and how the analysis accounted for dependence among cells from the same donor.
Transparent reporting is not just a matter of listing sample sizes. It connects the study design to the statistical uncertainty. In particular, the report should identify the unit that was independently sampled or assigned to a condition, give the number of such units in each group, describe the distribution of cells across them, and state how uncertainty was calculated. The introductory material on biological replication motivates the distinction between donors and cells; here the emphasis is on making that distinction auditable in a report.
What to Report
A useful report separates counts by design level rather than compressing them into one sample-size number. At minimum, state the number of donors enrolled, the number retained for each analysis, and the number in each condition or comparison group. If donors contribute to multiple conditions, say so and identify the pairing or repeated-measures structure. State exclusions and missing samples at the donor level, not only as a total number of discarded cells.
Then summarize cell yields at the level relevant to the analysis. Give the number of cells per donor after quality control, preferably by condition and by cell population when those populations are analyzed separately. A range and a median are concise; a table or donor-level listing is preferable when counts are highly uneven or when the exact allocation matters. Make clear whether the reported counts are before or after filtering, and identify the filters that changed the counts. Report both total cells and donor counts, but do not let the total-cell count stand in for replication.
The report should also name the inferential unit and explain how within-donor dependence was handled. Depending on the analysis, that explanation may describe donor-level summaries, a model that accounts for donor clustering, or a design-based procedure that respects donor-level assignment or sampling. State the outcome and estimand in understandable units, the method used to quantify uncertainty, and any relevant assumptions or degrees of freedom. If a model has donor-specific effects, describe the structure used rather than merely saying that the analysis was “donor-aware.”
Worked Example: Reporting Cell Yields Without Hiding Imbalance
Suppose a hypothetical study has four control donors and four treated donors. After quality control, the numbers of cells in the target population are 120, 150, 180, and 210 for the control donors, and 90, 130, 240, and 280 for the treated donors. Calculate the group totals and summarize the cell-count distribution.
For the control group, the total is \(120+150+180+210=660\) cells. The sorted counts are already in order; the median is \((150+180)/2=165\) cells, and the range is 120–210 cells. For the treated group, the total is \(90+130+240+280=740\) cells. The sorted counts are 90, 130, 240, and 280, so the median is \((130+240)/2=185\) cells, and the range is 90–280 cells.
A transparent report would state that there were four donors per group, with 660 control cells and 740 treated cells retained in the target population; donor-level cell counts ranged from 120 to 210 in controls (median 165) and from 90 to 280 in treated donors (median 185). It would also say how the cells were filtered and how the donor structure entered the analysis. The larger treated total does not mean that the treatment group has more independent biological replicates: both groups contain four donors.
Uncertainty Belongs at the Level of the Inference
A report should distinguish uncertainty about an individual donor’s measured value from uncertainty about a population-level quantity. For a population comparison, donor-to-donor variation is central. If an analysis first produces one contrast estimate per donor, the mean contrast and its uncertainty can be summarized across independent donors. This is different from treating every cell as an independent observation and computing uncertainty as though cells from the same donor were unrelated.
For illustration, suppose four independent hypothetical donors have donor-level treatment contrasts of 0.20, 0.40, 0.50, and 0.70 log2 units. The sample mean is 0.45 log2 units. The sample standard deviation is 0.2082 log2 units, giving a standard error of \(0.2082/\sqrt{4}=0.1041\) log2 units. With independent, approximately normally distributed donor contrasts, a two-sided 95% \(t\) interval uses \(df=4-1=3\) and \(t^*=3.182\). The interval is \(0.45\pm3.182(0.1041)\), or approximately 0.119 to 0.781 log2 units. This interval quantifies uncertainty in the mean donor contrast under the stated assumptions; it is not a probability statement about where a fixed parameter lies.
