Scoring Marker Evidence for Individual Cells

What a Per-Cell Marker Score Measures

A marker panel summarizes genes associated with a candidate cell type. Scoring that panel in an individual cell asks a narrower question than testing whether genes differ between clusters: how much expression evidence for this panel is present in this cell’s profile? The answer is a descriptive score, conditional on the chosen panel and expression representation. It is not, by itself, the probability that the cell belongs to the type.

Let \(Y_{ig}\) be the observed count for gene \(g\) in cell \(i\), and let \(M_k\) be the marker panel for candidate type \(k\), containing \(m_k\) genes. Scores are useful only when the panel is specified and the genes are measured consistently. The earlier material on building marker panels provides the context for choosing those genes. Here the focus is how to summarize their evidence within cells.

The two approaches developed here are a within-cell rank score, which summarizes where panel genes fall in the cell’s expression ranking, and a normalized-expression score, which averages transformed, library-size-normalized expression values. Neither requires the marker genes to be statistically independent. Correlated markers can contribute overlapping evidence, so a score should not be interpreted as if every gene were an independent confirmation.

Rank-Based Scores

For a cell with \(G\) analyzed genes, rank the genes by their expression in that cell, with rank 1 assigned to the lowest expression and rank \(G\) to the highest. Use midranks for ties: if four genes share two adjacent ranks, each receives the average of those ranks. Convert each rank to a percentile,

where \(r_{ig}\) is the within-cell rank of gene \(g\). For \(G>1\), \(q_{ig}\) ranges from 0 to 1. The rank-based score for panel \(M_k\) is the average percentile rank of its genes:

A higher score means that, on average, the panel genes rank higher among the analyzed genes in that cell. The score is relative to that cell’s measured expression profile; it is not an absolute expression scale. It can be computed from raw counts or from another expression representation, but the gene set and tie handling should be held fixed when comparing cells.

A related rank summary is the fraction of panel genes among the cell’s top \(K\) genes. It is easy to interpret as a proportion of panel genes reaching a chosen rank threshold, but depends on the choice of \(K\); ties at the cutoff also require a stated rule. The average percentile uses more of the ranking, whereas the top-\(K\) fraction emphasizes whether genes cross a particular threshold.

Normalized-Expression Scores

A normalized-expression score retains information about the transformed expression values rather than replacing them with ranks. One common construction first scales each cell’s counts to a common library-size target and then applies a log transformation. For a target of 10,000 counts per cell, define

where \(L_i=\sum_g Y_{ig}\) is the total count across the genes used to define the cell’s library size. The natural logarithm is used here. The marker score is the mean transformed expression of the panel:

This score is in log-normalized-expression units. It is not a count, a fold change, or a probability. Averaging gives each included marker equal weight, but a highly expressed marker can still raise the average substantially. The value also depends on the normalization target, transformation, and panel composition, so scores from different pipelines are not automatically comparable.

Why Ranks Can Help—and What They Lose

If a cell’s expression values are all transformed by the same strictly increasing function, their order is unchanged. In particular, for any two genes \(g\) and \(h\), if \(Y_{ig}<Y_{ih}\), then \(f(Y_{ig})<f(Y_{ih})\). Thus, applying a strictly increasing log transformation to the values within a cell preserves the ordering of non-tied genes. A rank score is consequently insensitive to the numerical spacing between expression values: a small gap and a large gap contribute the same ordering information.

This property can be useful when cells differ in overall scale or when a few large values would dominate a mean. But ranks discard magnitude. A panel gene just above another gene and one far above it can occupy similar ranks; the score does not show how much more highly expressed it is. Moreover, when counts are sparse, many genes have zero counts and share tied ranks. A panel consisting mostly of zeros may receive a low score even if one marker is prominent, or a score affected by how many other genes are tied at zero.

The normalized-expression mean preserves some magnitude information but has its own sensitivity to zeros, high values, the normalization method, and panel membership. It is often useful to inspect the fraction of panel genes detected, \(m_k^{-1}\sum_{g\in M_k} I(Y_{ig}>0)\), alongside either score. This detection fraction is a complement, not a replacement: it records how many genes are nonzero but ignores how large their expression values are.

Comparing Candidate Panels and Checking Scores

Comparisons are most defensible when all candidate panels are scored using the same cells, gene universe, normalization, transformation, and rank convention. An average prevents a panel with more genes from automatically receiving a larger total merely because it has more terms; it does not make panels equivalent. A panel with many broadly expressed genes can have a different baseline from a panel of highly specific genes. If panel sizes or compositions differ, compare the actual genes and score distributions rather than treating small score differences as decisive.

Useful checks include plotting scores across cells, examining marker-level values rather than only the panel average, and reporting detection fractions for sparse panels. Check whether scores change substantially when a single marker is removed; a large change warns that the result depends heavily on that gene. Confirm that genes absent from the measured feature set were not silently treated as zero: an unmeasured gene is not the same as a measured gene with zero counts. Also check whether differences persist under a reasonable alternative score or transformation. Such checks assess robustness; they do not turn a descriptive score into a formal test.

A common mistake is to say, “This cell’s marker score is 0.8, so it has an 80% chance of being that type.” That conclusion is unjustified: the score has no probability calibration, and its numerical scale is defined by the scoring rule. A second mistake is to remove zero-count panel genes before averaging, which inflates the score by conditioning on detection. Keep the panel definition fixed, include measured zeros as zeros, and describe the score in terms of its formula and scale. Scores can help compare marker evidence across cells or candidate panels, but they do not account automatically for competing cell types, marker dependence, or uncertainty in the panel itself.