Missing Samples and Incomplete Cell-Type Profiles

Why Missingness Changes the Comparison

A donor-condition profile can be absent because a specimen was not collected, an assay failed, or its measurements were not recorded. A cell type can also have a recorded count of zero in a successfully processed sample. These are different data states: a zero is an observation, while a missing value means the relevant quantity was not observed. Treating missing profiles as zeros can change both the proportions and the comparison being analyzed.

The consequences are not limited to arithmetic. If donors with missing samples differ systematically from donors with complete samples, excluding them changes who contributes to the result. A complete-case estimate then describes the donors with the required observed data; it does not automatically describe every recruited donor or a broader population.

Represent the Data State Before Analyzing It

For each planned donor-condition sample, record whether the sample was collected, processed, and included in the analysis. For each cell-type count, retain the count together with a status that distinguishes an observed count—including zero—from a missing or unusable measurement. Keep the reason for missingness when it is known. This makes it possible to identify whether a missing value concerns an entire sample, one category, or a specific processing step.

A count of zero is meaningful only when the profile was observed and the category was in the measurement and annotation scheme. If a cell type was not included in the annotation scheme, its absent row is not evidence of a zero. If a sample failed before a usable profile was produced, the counts for that sample are missing rather than zero. Even a valid observed zero does not prove the biological cell type is absent from the donor: it means none were observed under the measurement and classification process used.

This distinction matters for proportions. A proportion for a cell type is calculated from an observed count and a specified denominator. If the required count or denominator is missing, the proportion is unavailable; inserting zero would fabricate a value. A zero count in a fully observed profile, by contrast, yields a zero observed proportion when the denominator is positive.

Missingness Mechanisms and Their Implications

A useful first description concerns how the probability of missingness relates to measured or unmeasured data. Let \(R=1\) indicate that the outcome needed for an analysis is observed for a donor, and \(R=0\) indicate that it is missing. These standard missingness labels describe assumptions about the data-generating process; they cannot usually be established from the observed values alone.

• Missing completely at random (MCAR): whether a value is missing is independent of both the outcome and observed covariates. For example, a genuinely random administrative loss might be MCAR.
• Missing at random (MAR): after conditioning on observed information, such as condition or a recorded donor characteristic, missingness does not additionally depend on the missing outcome.
• Missing not at random (MNAR): even after conditioning on observed information, missingness depends on the unobserved value itself or on other unobserved information. For example, a failure process more likely for profiles with an unrecorded extreme abundance may be MNAR.

These are assumptions, not labels that can be assigned just by looking at a table of observed counts. Recording reasons for missingness and comparing completion rates across observed conditions, batches, and donor characteristics can reveal concerning patterns, but cannot rule out dependence on unobserved outcomes. A standard complete-case analysis is easiest to interpret as representing the target donors when missingness is MCAR. Under MAR, adjustment using relevant observed variables may be possible if a suitable model and its assumptions are justified. Under MNAR, observed data alone generally do not identify the missing outcomes without additional assumptions or information.

Why Complete Cases Can Represent a Different Group

A complete-case analysis keeps only donors with all measurements required for the comparison. It can be a clear and defensible choice when the analysis is explicitly about those complete donors. But when the intended target is all recruited donors, or a population represented by them, selection into the complete cases can alter the target.

A short identity makes the issue precise. For a donor-level outcome \(Y\), let \(R\) indicate whether \(Y\) is observed, with \(P(R=1)>0\). The complete-case mean is \(E[Y\mid R=1]\). By the definition of covariance,

Dividing by \(P(R=1)\) gives

Thus, if observation is MCAR, \(Y\) and \(R\) are independent and the covariance is zero: the complete-case mean targets the same mean in expectation. If observation is related to \(Y\), the covariance need not be zero, and the complete-case mean can differ from the mean among all target donors. This identity explains the selection concern; it does not imply that a nonzero difference can be diagnosed exactly when outcomes are missing.

Assessing How Exclusion Changes the Target

The target of an analysis should be stated in terms of who is represented. For example, a paired comparison restricted to complete pairs may target donors who provided both conditions and had usable profiles. If donors with missing conditions have different observed characteristics or belong disproportionately to one condition or batch, that group may differ from the intended target population. The analysis does not become invalid merely because some samples are missing; rather, its scope and assumptions must be explicit.

This example shows two related changes: the observed case mix differs from the recruited case mix, and the missing outcome could affect the full-group mean. Reporting the number and characteristics of excluded donors helps readers assess the scope of the result. It does not, by itself, remove selection bias.

Practical Choices, Diagnostics, and Limits

Before analysis, determine which samples and categories are required by the intended comparison. Then check whether each unavailable value reflects a missing specimen, a failed assay, an unrecorded count, or a category that was not in the annotation scheme. These situations have different implications and should not be collapsed into one numerical value.

Complete-case analysis is transparent and straightforward, but it loses information and may select a nonrepresentative subset. A model-based approach can use observed covariates to address missingness under explicit assumptions, such as MAR, but it cannot recover information unsupported by the data or make MNAR dependence disappear. Restricting the scientific question to donors with complete profiles can be appropriate when that is genuinely the target; it should not be presented as an estimate for all recruited donors without justification. In every approach, a missing profile is not a zero profile.

Diagnostics should include completion counts by condition, donor-level missingness patterns, reasons for failure where available, and comparisons of observed characteristics between complete and incomplete cases. Large or condition-specific losses, sparse complete pairs, and changing donor sets across cell types are warnings that the interpretation may depend heavily on inclusion. These checks describe the observed process; they do not prove MCAR or distinguish MAR from MNAR in general.

• Pitfall: “No row for this cell type means its count is zero.” This is only justified when the profile was observed and the category was included in the measurement and annotation scheme. Otherwise the value may be unavailable or undefined.
• Pitfall: “The complete-case mean is the mean for all recruited donors.” That follows under conditions such as MCAR, not merely because a mean was calculated. State the complete-case target and justify any broader interpretation.
• Pitfall: “A missing second condition can be filled with the first condition.” This imposes a zero within-donor change without evidence. Keep the pair incomplete or use a method whose assumptions explicitly address the missing outcome.