What Pairing Means in Multimodal Assays
A multimodal assay records more than one kind of molecular measurement from the same biological unit. The statistical value of such data depends not only on which measurements were collected, but also on whether their identities are linked. In CITE-seq, RNA measurements and antibody-derived tag (ADT) measurements can be linked to the same cell. In a single-cell multiome assay, RNA and chromatin-accessibility measurements can be linked to the same cell or nucleus, depending on the assay. That link permits joint, within-unit analyses that would not be available if each modality came from unrelated cells.
Let \(d\) index donors, \(c\) cells or nuclei within a donor, \(g\) RNA features, \(p\) antibody-tag features, and \(k\) accessibility features. Write \(Y_{dcg}\) for an RNA measurement, \(A_{dcp}\) for an ADT measurement, and \(Z_{dck}\) for an accessibility measurement. These symbols identify distinct types of measurements; they do not imply that values in different modalities have the same scale or interpretation.
A barcode is evidence of a shared identity only when the assay and data processing support that interpretation. A barcode collision, doublet, sample-label error, or modality-specific quality failure can produce a misleading or incomplete pair. Further, the cell is generally a measurement unit nested within a donor, not an independent biological replicate. For population-level conclusions, donor structure and the study design still matter.
Which Statistical Comparisons Does Pairing Support?
With valid pairs, a researcher can examine whether two features co-vary across the same cells, whether their detection patterns coincide, or whether a cell-level summary in one modality is associated with a summary in another. For example, paired RNA and ADT measurements can support an analysis of association between a selected transcript and a selected protein tag. Paired RNA and accessibility measurements can support an analysis of association between a selected transcript and a prespecified accessibility feature. Such analyses describe joint variation; they do not by themselves establish a regulatory mechanism.
The basic reason pairing matters can be seen from the variance of a difference. If \(X_c\) and \(W_c\) are two measurements for the same unit, then
The covariance term exists because the values belong to the same units. If the within-unit covariance is positive, the variance of a difference can be smaller than it would be under an independence assumption. This is the logic behind paired comparisons when the two measurements represent comparable outcomes under two conditions. It does not imply that any two modalities should be subtracted: RNA counts and ADT counts, for example, have different measurement processes and are not automatically commensurate outcomes.
Pairing also allows the joint distribution to be retained. If the RNA and accessibility measurements for a cell are separated into unrelated lists, their individual marginal distributions remain, but the cell-by-cell association is lost. Matching cells after the fact by similar expression or by cluster membership does not recreate a genuine experimental pair; it can also introduce selection effects.
Worked Example: RNA–Protein Association Across Paired CITE-seq Cells
Suppose five hypothetical cells from one donor have already passed modality quality checks. For illustration, \(X_c\) is a transformed RNA summary for a selected gene and \(W_c\) is a transformed ADT summary for a selected protein tag. The values are paired by cell, and the scales are being used for an association calculation, not treated as directly equivalent.
| Cell | \(X_c\), RNA summary | \(W_c\), ADT summary |
|---|---|---|
| 1 | 1 | 2 |
| 2 | 2 | 1 |
| 3 | 3 | 4 |
| 4 | 4 | 3 |
| 5 | 5 | 5 |
The sample means are \(\bar{x}=(1+2+3+4+5)/5=3\) and \(\bar{w}=(2+1+4+3+5)/5=3\). The sample Pearson correlation is
The cross-products in cell order are \(2, 2, 0, 0, 4\), which sum to \(8\). Each sum of squared deviations is \(4+1+0+1+4=10\). Therefore,
In this small hypothetical set, the paired summaries have a positive sample linear association. The calculation depends on the row pairing: changing which ADT value belongs to which cell changes the cross-products. It does not show that RNA abundance causes protein abundance, and five cells from one donor do not provide five independent donor-level replicates. A population-level inference would need a design and analysis that account for donor-to-donor variation and other relevant sources of dependence.
Pairing Is Not the Same as Replication or a Matched Treatment Design
Three different ideas are easy to conflate. First, modality pairing means two measurements are linked within the same cell. Second, biological replication concerns independent biological units, commonly donors. Third, a paired condition design means the same biological unit contributes an outcome under each of two conditions, such as the same donor measured before and after treatment. A CITE-seq cell containing both RNA and ADT measurements is modality-paired; it is not, for that reason alone, a replicate donor or a cell observed under two conditions.
When the same donors contribute to two conditions, a donor-level paired contrast can be appropriate. The unit of pairing is then the donor, even if thousands of cells were measured within each donor. The outcome should be defined on a comparable scale across conditions, and each donor should have usable data in both conditions. This distinction follows the earlier material on independent donor counts and repeated structure: adding cells improves measurement within a donor, but it does not create additional independent donors.
Worked Example: A Matched-Donor Condition Contrast
Suppose four hypothetical donors each contribute cells under both a baseline and a follow-up condition. For a selected RNA feature, an analyst calculates one donor-level summary in each condition using a prespecified, comparable procedure. The cell identities do not persist across conditions; the matching is by donor. The follow-up-minus-baseline differences, in arbitrary normalized summary units, are \(1.2,\ 0.8,\ -0.2,\ 1.0\).
The mean donor-level difference is
The deviations from \(0.700\) are \(0.5,\ 0.1,\ -0.9,\ 0.3\), so the sum of squared deviations is \(0.25+0.01+0.81+0.09=1.16\). The sample standard deviation of the donor differences and the standard error of their mean are
The descriptive estimate is an average increase of \(0.700\) normalized summary units from baseline to follow-up among these four donors. This calculation treats donor as the independent paired unit; it does not treat each cell as an independent matched pair. With only four donors, any inferential conclusion would be uncertain and would need assumptions about the sampling and analysis design. The observed contrast alone does not prove that the condition caused the change.
