Worked Example of Uncertain PBMC Annotation

From PBMC Evidence to a Cautious Label

Peripheral blood mononuclear cells (PBMCs) include several immune-cell lineages, and some lineages contain closely related subtypes. A cell may have convincing evidence for a broad lineage while offering little evidence for one subtype over another. For example, a cell can show a clear T-cell marker pattern even when the evidence distinguishing CD4 T cells from CD8 T cells is weak. An annotation should express that distinction rather than turn an uncertain subtype guess into an apparently certain label.

This worked tutorial uses two evidence sources: marker scores, which summarize expression patterns for selected genes, and reference probabilities, which describe a model’s support for candidate labels. Their numerical scales have different meanings. A marker score is not a probability, and it should not be added to a reference probability as if both measured the same quantity. Instead, examine each source on its own terms, then ask whether they support compatible levels of biological specificity.

Definition: A marker score for a cell and a marker-gene set is a summary of the cell’s expression of those genes relative to a specified normalization and scoring procedure. It indicates relative enrichment under that procedure; it is not, by itself, the probability that the cell belongs to a cell type. A reference probability \(q_{ik}\) is the model-reported probability for cell \(i\) and candidate label \(k\). For a set of mutually exclusive candidate labels considered by the model, the probabilities are nonnegative and sum to 1. Interpret them as probabilities for the cell’s label only to the extent justified by the model and its calibration in the relevant setting.

For the hypothetical examples, marker scores are reported on one common, already normalized scale. Assume each score is a mean centered expression value for the listed marker set, computed using the same procedure across cells; higher values indicate greater relative expression of that set. The scores are illustrative and do not have a universal cutoff. The reference model reports probabilities for mutually exclusive candidate subtypes. The calculations below use those model outputs as reported, while separately checking whether marker patterns are biologically coherent.

A Practical Rule for Choosing the Level of Annotation

Begin with the question of lineage, then consider subtype. A broad lineage can be supported by a group of markers shared across its subtypes, or by summing reference probabilities over those subtypes. Subtype resolution requires more: the reference probabilities should favor one subtype clearly, and the marker pattern should not contradict that assignment. A leading probability alone is not enough if its nearest competitor is almost as large.

A useful summary is the probability margin: the largest candidate probability minus the second-largest. A large maximum with a small margin means the top subtype is only narrowly preferred. Conversely, probabilities spread over multiple subtypes may still imply strong support for their shared broad lineage. The numerical thresholds used in the examples are an explicit illustrative decision policy, not universal standards. A real analysis should choose and validate its criteria for the scientific question and data.

Decision principle: Assign a subtype only when the reference output provides sufficiently clear support under a stated policy and the relevant marker evidence is coherent. If the evidence supports a lineage but does not distinguish its subtypes, report the lineage with the subtype unresolved. If the evidence does not support even a broad lineage reliably, retain a broader ambiguous or unassigned label.

Worked PBMC Annotations

Worked Example: A T Cell With an Uncertain Subtype

Suppose a hypothetical PBMC cell has a CD3D/CD3E marker score of \(1.8\). Its subtype reference probabilities are \(q_{\mathrm{CD4}}=0.49\), \(q_{\mathrm{CD8}}=0.43\), and \(q_{\mathrm{other\ T}}=0.08\). Assume the marker score is high relative to the same analysis’s background cells and the reference includes these plausible T-cell subtypes.

The reference supports the broad T-cell lineage with probability \(0.49+0.43+0.08=1.00\). The highest subtype probability is \(0.49\), and the runner-up is \(0.43\), so the margin is \(0.49-0.43=0.06\). The marker score supports T-cell identity, but this shared T-cell marker set does not distinguish CD4 from CD8.

Under an illustrative policy requiring a top subtype probability of at least \(0.70\) and a margin of at least \(0.20\), neither requirement is met: \(0.49<0.70\) and \(0.06<0.20\). The appropriate annotation is therefore T cell, subtype unresolved, not CD4 T cell simply because 0.49 is the largest probability. This preserves the clear lineage evidence and the unresolved subtype evidence.

Worked Example: A B Cell With Concordant Evidence

Consider a second hypothetical cell. Its MS4A1/CD79A marker score is \(1.5\), while the scores for T-cell and myeloid marker sets are \(-0.2\) and \(0.1\). The reference probabilities are \(q_{\mathrm{B}}=0.91\), \(q_{\mathrm{T}}=0.05\), and \(q_{\mathrm{myeloid}}=0.04\). Assume the reference’s candidate labels are relevant to these PBMCs and the scores are comparable because they were computed with the same procedure.

The top probability is \(0.91\), the runner-up is \(0.05\), and the margin is \(0.91-0.05=0.86\). The B-cell marker score is elevated relative to the other lineage scores, and the reference strongly favors B cells. Both evidence sources therefore support the same broad label. The illustrative subtype threshold is exceeded if B cell is the available label at this resolution; the cell can be annotated B cell.

This conclusion does not claim that the marker score is a 91% probability. The 91% is the reference model’s probability for its B-cell candidate, while the score is a separate expression summary. Their agreement strengthens the practical case for the label, but does not make either quantity a probability derived from the other.

Worked Example: Monocyte Evidence That Does Not Resolve Subtype

A third hypothetical cell has marker scores of \(1.2\) for LYZ/S100A8/S100A9, \(0.9\) for FCGR3A/MS4A7, and \(0.1\) for a lymphocyte marker set. The reference probabilities are \(q_{\mathrm{classical}}=0.52\), \(q_{\mathrm{nonclassical}}=0.38\), and \(q_{\mathrm{other\ monocyte}}=0.10\). The two first marker sets are associated with different monocyte patterns, so both are relevant to the subtype question.

