Why Plan Complete Pairs?
A multi-omics question often concerns how two molecular layers relate within the same biological subject. To address that question, a study must do more than collect an RNA profile from some participants and a protein profile from others: it must specify which subjects are eligible, which assays each eligible subject is expected to provide, and how the records will be linked. Planning these elements in advance makes the intended paired analysis set explicit rather than leaving it to be reconstructed from assay files later.
A complete-pair design aims to collect all required assays from every eligible subject. In practice, a specimen may be unusable, an assay may fail, or a participant may withdraw. The planned design and the observed analysis set are therefore not necessarily identical. Defining both precisely helps quantify that difference and prevents an incomplete record from being mistakenly treated as a complete pair.
The word “pair” refers to two assay records belonging to the same subject under the specified study conditions. It does not mean that an RNA feature must have a one-to-one counterpart among protein features. A study may integrate different feature sets while still requiring that both assay profiles come from each subject in \(C\). The earlier material on mapping subjects to assays provides the general framework for identifying which records belong together; here the emphasis is on planning and checking complete coverage.
Specify the Plan Before Collecting Data
A usable plan states the target population and eligibility rules, the required assays, and the criteria for a valid result. It also describes the biological material and collection conditions sufficiently to make the intended pairing meaningful. For example, RNA and protein measurements might both be required from a specified tissue collected at a defined visit. If one assay uses a different visit or tissue without that being part of the design, the records may be linked to the same person but may not represent the planned pair.
Eligibility is established before defining assay coverage. Examples of eligibility criteria include age range, diagnosis, study site, availability of the specified specimen, or consent for both assays. The criteria should be applied consistently and documented at the subject level. Assay success is a separate matter: an eligible subject remains in \(E\) even if a later assay fails, but that subject will not be in \(C\) unless both assay results are valid and linkable.
A protocol or tracking table should make the plan operational. It can include a study subject identifier, eligibility status, collection visit, specimen identifiers, assay status for each platform, result-validity status, and reasons for missing or invalid results. Direct identifiers should not be used as analysis keys when a secure study identifier can link records. The linkage rule must be defined so that two records are not assigned to the same subject merely because their labels look similar.
Worked Example: Defining the Eligible Pair Set
Hypothetical example. A study plans to profile RNA and protein in blood collected at the baseline visit from adults aged 40–65 with a specified diagnosis. Forty people are screened; 32 satisfy all eligibility criteria and consent to both assays. Define the sets and determine the maximum planned complete-pair count before assay failures.
Let \(E\) contain the 32 eligible subjects. The protocol requires a baseline blood specimen for both assays from every subject in \(E\). Before any assay results are available, the intended design has 32 planned pairs: one RNA profile and one protein profile per eligible subject. The maximum possible observed complete-pair count is therefore \(|E|=32\).
This count assumes the planned specimens can be collected and that both assays yield valid, linkable results. It does not imply that all 32 subjects will necessarily enter \(C\). A screened person who does not meet the criteria is not in \(E\), and is not counted as an assay failure. An eligible person whose protein assay later fails remains in \(E\), but cannot be in \(C\) unless a valid protein result is obtained under the protocol's rules.
The plan is complete-pair because both assays are required for each eligible subject. Merely stating that the study will include 32 RNA samples and 32 protein samples would be insufficient: those totals alone would not establish that the samples came from the same 32 subjects.
Count the Observed Complete Pairs
After assay processing, \(R\) and \(P\) record coverage among eligible subjects. The intersection \(R\cap P\) is essential: a subject with only an RNA result or only a protein result is not a complete pair. The following identity separates the four possible coverage patterns within \(E\). It follows by dividing the eligible subjects into disjoint groups: both assays, RNA only, protein only, and neither assay.
The groups on the right are disjoint and together contain every member of \(E\). Equivalently, because \(R,P\subseteq E\), inclusion-exclusion gives the complete-pair count as
This calculation is a useful audit: counting assay results separately is not enough to recover the overlap unless the number of subjects with at least one valid assay is also known. When a subject-level tracking table is available, count the intersection directly and check it against the four-cell breakdown.
Worked Example: Auditing Two-Platform Coverage
Hypothetical example. Among 40 eligible subjects, 36 have a valid RNA result and 34 have a valid protein result. The subject-level linkage audit finds that 32 have at least one valid assay. Find the number with both assays and classify the remaining eligible subjects.
Because \(R\) and \(P\) contain only eligible subjects, inclusion-exclusion applies within \(E\):
This arithmetic is impossible: an intersection cannot be larger than either set, but \(38>34\). The reported counts are inconsistent. This is exactly why a coverage audit should check the set identities rather than accept totals at face value. In particular, the stated 32 subjects with at least one assay cannot be correct when 36 have RNA results.
Suppose the audit corrects the count with at least one assay to 38. Then
There are \(36-32=4\) RNA-only subjects and \(34-32=2\) protein-only subjects. The number with neither assay is \(40-38=2\). The complete four-cell check is \(32+4+2+2=40\), matching \(|E|\). Thus \(n_C=32\) eligible subjects have both valid, linkable results.
Check the Meaning of “Valid” and “Paired”
A result should count toward \(R\) or \(P\) only under criteria defined for the study. Depending on the assay and research question, those criteria may include successful processing, required quality-control status, adequate specimen identity, and availability of the intended measurement. A file existing is not by itself evidence of a valid result. Conversely, a result should not be excluded after seeing its values merely because it is inconvenient; the usability rule should be prespecified and applied consistently.
