Why Availability Must Be Part of the Analysis
In an integrative cohort, subjects may contribute different combinations of RNA, protein, and metabolite measurements. One subject might have RNA and protein data but no metabolite assay; another might have only RNA. This is not just a matter of how a data table is displayed. It determines which subjects contribute to each estimate and which cross-layer relationships can be examined directly.
A multi-omics analysis should therefore track availability at the subject-by-assay level. A result based on subjects with RNA measurements does not automatically describe every enrolled subject, and an association between two layers can only use subjects with both measurements unless a model supplies additional information under explicit assumptions. The central discipline is to name the observed subject set and denominator for each result.
Availability may differ because of sample volume, assay failure, study design, or other causes. The availability pattern alone does not tell us why measurements are missing or whether subjects with observed assays are representative of the full cohort. Those questions matter when moving from a description of the observed data to a broader claim.
Define the Analysis Set Before Calculating
Suppose the cohort contains \(N\) enrolled subjects and \(Y_{ij}\) denotes the value for subject \(i\) on assay \(j\). A mean for assay \(j\), calculated from observed values, is
This is the mean among subjects with an observed value for assay \(j\). It is not automatically the mean that would have been obtained if all \(N\) subjects had been measured. For a relationship between two assays, the directly observed pairs are those in \(S_j\cap S_k\). For example, a correlation between RNA and protein values for a gene uses the subjects for whom both values are observed, not everyone with either assay.
When availability is related to the value being summarized, the observed mean can differ systematically from the cohort mean. A short justification makes the issue explicit. Let \(Y\) be an assay value defined for every subject in the target cohort, and let \(A\) indicate that it is observed. The observed-subject mean targets the distribution of \(Y\mid A=1\). To equate its population counterpart with the full-cohort mean, a sufficient condition is that availability is independent of the value, \(A\perp Y\), and that the probability of observation is positive. Under that condition, \(E(Y\mid A=1)=E(Y)\). If availability depends on \(Y\), this equality need not hold. Independence is not guaranteed by having a large observed sample.
This distinction is about the target of the summary, not whether the arithmetic on observed values is correct. The observed mean accurately summarizes its observed subjects even when it is not representative of the whole cohort.
Worked Example: Mapping the Overlap in a Cohort
Hypothetical data. A cohort has 120 enrolled subjects. RNA is observed for 100, protein for 72, and metabolite data for 60. There are 60 subjects with both RNA and protein, 45 with both RNA and metabolite data, 38 with both protein and metabolite data, and 30 with all three assays. Determine the denominator for each pairwise analysis and for an analysis requiring a complete profile.
A single-assay RNA summary uses \(n_R=100\) subjects; the corresponding protein and metabolite summaries use \(n_P=72\) and \(n_M=60\). The RNA–protein analysis uses \(|S_R\cap S_P|=60\) paired subjects. The RNA–metabolite and protein–metabolite analyses use 45 and 38 paired subjects, respectively. A joint analysis requiring all three measurements uses the 30-subject intersection.
The denominator for each analysis is therefore determined by its measurement requirements, not by the overall cohort size. The RNA–protein correlation cannot use 100 RNA values and 72 protein values as though they were paired: only 60 subjects have both values. Likewise, the 30 subjects with all three measurements are not the denominator for an RNA-only summary unless the analysis deliberately restricts itself to that subset.
These counts are internally possible: the three pairwise intersections each contain at least the 30 subjects in the three-way intersection. They do not, by themselves, establish why the remaining assays are unavailable or whether the observed subjects represent all 120.
Analyze Cross-Layer Relationships on Matched Subjects
For a directly observed cross-layer comparison, first define the paired set and then calculate the statistic on those pairs. For example, the sample correlation between RNA and protein measurements is defined using subjects with both measurements. Its interpretation is conditional on that observed paired set unless additional assumptions justify generalizing beyond it. Assumptions for the usual sample correlation as a description of the observed pairs are that each subject contributes one correctly matched pair, the measurements are on meaningful quantitative scales, and the pairs are independent across subjects for the usual sampling interpretation. A correlation describes association, not causation.
Worked Example: RNA–Protein Correlation in the Observed Overlap
Hypothetical data. For a gene, four subjects have both RNA and protein values, recorded on comparable standardized scales:
| Subject | RNA value | Protein value |
|---|---|---|
| A | 1 | 2 |
| B | 2 | 1 |
| C | 3 | 4 |
| D | 4 | 3 |
Assume these four rows are correctly matched measurements from four distinct subjects. Each of the four has both assays, so the analysis denominator is \(n=4\). The RNA mean and protein mean are both 2.5. Using the sample correlation formula, the centered cross-products sum to 3, and each centered sum of squares is 5:
In this hypothetical paired subset, the sample correlation is 0.600, indicating a positive linear association among the four observed RNA–protein pairs. It is not evidence that the same correlation holds for subjects without both assays, and four pairs provide limited information about a broader cohort relationship. The calculation uses matched subjects; it does not pair values from different subjects or treat unpaired measurements as if they were linked.
Availability Can Change the Target of a Conclusion
To assess how availability may qualify a result, summarize who has each assay and compare measured characteristics across availability groups when those characteristics are known. Such comparisons are diagnostic descriptions: a difference can reveal that the observed subset differs on measured variables, but similarity on a few variables does not prove that availability is independent of the unobserved omics values. A clear report distinguishes what was observed from what is inferred.