Worked Multiome Example: Preserving Cell-Level Joint Information
Consider six hypothetical nuclei with a binary indicator for detection of a selected RNA feature and a binary indicator for accessibility of a prespecified candidate peak. This example assumes that both measurements passed the relevant modality-specific quality checks and that the peak was selected in advance for illustration. The table retains the pairing by nucleus.
Worked Example: Paired Detection Patterns in Multiome
Suppose the six paired observations are \((1,1),(1,1),(1,1),(1,0),(0,1),(0,0)\), where the first entry indicates RNA detection and the second indicates accessibility detection. The paired \(2\times2\) table is:
| Accessibility detected | Accessibility not detected | |
|---|---|---|
| RNA detected | 3 | 1 |
| RNA not detected | 1 | 1 |
RNA is detected in \(4/6=0.667\) nuclei, and accessibility is detected in \(4/6=0.667\) nuclei. Equal marginal detection proportions do not mean the two indicators are unrelated: three nuclei show both detections, while one shows neither. For a compact descriptive measure of association in this binary table, the phi coefficient is
where \(a=3,\ b=1,\ c=1,\ d=1\) are the table entries in the order shown. The modest positive descriptive association is based on only six nuclei and should not be presented as strong evidence of a general relationship. It is also not evidence that the peak directly regulates the RNA feature. Even if a peak is biologically plausible for a gene, a genomic or functional relationship requires its own justification; sharing a nucleus barcode does not establish that mapping.
If the accessibility indicators were shuffled among nuclei, the two marginal detection proportions would stay at \(4/6\), but the table entries and association could change. That change illustrates exactly what is lost when paired rows are discarded.
Assumptions, Diagnostics, and Common Failure Modes
The validity of a paired analysis begins with data linkage, not with a statistical test. Check that modality records share the intended cell or nucleus identifier, that identifiers are unique within the relevant sample, and that sample and donor labels agree across modalities. Determine whether some cells have only one usable modality. An absent value due to assay failure or filtering is missing, not a zero measurement; coding it as zero changes the data and can create spurious patterns.
The statistical assumptions depend on the comparison. A descriptive cell-level correlation requires correctly paired observations and a clearly specified feature and scale. A conventional inferential correlation test typically relies on independent pairs across units and, for its exact small-sample reference distribution, a bivariate normal model; cells nested within donors violate simple independence when treated as unrelated observations. Binary association summaries likewise do not eliminate the need to account for donor structure when making population claims. For condition contrasts, the pairing must correspond to the same donor or other genuine repeated unit, and the outcome must have a meaningful common definition across conditions.
Useful checks include comparing the numbers of usable cells in each modality and their overlap, reviewing modality-specific quality metrics, checking for duplicate barcodes and suspected doublets, and summarizing missingness by donor and condition. A large discrepancy between modality cell lists may indicate deliberate filtering, low-quality measurements, or a linkage problem; the cause matters. Check whether results are dominated by one donor, whether cell-level patterns are consistent across donors, and whether the association changes substantially under reasonable quality-control choices. These diagnostics help reveal problems but cannot establish that every retained pair is correct.
- Calling cells independent biological replicates. This inflates the apparent amount of independent information when many cells come from a small number of donors. Keep the donor structure in the design and interpretation.
- Subtracting unlike modalities because they are paired. RNA and ADT counts, or RNA and accessibility counts, are produced by different measurement processes. A shared cell identity does not make raw values comparable or make their difference meaningful.
- Confusing matched modalities with matched conditions. RNA and protein can be paired within one cell, but this does not create a before-and-after pair. For condition comparisons, identify the true repeated unit, often the donor.
- Treating missing modality data as a negative result. A failed or absent measurement is not the same as a measured zero. Define the eligible paired set and describe how missing pairs were handled.
- Interpreting within-cell association as causation. Co-variation can reflect shared cell state, donor, technical factors, or other variables. Pairing alone does not identify a causal effect.
The main alternative to paired analysis is an unpaired comparison, which is appropriate when the observations truly come from different units and there is no valid matching. An unpaired analysis of separate modality lists can compare marginal distributions, but it cannot estimate the within-cell association because the joint identities are unavailable. Conversely, using a paired method when the identifiers do not represent genuine matches imposes a false structure. The analysis should follow the sampling and linkage design rather than the convenience of a software data layout.
Check Your Understanding
Answer each question, then compare with the brief solutions below.
- In CITE-seq, what makes an RNA record and an ADT record a valid within-cell pair?
- Two modality lists each contain 500 cells, but only 420 cell identifiers overlap. Why is it incorrect to assign the remaining records to each other by row order?
- In a study with 8 donors and 1,000 cells per donor, what is the biological replication count for a donor-level condition comparison, and what does cell-level modality pairing add?
- Why does a shared cell barcode not justify subtracting an RNA count from an ADT count?
- Four matched donors have follow-up-minus-baseline summaries of \(0.4,\ 0.8,\ -0.2,\ 1.0\). Calculate the mean paired difference and state its interpretation.
Solutions. (1) The records must share a reliable cell identity under the assay and data processing, with compatible sample labels and no known linkage failure. (2) Row order does not establish biological identity; unmatched records are not valid pairs, and pairing them would invent joint observations. (3) There are 8 biological donor replicates, not 8,000. Cell-level modality pairing supports within-cell joint analyses but does not increase the number of independent donors. (4) The modalities have different measurement processes and scales, so pairing identifies a shared unit but does not make their numerical difference meaningful. (5) The mean is \((0.4+0.8-0.2+1.0)/4=2.0/4=0.500\) summary units. It is the average follow-up-minus-baseline difference among these four donors, not by itself evidence of a causal effect or a population-wide change.