The summed probability for the broad monocyte lineage is \(0.52+0.38+0.10=1.00\). The top subtype probability is \(0.52\), and the margin over the next candidate is \(0.52-0.38=0.14\). The reference therefore does not meet the illustrative requirements \(0.70\) for the top probability and \(0.20\) for the margin. The marker scores also show expression of both subtype-associated sets rather than an unambiguous pattern.

The defensible label is monocyte, subtype unresolved. The elevated scores do not establish a transition state or prove that the cell belongs to both subtypes; they show only that this scoring result does not cleanly separate the relevant patterns. Follow-up checks could assess whether the expression values are technically reliable and whether the same ambiguity appears in nearby cells, but the current evidence does not justify forcing a classical or nonclassical label.

Why Broad Probabilities Can Be More Stable

The aggregation used above follows directly from the probability rule for a union of mutually exclusive events. Suppose a model’s mutually exclusive subtype labels \(k\) partition a broad lineage \(L\). The event that a cell belongs to \(L\) is then the union of the events that it belongs to each subtype \(k\) within \(L\). Because those subtype events are disjoint, their probabilities add.

q_i(L)=\sum_{k\in L}q_{ik}

For the monocyte example, the model assigns \(0.52\), \(0.38\), and \(0.10\) to three monocyte subtypes, giving \(q_i(L)=1.00\). The arithmetic supports a broad monocyte call under the model’s candidate set, but does not establish that the model considered every possible cell identity. In particular, a sum over only monocyte labels cannot by itself rule out an omitted cell type or an unsuitable reference.

This calculation also explains why a broad label can be well supported when no subtype is. The total probability can be distributed across several subtypes that share the same lineage. Subtype uncertainty and lineage uncertainty are therefore different questions, not contradictory readings of one number.

Diagnostics, Alternatives, and Limitations

Before finalizing a label, check whether the apparent evidence is trustworthy. Confirm that marker scores use a consistent normalization and scoring procedure across the cells being compared. Inspect whether the genes in a marker set are detected at all; a low score caused by sparse detection is not necessarily evidence against the lineage. Check that the reference’s candidate labels fit the intended PBMC setting, and consider whether the cell’s library quality or technical processing could have affected the measured expression. A reference probability should not be treated as calibrated for a new setting merely because the probabilities sum to 1.

Several reasonable alternatives answer different questions. A single top-label rule always selects the largest probability, but can hide a negligible margin. An abstain or unresolved-label policy explicitly declines subtype assignment when evidence is insufficient. A set-valued prediction can retain several plausible labels rather than selecting one. Marker-only annotation can be useful when a reference is unsuitable, but its result depends on the chosen marker sets and scoring procedure. These approaches are not interchangeable: choose according to whether the goal is a single label, transparent uncertainty, or a set of plausible candidates.

Approach	What it provides	Key caution
Top reference label	One candidate with the largest reported probability	The winner may be only marginally ahead
Unresolved broad label	A lineage call without an unsupported subtype claim	Requires a defensible basis for the broader lineage
Marker-only assessment	Evidence based on selected expression patterns	Marker choice, expression sparsity, and overlap affect interpretation
Set-valued output	Multiple plausible candidate labels	Needs a clear interpretation and does not itself select a subtype

The thresholds \(0.70\) and \(0.20\) used in these examples are not biological constants or universal annotation standards. A different threshold may be appropriate after validation, and no cutoff repairs a misspecified reference or a poor marker score. Also, an unresolved subtype label is not a claim that the cell is biologically intermediate. It records what the available evidence does and does not resolve.

Common Mistake: Treating the Largest Probability as a Certain Label

A common error is to reason, “The largest probability is 0.52 for classical monocytes, so this cell is classical.” The calculation only says classical monocytes have the largest reported probability among the listed candidates. Here, the next probability is 0.38, the margin is 0.14, and the marker scores show evidence associated with more than one monocyte pattern. Calling the cell classical without qualification hides both the weak separation and the marker ambiguity. Report the broader monocyte lineage with subtype unresolved, or retain a set of plausible labels if that is the chosen reporting approach.

Key takeaway: Use marker scores to assess expression-pattern coherence and reference probabilities to assess model support. Assign only the level of detail both sources can justify; preserve uncertainty when the lineage is clearer than the subtype.

Check Your Understanding

For each question, use the stated evidence and distinguish what it supports from what it does not resolve.

A hypothetical cell has probabilities \(0.48\), \(0.44\), and \(0.08\) for three T-cell subtypes, and a high shared T-cell marker score. Under the illustrative thresholds in this tutorial, what should be reported?
A cell has probabilities \(0.78\) and \(0.22\) for two B-cell subtypes. Calculate the probability margin. Does the top probability and margin meet the illustrative thresholds?
Why is it incorrect to describe a marker score of \(1.5\) as a 150% probability of a cell type?
Two mutually exclusive subtypes within one lineage have probabilities \(0.35\) and \(0.45\), and the model’s remaining probability \(0.20\) is assigned outside that lineage. What is the model’s summed probability for the lineage, and does that sum identify which subtype is present?

Solutions. (1) The margin is \(0.48-0.44=0.04\), and the top probability is below \(0.70\); report T cell, subtype unresolved. (2) The margin is \(0.78-0.22=0.56\). Both the top probability (\(0.78\)) and margin (\(0.56\)) meet the illustrative thresholds, though marker coherence should still be checked before assigning a subtype. (3) A marker score is a relative expression summary on the defined scoring scale, not a probability; its value is not restricted to the interval from 0 to 1. (4) The lineage probability is \(0.35+0.45=0.80\). This supports the broad lineage under the model, but does not decide between its two subtypes, whose probabilities are \(0.35\) and \(0.45\).