Why a Cell Can Have More Than One Plausible Label
A cell may show RNA markers associated with one cell type, surface proteins associated with another, and chromatin accessibility compatible with either. Such disagreement is not automatically a reason to discard a modality or average the labels. It is evidence that the assignment depends on which markers are informative, how reliable each measurement is for this cell, and whether the candidate labels adequately describe the cell.
The goal is to evaluate marker-level evidence for specified candidate labels and make the uncertainty visible. A label supported by a calibrated combination of evidence is different from a label selected simply because it receives the most votes. Even when one candidate ranks highest, the evidence may be too weak or conflicted to justify a confident assignment.
Representing Evidence Without Forcing a Vote
Let \(C\) denote the cell-type label, with candidate values \(c_1,\ldots,c_K\). For one cell, let \(Y_R\), \(Y_P\), and \(Y_A\) denote the observed RNA, protein, and ATAC marker evidence. The evidence might be a marker pattern or a vector of measurements; it should be defined consistently with the model used to evaluate labels. For example, RNA evidence could summarize expression of positive and negative markers, while protein evidence could include measured surface-marker abundance and ATAC evidence could include accessibility at linked marker-associated regions.
A principled way to compare two labels \(c_1\) and \(c_2\) is a likelihood ratio: how much more compatible is the observed evidence with one label than the other? A ratio greater than 1 supports \(c_1\); a ratio less than 1 supports \(c_2\); a ratio near 1 contributes little discrimination. A prior probability represents the relative prevalence or prior plausibility of labels before considering this cell’s marker evidence. Priors should be specified for the intended reference population and not chosen after seeing which label wins.
Conditional independence is a modeling assumption, not a consequence of measuring multiple assays on the same cell. For example, correlated markers within RNA, or an RNA marker and an accessibility feature used to infer the same regulatory signal, may carry overlapping information. A model should account for such dependence, use a joint likelihood, or use a reduced set of evidence. If a modality is missing, its likelihood contribution is marginalized out or omitted under the specified model; missing evidence is not negative evidence.
Posterior Odds and a Short Derivation
For two labels \(c_1\) and \(c_2\), Bayes’ rule gives posterior odds as prior odds multiplied by the likelihood ratio. Under the conditional-independence assumption, the joint likelihood ratio factors into modality-specific ratios:
To see why, apply Bayes’ rule to each posterior probability. The common normalizing probability \(P(Y_R,Y_P,Y_A)\) cancels in their ratio. If the three evidence vectors are conditionally independent given the label, then \(P(Y_R,Y_P,Y_A\mid C=c)=\prod_m P(Y_m\mid C=c)\). Substituting this factorization yields the displayed result. Without conditional independence, the correct likelihood ratio is based on the joint distribution, not the product of three marginal ratios.
In practice, likelihoods may come from a model trained on cells with trusted labels, from a calibrated marker model, or from a carefully specified reference. Reliability should enter through how the evidence is modeled: a noisy or poorly measured marker should provide a likelihood ratio closer to 1 than a clean, discriminating marker. A modality-wide reliability score or a neighborhood weight is not automatically a likelihood ratio or a posterior probability. In particular, modality weights from a neighborhood method describe relative usefulness for that representation and should not be read as probabilities that a cell has a label.
Worked Example: Conflicting Evidence for T and B Labels
Hypothetical data. For one cell, an RNA marker pattern favors T over B, surface-protein evidence favors B, and ATAC evidence modestly favors T. Suppose a calibrated model provides the following comparable, unnormalized label scores, which already incorporate equal prior probabilities and the modeled evidence: \(S(T)=1.784\) and \(S(B)=2.713\). These scores are proportional to posterior probabilities; they are not probabilities themselves.
Normalize by their sum, \(1.784+2.713=4.497\):
The combined evidence ranks B above T, but the posterior probability for B is about 0.6033, not close to certainty. The result supports reporting B as the leading candidate while retaining substantial uncertainty and documenting the RNA–protein conflict. It does not justify saying that the cell is definitively a B cell. The interpretation also depends on the calibration and assumptions behind the scores.
Reliability Is Cell-Specific and Evidence-Specific
A modality can be reliable for one cell and weak for another. Low RNA library complexity can make apparent absence of a transcript uninformative. Background binding, low antibody signal, or saturation can limit protein evidence. Sparse or noisy ATAC measurements can make a closed-looking region weak evidence against a label. Conversely, strong quality controls and a highly specific marker can make a modality especially informative for a particular decision.
Reliability should therefore be considered at the level of the observed evidence: marker specificity, measurement quality, background, and the performance of the model in comparable cells. If an evidence model is calibrated by quality stratum, the likelihood ratio for low-quality evidence will typically be closer to 1. Do not multiply a hand-chosen “reliability weight” into a posterior and then describe the result as a calibrated probability unless that procedure has itself been justified and calibrated.
Worked Example: Weak Protein Evidence Should Not Decide the Label
Hypothetical data. Consider two labels, X and Y, with equal prior odds. In a low-quality cell, the calibrated RNA evidence has likelihood ratio \(2.4\) for X over Y, the protein evidence has likelihood ratio \(0.8\), and the ATAC evidence has likelihood ratio \(0.6\). Thus RNA favors X, while protein and ATAC modestly favor Y. The protein result is near neutral because its marker signal is weak and has been calibrated against comparable low-quality measurements.