Pairing also requires reliable subject-level linkage. A study identifier should map each assay record to one eligible subject without ambiguous duplicates. If multiple specimens or visits are collected, the plan must state which specimen and visit form the pair. For example, an RNA result from baseline and a protein result from a later visit may be a valid longitudinal collection, but it is not the baseline complete pair unless the protocol explicitly allows that combination.
The intended analysis unit should be clear. If each subject contributes one profile per assay, the complete-pair set contains one paired profile per subject. If repeated samples are planned, the protocol needs a rule for which time points or specimens are paired; counting several records from one person as several independent subjects would misrepresent the design. The subject remains the unit for subject-level pairing even when there are many measured features within each assay.
Worked Example: From Collection Plan to Analysis Set
Hypothetical example. A team plans a two-platform study of 50 eligible participants. Every participant is scheduled for one baseline tumor specimen for RNA sequencing and one baseline tumor specimen for protein measurement. After collection and processing, 47 RNA results and 45 protein results pass the prespecified validity rules. A verified subject-level audit identifies 43 participants with both results.
The planned set is \(E\), with \(|E|=50\). The observed assay sets satisfy \(R\subseteq E\), \(|R|=47\), and \(P\subseteq E\), \(|P|=45\). The paired analysis set has \(n_C=|R\cap P|=43\), as established by the direct audit.
The remaining cells follow from subtraction. RNA only: \(47-43=4\). Protein only: \(45-43=2\). Neither: \(50-(43+4+2)=1\). The check is \(43+4+2+1=50\), so every eligible subject is accounted for exactly once. The analysis set contains 43 people, not 47, 45, or 50.
The collection schedule specifies both assays on the same specimen type and at the same visit, and the audit confirms subject linkage. Those facts support treating the 43 records as the planned pairs. They do not establish that the observed subjects represent all eligible participants or that missing assay results have no analytic consequences; those are separate considerations.
Planning for Failure, Diagnosing Problems, and Alternatives
A complete-pair plan should anticipate that collection or assay failure may reduce \(n_C\). If planning uses an expected completion proportion \(q\), then a rough operational calculation for the number to enroll is \(N_{\text{enroll}}\approx N_{\text{target}}/q\), where \(N_{\text{target}}\) is the desired number of complete pairs. For instance, if the team aims for 80 complete pairs and expects 0.80 of enrolled eligible subjects to produce both valid results, the rough enrollment target is \(80/0.80=100\). This is a planning approximation, not a power calculation; it depends on the assumed completion rate and does not guarantee the target.
Useful diagnostics include checking that every assay record maps to exactly one eligible subject, that each subject is counted once in each coverage cell, and that the four cells sum to \(|E|\). Compare planned and observed assay statuses, summarize reasons for invalid or absent results, and check whether failures cluster by collection site, visit, specimen type, or other recorded factors. Such patterns can reveal workflow problems or systematic differences in who enters the paired set. The reason for an absent assay should be retained rather than collapsed into an unexplained blank.
The main alternative is to analyze each assay using all subjects with that assay available, even when the subject lacks the other platform. That can retain more observations for analyses that do not require joint profiles, but those assay-specific sets are not a complete-pair set. Another option is to design collection so that the platforms use different subjects; this changes the design and the information available for within-subject integration. The choice depends on the research question, not on which arrangement is easiest after data collection.
A complete-pair design can simplify subject-level comparisons across layers because both measurements are observed on the same subjects. Its limitation is that the analysis set may be smaller than the eligible cohort, and it may differ systematically from that cohort if assay completion is related to subject or specimen characteristics. Pairing alone does not remove technical batch effects, measurement-scale differences, confounding, or other sources of bias. Nor does observing two molecular layers in the same subject establish a causal relationship between them.
A Practical Planning Sequence
Specify who enters \(E\), when eligibility is assessed, and how exclusions are recorded.
For each eligible subject, state the specimen, visit, and assay results needed for a complete pair.
Define what qualifies for membership in each assay set and how records are assigned to subjects.
Record both assays, RNA only, protein only, or neither for every eligible subject.
Calculate \(C=R\cap P\), verify the coverage identity, and describe how observed coverage differs from the plan.
Check Your Understanding
Answer each question, then compare with the solutions below.
- Among 25 eligible subjects, 22 have valid RNA results, 20 have valid protein results, and 23 have at least one valid result. How many have both?
- In Question 1, how many subjects have RNA only, protein only, and neither assay?
- Explain why 18 RNA results and 18 protein results do not prove that a study has 18 complete pairs.
- A subject is eligible but has no valid protein result. Is the subject in \(E\), in \(P\), and in \(C\)? State the answer under the definitions in this tutorial.
- A paired collection uses an RNA sample from baseline and a protein sample from a different visit. What planning question must be resolved before treating these as a complete pair?
Solutions. (1) By inclusion-exclusion, \(n_C=22+20-23=19\). (2) RNA only is \(22-19=3\); protein only is \(20-19=1\); neither is \(25-(19+3+1)=2\). The cells sum to \(25\). (3) The assay totals do not reveal subject overlap; the same 18 subjects may not have both results. The intersection must be checked using subject-level linkage. (4) The subject is in \(E\), not in \(P\), and therefore not in \(C=R\cap P\). (5) The protocol must specify whether the intended pair is required to come from the same visit or whether that particular cross-visit pairing is scientifically defined and permitted; otherwise it is not the planned same-visit complete pair.