Why Examine Doublet Scores by Cluster?
A doublet score or call describes an individual barcode, but quality-control decisions are often made while inspecting clusters. A cluster with an unusually high share of high-scoring cells may represent a group enriched for doublets. It may also be a real population that happens to resemble the artificial doublets used to calibrate scores, or a genuine transitional population with markers from more than one cell type. Cluster-level diagnostics help organize the evidence; they do not establish cell identity by themselves.
The aim is to ask whether several distinct observations tell a consistent story. Are high scores concentrated in one cluster? Do individual cells in it show strong, simultaneous expression of markers that usually distinguish separate lineages? Are their counts unusually large compared with relevant cells from the same sample? Does the cluster occupy an isolated or intermediate position in the embedding? Each answer has limitations, so interpretation depends on the pattern across evidence, not on a single cutoff.
An enrichment ratio greater than 1 means a higher called-doublet rate in that cluster than across the dataset; it does not mean that every cell in the cluster is a doublet. The excess expresses the difference in percentage points, which can be easier to interpret than a ratio. Report the cluster size and the underlying counts alongside either summary: a high rate based on a few cells is much less stable than the same rate in a large cluster.
Quantifying Enrichment and Its Assumptions
A simple reference calculation treats the cluster assignments as fixed and imagines that the \(D\) calls could have been distributed among the \(N\) cells without regard to cluster. Conditional on the total number of calls, this is a random allocation model: every set of \(D\) cells is equally likely to be called. Under this reference, the expected number of calls in a cluster of size \(n_k\) is \(n_kD/N\). This is a useful benchmark for describing concentration, not a guarantee that calls are actually independent of cluster membership.
If the random-allocation assumptions were reasonable, the number of calls in cluster \(k\) would have a hypergeometric distribution, with variance shown below. The variance accounts for fixing the total \(D\): if calls are assigned to one cluster, fewer remain for others. A standardized difference can flag an unusually large departure from the reference. In ordinary single-cell analysis, however, scores and clusters are often derived from the same expression data. That dependence, along with cluster discovery and the choice of threshold, means a standardized value should generally be treated as a diagnostic signal, not as a standalone confirmatory test.
The expectation follows because each of the \(n_k\) cells has probability \(D/N\) of being among the calls under random allocation, so the expected count is the sum of those probabilities. The variance is the standard hypergeometric variance, including the finite-population factor \((N-n_k)/(N-1)\). If cluster membership and calls were generated independently before inspection, this benchmark can be a reasonable screening reference. If clusters were identified using the same features that drive scores, or if the score model behaves differently across cell types, the benchmark does not by itself provide valid evidence of a biological doublet excess.
Worked Example: A Cluster With an Elevated Call Rate
Suppose a hypothetical dataset has \(N=500\) cells, of which \(D=50\) are called doublets. One cluster contains \(n_k=60\) cells, and \(D_k=18\) are called. Calculate its rate, enrichment, excess, and departure from the random-allocation benchmark.
The dataset-wide rate is \(\hat{p}_D=50/500=0.10\), or 10%. The cluster rate is \(\hat{p}_{D,k}=18/60=0.30\), or 30%. Thus \(E_k=0.30/0.10=3.0\): its called-doublet rate is three times the dataset-wide rate. The excess is \(0.30-0.10=0.20\), or 20 percentage points.
Under random allocation, the expected cluster count is \(60(50/500)=6\) calls. Its reference variance is \(60(0.10)(0.90)(440/499)=4.762\), giving a standard deviation of \(\sqrt{4.762}=2.182\) calls. The descriptive standardized difference is \((18-6)/2.182=5.5\). The observed concentration is substantial relative to this reference, but the value is not automatically a valid inferential test: score and cluster construction may be dependent. The appropriate conclusion is that this cluster warrants closer inspection, not that all 18 calls have been independently verified.