With few donors, the distributional assumptions behind a donor-level interval are consequential and hard to assess. A report should give the number of independent donors, the interval method, and the degrees of freedom or other inferential calibration when applicable. If the method relies on a model, report the model assumptions and the uncertainty procedure, not just the final interval or p-value. Simulation-based calibration and residual diagnostics can inform whether the chosen procedure behaves plausibly, but they do not turn cells into independent donors.
Worked Example: A Donor-Level Interval and Its Assumptions
Use the four hypothetical donor contrasts above: 0.20, 0.40, 0.50, and 0.70 log2 units. Check the mean, standard error, and 95% \(t\) interval, and explain what can be concluded.
The mean is \(\bar{x}=(0.20+0.40+0.50+0.70)/4=1.80/4=0.450\) log2 units. Deviations from the mean are \(-0.25,-0.05,0.05,0.25\). Their squared sum is \(0.0625+0.0025+0.0025+0.0625=0.1300\), so \(s=\sqrt{0.1300/3}=0.2082\) log2 units and \(SE=s/\sqrt{4}=0.1041\) log2 units.
Assuming independent donors and an approximately normal distribution of donor contrasts, the 95% interval is
The estimated mean contrast is positive, and the interval excludes zero under this calculation. However, there are only four donors, so the normality assumption is difficult to evaluate and the interval is sensitive to individual donor values. The appropriate report presents the estimate and interval in log2 units, names the donor-level analysis and assumptions, and avoids implying that four donors provide extensive population coverage.
Why Within-Donor Dependence Changes the Accounting
Cells from one donor often resemble one another because they share biological, clinical, and technical context. A simple illustration is an intraclass correlation \(\rho\), the correlation between two observations from the same donor under an exchangeable-correlation approximation. If there are \(D\) donors and \(m\) cells per donor, the variance of a grand mean is not generally the variance calculated as if all \(Dm\) cells were independent.
To see the effect, suppose each cell-level measurement has variance \(\sigma^2\), and any pair of cells from the same donor has covariance \(\rho\sigma^2\), while different donors are independent. There are \(Dm\) individual variance terms and \(D m(m-1)\) ordered within-donor covariance terms in the variance of the sum. Dividing by \((Dm)^2\) for the grand mean gives:
The factor \(1+(m-1)\rho\) is the design effect for this equal-cluster-size approximation. It shows why even modest within-donor correlation can substantially reduce the information in a large cell count. For unequal cell counts or more complex dependence, this simple formula need not apply; it is an illustration, not a universal correction. In particular, an “effective cell count” derived from it is not a replacement for the number of independent donors when making donor-population claims.
Worked Example: Interpreting a Design Effect
Consider a hypothetical dataset with 10 independent donors and 100 cells per donor, for 1,000 cells total. Suppose, for illustration only, that within-donor correlation is \(\rho=0.10\) and the equal-cluster-size approximation applies. Calculate the design effect and the corresponding effective cell count.
The design effect is \(1+(m-1)\rho=1+(100-1)(0.10)=1+9.9=10.9\). The approximation to the effective number of independent cell observations for estimating a grand mean is \(1{,}000/10.9=91.74\), or about 92. This is far below 1,000 because cells within a donor carry overlapping information.
This calculation does not mean the study has 92 independent donors. It has 10 independent donors, and a donor-level inference must reflect those 10 units and the study design. A careful report could give the total and per-donor cell counts, state that cells were clustered within 10 donors, and describe the method used to account for that clustering. It should not use the approximate effective cell count as the sample size for a donor-level test.
