Diagnosing Subgroup Instability in Multi-Omics Results

Why Subgroup Stability Needs to Be Checked

A multi-omics analysis can return clear-looking subgroups and a list of features that distinguish them. But those results may depend heavily on a few people, especially when the cohort is small or one subgroup contains only a handful of subjects. Resampling provides a direct way to ask a narrower question: if the same cohort were perturbed slightly, would the assignments and defining features remain similar?

This is a sensitivity analysis, not a test that proves the subgroups are biologically real. It assesses the stability of the complete analysis procedure in the observed cohort. A finding that persists under resampling is less dependent on the particular subjects included, but that alone does not establish clinical meaning, causation, or reproducibility in a separate cohort. The earlier material on Integrative Clustering for Autoimmune Disease Endotypes motivates the subgroup setting; here the focus is diagnosing how much its results depend on the observed sample.

Resampling the Subjects and the Analysis

The resampling unit should usually be the subject, not an individual measurement or omics feature. If a person has expression, protein, and metabolite measurements, all of that person’s available layers should travel together in a resample. Resampling features independently across layers would break the within-person correspondence that the integrative analysis is intended to use.

A practical choice is repeated subsampling without replacement: draw a specified fraction of the cohort, rerun the analysis, and compare the resulting subgroup structure with the reference structure. The fraction is a design choice, not a universal constant. Smaller subsamples create stronger perturbations but may leave too little information to fit the method reliably. The bootstrap, which samples subjects with replacement, is another option; duplicated subjects then contribute repeated weight, so its perturbation is not identical to subsampling.

State which parts of the pipeline are refitted. If normalization, feature filtering, dimensionality reduction, tuning, or subgroup assignment uses information from the cohort, those steps should generally be repeated inside each resample. Otherwise, the resampling can understate instability by treating sample-dependent choices as fixed. If the goal is specifically to isolate assignment instability conditional on a chosen feature set or number of groups, hold that choice fixed and say so. If the original procedure selects the number of groups, repeat that selection as part of the pipeline or report separately that stability is conditional on the chosen number.

Cluster labels such as “group 1” and “group 2” have no intrinsic meaning: an algorithm can swap their numbers without changing the partition. For this reason, compare partitions using label-invariant summaries. One useful summary is the co-assignment frequency for a pair of subjects. For every resample containing both subjects, record whether the fitted method places them together. The proportion of such resamples in which they are together gives a value between 0 and 1. A value near 1 indicates persistent co-assignment; a value near 0 indicates persistent separation; intermediate values indicate sensitivity.

Here \(B\) is the number of resamples, and \(I(\cdot)\) equals 1 when its condition is true and 0 otherwise. The denominator matters: a pair’s frequency is calculated only over resamples where both subjects were available. If the denominator is small, report that the estimate is based on little resampling information. A co-assignment matrix can reveal robust cores, ambiguous boundaries, and subjects whose assignments change often without requiring a one-to-one match between arbitrary labels.

Measuring Feature Stability

A subgroup’s defining features can be unstable even when its broad partition is fairly consistent. For each resample, record which features the prespecified procedure selects or identifies as distinguishing the groups. A feature’s selection frequency is the number of resamples in which it is selected divided by the number of resamples in which the procedure ran. If features have an estimated direction or contrast, also record whether the direction agrees with the reference result. Selection frequency and direction consistency answer different questions: a feature can be selected often while its estimated direction changes.

The definition of “selected” must match the analysis. It might mean passing a stated threshold, appearing among a fixed number of highest-ranked features, or being retained by a specified feature-selection step. Report the rule and any thresholds. If features are highly correlated, several may substitute for one another across resamples. In that case, low stability for any single feature can coexist with stability of a broader feature set or pathway; do not interpret a lone frequency without considering this possibility.

A set-level summary can complement individual frequencies. For example, compare a resampled feature set with the reference feature set using the Jaccard index: the number of features shared divided by the number in their union. If the reference set is \(\{A,B,C,D\}\) and a resample selects \(\{A,B,D,E\}\), the index is \(3/5=0.600\). This summarizes overlap but ignores feature direction, biological importance, and whether omitted features are substitutes for correlated ones. It should supplement, not replace, feature-level reporting.

Small Groups and Influential Subjects

Small groups are vulnerable because resampling may change their composition substantially. A few assignments can determine whether a subgroup appears coherent, and a feature’s apparent defining role may be driven by only one or two subjects. Report subgroup sizes in the reference fit and across resamples. Track whether a group disappears, splits, merges, or becomes too small for the intended feature summary. These events are findings about instability, not nuisances to be hidden by reporting only successful fits.

An influential-subject analysis complements repeated subsampling. Remove one subject at a time, refit the relevant pipeline, and inspect whether the partition or defining features change sharply. This is a targeted perturbation rather than a random resample. A subject may be influential because of an unusual profile, a data-quality issue, or a genuine rare pattern. Influence alone does not show that the subject is erroneous; investigate the measurements and report the sensitivity.

A Practical Diagnostic Sequence

A short justification explains why pairwise co-assignment avoids label switching. Let \(\pi_b(i)\) be the label assigned to subject \(i\) in resample \(b\). If a fit’s labels are relabelled by any one-to-one mapping \(g\), then

The equality holds because a one-to-one mapping preserves whether two labels are equal. Consequently, the co-assignment indicator—and therefore its frequency—is unchanged by arbitrary renaming of the groups. This property makes pairwise summaries appropriate when labels themselves are not aligned across fits.

Comparisons, Diagnostics, and Limitations

There is no universal threshold at which a subgroup is “stable.” A frequency of 0.80 may be reassuring for one purpose and inadequate for a high-stakes claim. Interpret summaries against the intended use, subgroup sizes, number of successful fits, and amount of variation across resamples. Watch for a pipeline that frequently fails, produces dramatically different group counts, or yields feature directions that reverse. A single overall score can conceal those failures.

Resampling within one cohort does not test whether the same subgroup structure will appear in a different cohort. It also cannot correct systematic sampling bias, assay measurement error, confounding, or a misspecified analysis. In particular, a stable result can consistently reflect a technical artifact if that artifact is shared across the cohort. Stability is therefore one component of validation, not a substitute for independent evidence.

Common Mistake

Another frequent error is to resample each omics layer separately, breaking subject correspondence, or to reuse preprocessing estimates learned from the full cohort without stating that choice. Both can make the exercise answer a different question than intended. A clear report names the resampling unit, pipeline steps repeated, stability summaries, and the failures or limitations observed.