Combine Scores With Cell-Level Expression and Counts
A cluster summary can conceal very different cell-level patterns. Check the distribution of scores within the cluster, including whether high scores are concentrated in a subset or spread across most cells. Then inspect co-expression in individual cells. For a suspected mixture of two lineages, the relevant question is whether cells themselves show appreciable expression of markers from both lineages, rather than whether the cluster’s average expression profile includes markers from both.
Marker evidence is stronger when several informative markers from each lineage are expressed together in the same high-scoring cells, at levels consistent with substantial expression rather than isolated low counts. A cluster-level average can combine one group expressing marker A with another group expressing marker B and create an apparent mixed profile even when no cell co-expresses them. Conversely, sparse detection can make genuine co-expression hard to observe. Marker patterns therefore support an interpretation; they do not identify doublets with certainty.
Counts provide another supporting check. Doublets can contain more RNA molecules and detected genes than singlets, but count depth varies for biological and technical reasons. Compare counts with suitable cells from the same sample, and consider the distribution rather than declaring a cluster a doublet cluster because its mean or median is high. High counts plus high scores and coherent mixed-lineage expression are more persuasive together than any one feature alone.
Worked Example: Mixed Markers and High Counts
In a hypothetical sample, a cluster contains 30 cells, 15 called doublets. Across the dataset, 40 of 400 cells are called. For each cluster cell, researchers inspect markers for two lineages that are usually distinct. Twelve of the 15 called cells have substantial expression of markers from both lineages in the same cell; 3 of the other 15 cluster cells do. The cluster’s median count is 13,200 molecules, compared with 6,800 in a set of same-sample singlet-like cells.
The cluster rate is \(15/30=0.50\); the dataset-wide rate is \(40/400=0.10\). Its enrichment ratio is \(0.50/0.10=5.0\), and its excess is \(0.50-0.10=0.40\), or 40 percentage points. Mixed-marker co-expression occurs in \(12/15=0.80\), or 80%, of called cells, versus \(3/15=0.20\), or 20%, of the other cluster cells. The median count is \(13{,}200/6{,}800=1.941\) times the comparison median.
These observations align: the cluster has a high call rate, many called cells show same-cell co-expression, and its median count is higher than a same-sample comparison group. This makes doublet enrichment a plausible interpretation. It still does not prove that every high-scoring cell is a doublet. Check marker specificity, score distributions, count comparability, and whether a biologically meaningful mixed or activated state could explain some cells.
Use Cluster Position Carefully
Position in a low-dimensional embedding can add context. A cluster of high-scoring cells lying between two otherwise distinct populations may be compatible with mixed profiles; a small isolated group that also has high scores and mixed markers may also deserve scrutiny. But embedding distance is not a direct measure of biological distance. Dimensionality reduction can distort local and global geometry, and a genuine transitional population may lie between established cell types.
A plausible transition is supported more by a coherent pattern than by its position alone: intermediate or smoothly changing expression of relevant markers across cells, a corresponding biological program, and no strong cluster-wide combination of features pointing to doublets. The reverse is also important: a cluster need not be between two groups to contain doublets. Treat position as one piece of supporting evidence, not a decision rule.
Worked Example: A Bridge Cluster or a Doublet-Rich Group?
Consider a hypothetical embedding with two established populations and a group of 30 cells arranged between them. Two cells in the group are called doublets; 10 of 200 cells overall are called. Across the bridge group, one lineage marker decreases gradually from 18 to 4 detected counts per cell while a second rises from 3 to 17. No abrupt subgroup has strong expression of both marker sets, and the group’s median count is 6,900 molecules versus 6,700 among same-sample comparison cells.
The bridge call rate is \(2/30=0.0667\), while the overall rate is \(10/200=0.0500\). The enrichment ratio is \(0.0667/0.0500=1.33\), and the excess is about 0.0167, or 1.67 percentage points. The modest difference, gradual opposing marker patterns, lack of a strong same-cell mixed-marker subgroup, and similar median counts collectively fit a genuine transitional population better than a strongly doublet-enriched cluster.