Choosing and Describing an Analysis
Several analysis strategies can respect biological replication, but they answer questions in different ways and require different reporting details. The report should identify which strategy was used and why it matches the design and target inference.
| Approach | What to report | Important limitation |
|---|---|---|
| Donor-level summaries | How cell measurements became a donor-level value; donor count; summary, interval method, and units | Summaries may discard within-donor detail, and precision depends on the number of donors |
| Hierarchical or mixed model | Fixed and donor-level effects, dependence structure, estimation method, uncertainty method, and model checks | Results depend on model assumptions; few donors can make some components difficult to estimate |
| Cell-independent analysis | If used, explicitly describe the independence assumption and its design justification | Usually unsuitable when cells from a donor are correlated; can understate uncertainty and overstate evidence |
A cell-level model is not automatically donor-aware merely because it contains many observations. The report must explain the structure that links cells from the same donor and how uncertainty accounts for it. Conversely, analyzing donor-level summaries does not by itself solve every design problem: paired conditions, repeated visits, or donor-level covariates require the analysis to reflect those structures. Model-based and design-based inference are distinct frameworks, and neither permits silently replacing the experimental unit with the cell count.
Diagnostics, Failure Modes, and Limitations
Before interpreting a reported result, check whether the described data structure and analysis agree. The following warning signs deserve attention:
- Only a total cell count is given. Ask how many donors contributed, how cells were distributed across them, and whether any donor was excluded.
- The donor count differs between the design and the analysis. Look for missing samples, filtering, or group-specific exclusions, and check that these are explained.
- Cell counts are highly imbalanced. A few donors may dominate cell-level summaries or model fit. Report the distribution and assess whether the stated method handles the imbalance.
- Uncertainty is reported without a method. A p-value or interval cannot be evaluated without knowing the independent unit, model or procedure, and relevant assumptions.
- Paired or repeated observations are described as independent. Measurements from the same donor are linked; the analysis and reporting should preserve that structure.
No single reporting format can remove limitations in the design. Few donors constrain the ability to estimate between-donor variability, even when each donor contributes many cells. A narrow interval from a model may rely strongly on its distributional assumptions, especially with few independent units. Conversely, a broad donor-level interval can reflect genuine heterogeneity as well as sampling uncertainty. Report both the uncertainty measure and the donor-level evidence needed to interpret it; do not use cell abundance as a substitute for donor diversity.
A practical reporting sequence is: name the independent unit; give the number of units by group and analysis; show cell counts per unit and the filtering flow; describe within-unit dependence and the method used to handle it; then report the estimate, uncertainty, units, and limitations. This sequence makes it possible for readers to assess replication without requiring them to infer the design from a large cell total.
Check Your Understanding
Answer each question using the distinctions between donors, cells, and inferential uncertainty.
- A study has 12 donors and 600 cells, with 50 cells from each donor. What are the donor count and the cell count, and which count represents biological replication for a donor-population comparison?
- A study has 6 donors in each of two independent groups. Each donor contributes 100 cells. Explain why the total of 1,200 cells does not give 1,200 independent replicates.
- Four independent donor-level estimates are 1, 2, 3, and 4 units. Calculate their mean and sample standard error. What assumptions would be needed for a conventional \(t\) interval across donors?
- What information should be reported when cell yields vary widely across donors?
- A dataset contains repeated samples from each donor at two time points. What should be disclosed about the independent unit and dependence structure?
Solutions. (1) There are 12 donors and 600 cells. For a donor-population comparison, the biological replication is represented by the 12 independent donors, not by 600 independent units. (2) There are 12 donors and 1,200 cells. Cells from the same donor may be correlated, so the analysis must account for donor clustering; the independent group-level units are the donors if donors were independently sampled or assigned. (3) The mean is \((1+2+3+4)/4=2.5\) units. The sample standard deviation is \(\sqrt{5/3}=1.291\) units, so the standard error is \(1.291/\sqrt{4}=0.6455\) units. A conventional \(t\) interval assumes independent donor estimates and an approximately normal distribution of donor-level values; with four donors, that assumption is difficult to assess. (4) Report donor counts, cells per donor after filtering, their distribution (such as range and median), group totals, and the filtering or exclusion process. Also state how the analysis handles the imbalance and within-donor dependence. (5) State that the same donors contribute repeated measurements, identify the number of donors and samples at each time point, and describe how the analysis accounts for within-donor dependence across both cells and time points.