Quality Control as a Cell-Validity Decision

Quality Control Is a Decision, Not a Verdict on Biological Interest

A count matrix can be structurally well formed and still contain barcodes whose counts do not provide adequate evidence of a technically valid cell. Conversely, a cell with an unusual expression profile may be technically valid. Quality control (QC) therefore asks a specific question: given the available technical evidence, should this candidate cell be retained as valid for the intended data set? It does not ask whether the cell is common, easy to interpret, or useful for every later analysis.

The decision has two possible errors. Retaining an invalid candidate is a false retention; removing a valid cell is a false removal. Those errors need not have equal consequences. A decision rule should make the target, evidence, and relative costs explicit rather than treating a single threshold as universally correct.

Here, “technically valid” is an operational target: the barcode is sufficiently supported as representing a cell-associated observation under the assay and the intended data-generation context. It is not a claim that every molecule is error-free, that the cell belongs to a particular biological class, or that the cell will be useful for every downstream question. The earlier material on count-matrix structure errors concerns whether the data are represented correctly; cell validity is a separate decision about which observations to retain.

The probability \(p\) is conditional on the evidence and on the model or judgment used to assess it. It is not automatically available just because a candidate has a count profile. If evidence is summarized by a score rather than a calibrated probability, the score must not be substituted for \(p\) without a justified mapping. The decision framework below specifies what to do if a defensible probability and error costs are available; it does not prescribe a particular cell-calling or metric-based method.

Deriving the Cost-Sensitive Decision Rule

Assume the decision is to retain or remove the candidate, the validity state is \(V=1\) or \(V=0\), and the two stated costs describe the losses from the corresponding errors. Correct decisions have loss zero. These assumptions define a simple two-action decision problem; they do not assert that every real analysis has only two relevant actions or that the costs are easy to quantify.

Conditional on the evidence, retaining has expected loss only when the candidate is invalid. Its probability of being invalid is \(1-p\). Removing has expected loss only when the candidate is valid, with probability \(p\). Thus the expected losses are:

Choose the action with the smaller expected loss. For positive total cost, retaining is at least as good as removing when:

The threshold is nonincreasing as \(C_{\mathrm{FM}}\) increases, and it is strictly decreasing when \(C_{\mathrm{FR}}>0\). It is nondecreasing as \(C_{\mathrm{FR}}\) increases, and it is strictly increasing when \(C_{\mathrm{FM}}>0\). These qualifications matter at the boundaries: if \(C_{\mathrm{FR}}=0\) and \(C_{\mathrm{FM}}>0\), the threshold remains zero as \(C_{\mathrm{FM}}\) varies; if \(C_{\mathrm{FM}}=0\) and \(C_{\mathrm{FR}}>0\), the threshold is one. A higher cost of false removal therefore never raises the threshold, but the decrease is not always strict.

A probability threshold of one-half follows only when the two error costs are equal and positive. It is not a universal rule for retaining cells. Moreover, costs should represent the consequences relevant to the analysis, not be chosen merely to make a preferred outcome occur.

Technical Validity, Biological Rarity, and Analysis Goals

A cell can be unusual and still be technically valid. Rarity describes how often a biological state occurs in the observed population; validity concerns whether the observation meets a technical criterion for inclusion as a cell-associated measurement. Neither a small cluster size nor a surprising expression pattern, by itself, establishes technical invalidity. Conversely, a familiar or common profile does not guarantee validity.

The intended data set also matters. A QC decision defines which observations are considered sufficiently valid for a specified purpose. A later analysis may deliberately focus on a subset—for example, a lineage or condition—without changing the technical validity of cells outside that subset. Such downstream selection should be described as selection for that analysis, not silently recast as QC. Keeping the decisions separate helps prevent an analysis goal from becoming an unsupported claim about assay quality.

In practice, costs may not have natural numerical units. They can be specified as relative losses: for example, one error may be judged three times as consequential as the other. If the costs are only qualitative, the resulting threshold is a structured way to discuss the trade-off, not a precisely estimated optimum. It is also possible to add an “uncertain; review” action. That requires specifying the review cost and how review changes the chance of a correct decision; it cannot be justified by the two-action formula alone.

Assumptions, Diagnostics, and Alternatives

The rule is useful only to the extent that its inputs and decision target are meaningful. Before applying it, check that the validity label has a clear operational definition, that the evidence pertains to that definition, and that \(p\) is reasonably calibrated for the relevant assay and context. Calibration means, roughly, that among candidates assigned probabilities near \(q\), about a fraction \(q\) are valid under the target definition. A probability that is systematically too high or too low can yield an apparently exact but poorly justified decision.

Costs should be stated before interpreting a threshold. If false retention and false removal are treated as equally costly without discussion, the implied one-half threshold may conceal an important scientific trade-off. If costs vary by sample or analysis purpose, one common threshold may not represent the same decision in each setting. Uncertainty in the probabilities or costs should also be acknowledged; a borderline decision is less robust than one that remains unchanged over plausible values.

Several alternatives answer different questions. A fixed cutoff on a technical score is simple, but it does not by itself encode a probability of validity or the relative costs of the two errors. A one-half probability cutoff is the special case of equal positive costs. A manual review or abstention policy adds an action and requires its own loss assumptions. Finally, a downstream analyst may filter cells to define a target population; that is not equivalent to determining technical validity.

Useful warning signs include probabilities that do not correspond to the stated validity definition, a threshold chosen solely because it produces a desired cell count, or large changes in retained cells after small plausible changes to costs. These signs do not automatically make the decision wrong, but they call for a sensitivity check and transparent reporting of the assumptions. This tutorial does not prescribe the evidence-generating method; later QC material addresses particular diagnostics and cell-calling approaches.