This is a qualified interpretation, not proof that the population is transitional. A different score threshold or limited marker detection could change the evidence. The embedding’s bridge shape alone would not justify the conclusion; the cell-level expression pattern and other diagnostics provide the more direct support.
A Practical Diagnostic Sequence
For each cluster, report its size, number called, call rate, and enrichment or excess relative to the dataset-wide rate. Do not rank clusters by rate without considering their sizes.
Check whether high scores coincide with substantial co-expression of markers from otherwise distinct lineages in the same cells. Distinguish this from a cluster average that combines separate subgroups.
Use same-sample comparisons where possible. Look for consistent supporting evidence, while recognizing that high counts and intermediate embedding position each have non-doublet explanations.
Review whether conclusions change with reasonable score thresholds or cluster resolutions, and whether sample-specific patterns could drive the apparent enrichment. Record a cluster as a candidate for review rather than treating enrichment as automatic proof.
Diagnostics, Alternatives, and Common Pitfalls
A cluster-level rate is a compact summary, while per-cell scores and calls preserve within-cluster variation. The rate is useful for locating concentrations; per-cell inspection is needed to understand whether the signal is uniform or driven by a small subset. Likewise, a marker summary or count median is efficient for comparison, but distributions and cell-level joint patterns reveal mixtures that summaries can hide. No one summary replaces the others.
When comparing multiple clusters, account for the fact that inspecting many clusters makes some high rates likely by chance, especially in small clusters. Cluster assignments and thresholds may also have been chosen after looking at the same data. For exploratory diagnostics, report the comparisons transparently and avoid interpreting a nominal significance measure as decisive. If formal testing is planned, the testing procedure must address the dependence and multiplicity created by the analysis; a simple random-allocation calculation does not resolve those issues.
A frequent source of misleading comparisons is pooling samples. Samples can differ in loading and overall doublet rates, so a cluster concentrated in one sample can appear enriched even if its within-sample rate is ordinary. Check cluster membership and calls by sample, and compare cells under appropriate sample context before attributing enrichment to cell identity. Also check sensitivity to the call threshold: a cluster’s apparent enrichment may depend on a handful of cells near the cutoff.
- Mistake: “The cluster rate is three times the global rate, so every cell in it is a doublet.” The ratio compares rates, not individual identities. Inspect cell-level evidence and retain uncertainty about each call.
- Mistake: “Both lineage markers appear in the cluster average, so its cells are mixed.” Different cells may express different markers. Verify co-expression within individual cells.
- Mistake: “High counts prove doublets.” Counts can vary for reasons other than doublet formation. Compare with relevant cells from the same sample and combine this signal with other diagnostics.
- Mistake: “A group between two embedding clusters must be doublets.” Genuine transitional cells can occupy intermediate positions, and embeddings distort geometry. Examine the expression pattern and other evidence.
Check Your Understanding
Answer each question, then compare with the solutions below.
- A dataset has 600 cells and 60 calls. A cluster has 40 cells, 12 of them called. Find the cluster rate, global rate, enrichment ratio, and excess.
- Why is co-expression of opposing lineage markers in the same cells more informative than finding both marker sets in a cluster-level average?
- A high-scoring cluster has high counts but little same-cell mixed-marker expression. Give one reason not to conclude that all its cells are doublets.
- What does an intermediate position between two clusters establish about a population’s identity?
Solutions. (1) The cluster rate is \(12/40=0.30\); the global rate is \(60/600=0.10\); enrichment is \(0.30/0.10=3.0\); excess is \(0.30-0.10=0.20\), or 20 percentage points. (2) A cluster average can combine cells expressing different markers, whereas same-cell co-expression demonstrates that both marker patterns occur together in individual cells. (3) High counts have other biological and technical explanations, and the missing mixed-marker signal weakens one line of doublet evidence; inspect the score and other diagnostics before deciding. (4) It establishes only the group’s location in that embedding. Genuine transitional cells can be intermediate, and embedding geometry alone does not determine identity.