Worked Example: Response Rates by RNA Availability
Hypothetical data. Of 100 enrolled subjects, 80 have RNA measurements and 20 do not. Treatment response is known for everyone: 30 of the 80 subjects with RNA data respond, while 12 of the 20 without RNA data respond. Compare the observed response proportions.
Among subjects with RNA data, the response proportion is \(30/80=0.375\), or 37.5%. Among those without RNA data, it is \(12/20=0.600\), or 60.0%. The difference, calculated as the proportion with RNA data minus the proportion without RNA data, is \(0.375-0.600=-0.225\), or minus 22.5 percentage points. Overall, \(42/100=42.0\%\) of the cohort responded.
The measured response rate differs between the availability groups in this hypothetical cohort. Thus, an analysis restricted to subjects with RNA data has a different observed response mix from the full cohort. This comparison does not establish why RNA is unavailable, nor does it establish that the same difference applies to an unobserved molecular value. It does show why the RNA-available denominator and the availability pattern are relevant context for an RNA-based result.
In practice, availability summaries should be specific enough to audit. Report the number of enrolled subjects, the number with each assay, the relevant pairwise or complete-profile overlap, and the number used in each result. If availability differs across clinical groups or collection times, report that pattern where it affects interpretation. Do not imply that missing profiles were imputed, measured, or represented by zero unless that is truly how the data were generated.
Choosing an Analysis Strategy
There is no single analysis set that is best for every question. The choice depends on which measurements a result requires and which population or subject set the conclusion is intended to describe. The basic alternatives have different costs and assumptions.
| Approach | What it uses | Main benefit and limitation |
|---|---|---|
| Assay-specific observed set | All subjects observed for the assay being summarized | Uses the available measurements for a single-layer summary; describes that assay’s observed subjects. |
| Pairwise overlap | Subjects observed for both assays in a cross-layer comparison | Uses all directly observed pairs for that comparison; different comparisons can have different subject sets. |
| Complete-profile restriction | Subjects observed for every assay required by the analysis | Provides one common set for joint analyses; can discard many subjects and may select a nonrepresentative subset. |
| Model-based methods or imputation | Observed data plus a specified statistical model for unobserved values or missingness | Can target beyond the observed subset under explicit assumptions; conclusions depend on model adequacy and missingness assumptions. |
Pairwise analyses can use more subjects than a complete-profile analysis, but each pairwise result may describe a different subset. Consequently, comparing two pairwise correlations as if they were calculated on the same subjects can be misleading when their overlaps differ. Conversely, requiring a complete profile provides a common subject set for a joint calculation but may lose substantial information. Neither approach makes availability ignorable by itself.
Imputation and model-based methods are not automatic repairs. They require a defensible model, assumptions about the missingness process, and uncertainty calculations that reflect the estimation of missing values. A value unavailable because an assay was never run cannot be treated as a measured biological zero. If the model assumptions are not credible or cannot be assessed, report the observed-data analysis and qualify its target rather than presenting a model-dependent result as assumption-free.
Diagnostics, Reporting, and Common Pitfalls
Before interpreting an integrated result, check that subject identifiers are aligned across assay tables, availability counts agree with the actual nonmissing records, and each reported denominator matches the analysis set. Inspect the availability pattern by assay and by the study characteristics relevant to the question. Look for impossible combinations, duplicated subjects, and values that were coded as zero or another number when they should have been recorded as unavailable. These checks do not identify every cause of missingness, but they can uncover errors that would invalidate the analysis.
A useful reporting statement names both the result and its data basis: for example, “The RNA–protein correlation was calculated from 60 subjects with both assays; it describes the observed paired subset.” If a conclusion is intended to apply to the full cohort, state the assumptions that support that extension and the evidence available to assess them. Do not silently move from “among subjects with both assays” to “among all enrolled subjects.”
- Wrong: “The missing protein value was zero, so it was included as no protein expression.” Correction: An unobserved value is not a zero measurement. Preserve its unavailable status unless the assay’s scientific definition makes zero a genuine observed value.
- Wrong: “Every analysis uses the cohort size of 120.” Correction: State the assay-specific, pairwise, or complete-profile denominator for each result.
- Wrong: “The observed RNA mean estimates the full-cohort mean because 100 subjects is a large sample.” Correction: Sample size alone does not remove selection; representativeness depends on how availability relates to the values and target population.
- Wrong: “The complete-profile subset is safest because every subject has every assay.” Correction: A common subset can be useful, but restricting to it may discard data and select a subgroup; its size and availability pattern still need to be reported.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A cohort has 90 subjects, 70 with RNA data and 55 with protein data; 40 have both. What denominator belongs in a direct RNA–protein comparison?
- Among subjects with an observed assay, a sample mean is 8.2 units. Does this alone establish that the full-cohort mean is 8.2 units? State the key issue.
- In a hypothetical cohort, 18 of 30 subjects with a metabolite assay and 14 of 20 without it have a clinical feature. Calculate both proportions and their difference, defined as with-assay minus without-assay.
- Why might pairwise overlaps be preferable to a complete-profile subset for one analysis, and what qualification must be reported?
Solutions. (1) Use the 40 subjects with both RNA and protein measurements; the denominator is \(n=40\), not 70, 55, or 90. (2) No. The value is the mean among observed subjects; extension to the full cohort depends on how assay availability relates to the unobserved values and on the intended target. (3) The proportions are \(18/30=0.600\) and \(14/20=0.700\). Their difference is \(0.600-0.700=-0.100\), or minus 10.0 percentage points. (4) A pairwise overlap can retain subjects who lack an assay not needed for that particular comparison. Report its exact denominator and make clear that another pairwise result may use a different subject set.