Assuming these modality evidence summaries are conditionally independent given the label, the posterior odds for X over Y are:
Odds of 1.152 to 1 correspond to:
X ranks first, but the probabilities are close. The appropriately calibrated weak protein result has not been treated as a strong vote for Y; nor has it been discarded. The conclusion is an ambiguous assignment, with X as a slight leader. If the conditional-independence assumption is implausible, these multiplied ratios should be replaced with a model for the joint evidence.
From Evidence to a Reportable Assignment
A cell-type assignment is a decision made from evidence, not just the largest posterior probability. A reporting rule can specify a minimum posterior probability, a minimum margin between the leading and next candidate, and conditions under which the label is marked ambiguous. Those cutoffs should be chosen for the use case and, where possible, evaluated on independent labeled cells. There is no universal cutoff that makes every assignment scientifically adequate.
A useful report preserves both the ranking and the reason for uncertainty. It can state the leading label, its calibrated probability or score, the competing label, which markers and modalities supported each, and relevant quality concerns. If no candidate is sufficiently supported, use an explicit unresolved or ambiguous category. If an “unknown” or broader class is a plausible outcome, include it among the candidates rather than forcing every cell into a narrow reference label.
Worked Example: Three Plausible Labels
Hypothetical data. A cell has RNA evidence compatible with label A, protein evidence more compatible with B, and ATAC evidence that does not clearly distinguish B from C. Suppose a calibrated three-label model produces comparable unnormalized scores \(S(A)=0.32\), \(S(B)=0.30\), and \(S(C)=0.28\), with equal priors already incorporated. Their sum is \(0.32+0.30+0.28=0.90\).
A is the top-ranked label, but its probability is only 0.3556 and exceeds the next candidate by 0.0222. Under a prespecified reporting policy requiring a leading probability of at least 0.80 and a margin of at least 0.15, this cell is unresolved: it meets neither condition. The appropriate report is not “A” without qualification; it is an ambiguous assignment among A, B, and C, accompanied by the modality-level evidence.
Diagnostics, Alternatives, and Failure Modes
Before treating conflict as biology, check whether the measurements and marker interpretation support that conclusion. Examine modality-specific quality, marker specificity, background and detection limits, and whether the reference labels were defined consistently. Check that the cell’s marker pattern is not being driven by a small number of unreliable features. Consider whether a transitional state, a cell outside the reference, or more than one cell contributing to the profile could explain a mixed pattern. These are diagnostic possibilities, not conclusions that can be established from disagreement alone.
Also check calibration on held-out or otherwise independent cells with relevant labels. Among cells assigned a posterior near 0.6, for example, the leading label should be correct about 60% of the time in comparable calibration data if those probabilities are well calibrated. Poor calibration, a large out-of-reference fraction, or systematic underprediction of one modality’s errors can make apparently precise assignments misleading.
| Approach | What it does | Limitation for conflicting evidence |
|---|---|---|
| Majority vote across modalities | Selects the label supported by the most modalities. | Ignores marker specificity and unequal measurement quality; a weak modality counts as a full vote. |
| Single-modality assignment | Uses one chosen assay to assign the label. | Can be appropriate for a defined task, but discards informative evidence from other assays and can hide disagreement. |
| Joint likelihood or calibrated evidence model | Compares labels using evidence strength, priors, and modeled dependence. | Requires suitable calibration and defensible assumptions; misspecification can yield overconfident probabilities. |
A common mistake is to treat the highest score as a settled identity: “B has the largest score, so this is a B cell.” The correction is to ask whether that score is calibrated, how much it exceeds competing labels, and whether the modality evidence is reliable and appropriately modeled. Another mistake is to multiply every marker or modality contribution as if each were independent. If two features largely measure the same underlying signal, this can inflate evidence; model their dependence or avoid counting both as independent support.
No evidence-combination rule can repair an unsuitable candidate set, absent marker information, systematic assay bias, or a poorly calibrated reference. Nor does a posterior probability establish a cell’s identity with certainty. The aim is a transparent, reproducible decision that distinguishes strong support from weak or conflicting evidence.
Check Your Understanding
Answer each question, then compare with the brief solutions.
- For two labels, what does a modality-specific likelihood ratio of 0.25 indicate, and what does a ratio of 1 indicate?
- Why is it unsafe to multiply RNA and ATAC likelihood ratios automatically when both summarize overlapping marker evidence?
- A cell has posterior probabilities 0.52 and 0.48 for two labels. What can be concluded, and what should not be concluded?
- How should missing protein evidence be treated in a model rather than interpreted as a negative protein marker?
- Name two checks that can help distinguish a genuine modality conflict from an unreliable measurement or unsuitable reference.
Solutions. 1. A ratio of 0.25 means the observed evidence is four times as likely under the denominator label as under the numerator label; a ratio of 1 contributes no discrimination between them. 2. If the summaries are dependent, their product can count shared information more than once and overstate the evidence. 3. The first label ranks slightly higher, but the evidence is nearly tied; the cell should not be described as confidently assigned without a justified decision rule. 4. Omit or marginalize the missing modality under the specified model; absence of a measurement is not evidence that its marker is absent. 5. Examples include checking modality-specific quality and marker specificity, reviewing background or detection limits, and evaluating calibration on relevant held-out labeled cells.