Why Analysis-Set Decisions Matter
A bioequivalence result depends not only on the model and endpoint, but also on which subjects contribute data to the analysis. A missed dose, an incorrect dosing condition, or a sample collected outside the permitted window may affect whether an endpoint is interpretable. The decision to exclude a subject can therefore change an estimated treatment difference and its confidence interval.
The decision must follow rules specified before investigators know the treatment comparison results. An analysis set is not a convenient subset assembled after looking at which subjects move the confidence interval toward the acceptance limits. The practical task is to connect each deviation to a prespecified rule, record the resulting decision, and show how that decision affects the interpretation.
Names such as “full analysis set,” “per-protocol set,” and “safety set” are used with some variation across protocols and regulatory settings. Their labels alone do not determine who belongs in them. The protocol and statistical analysis plan should define membership operationally: for example, whether subjects must have received study treatment, whether both crossover periods must be evaluable, and which major deviations preclude inclusion in the primary bioequivalence analysis.
Disposition and analysis membership answer different questions. Disposition accounts for what happened to every randomized subject: treatment received, completion or withdrawal, and the reason for discontinuation. Analysis-set decisions then apply defined rules to that record. Keeping the two steps separate makes it possible to account for every subject without treating every deviation as grounds for exclusion.
From Deviation Log to Analysis Decision
A useful review begins with a log that records the subject, deviation, timing, potential consequence for the endpoint, prespecified rule, decision, and rationale. “Major” and “minor” can be useful classifications when defined in advance, but a label without a stated consequence is not a decision rule. For example, an omitted sample near the expected concentration maximum may affect \(C_{\max}\), while an omitted late sample may affect an area-under-the-curve endpoint. Whether either omission makes the endpoint unevaluable depends on the sampling schedule and the prespecified pharmacokinetic rules.
The review should distinguish at least three cases. First, a deviation may make a particular endpoint unavailable or invalid, such as when a required period has no usable concentration data. Second, a major deviation may meet a prespecified criterion for excluding the subject from the primary bioequivalence analysis even if some measurements can still be calculated. Third, a deviation may be documented but not affect analysis-set membership because the endpoint remains evaluable and no exclusion rule applies. The decision can differ by endpoint: a subject might contribute to one endpoint analysis but not another if the rules allow it.
Account for each randomized subject, including treatment received, periods completed, and withdrawals. Resolve discrepancies between clinical, laboratory, and analysis records.
Record what happened, when it happened, and which endpoint or period might be affected. Apply the protocol’s definitions rather than inventing a new threshold during analysis.
Determine eligibility separately for each relevant analysis set. Do not use the size or direction of a subject’s treatment contrast to decide membership.
Report set counts, reasons for exclusions, endpoint-specific evaluability, and how justified exclusions change estimates and intervals.
These decisions assume that the protocol and analysis plan give sufficiently clear rules, that deviations are recorded accurately, and that the rules are applied consistently without knowledge of the treatment comparison where practicable. The underlying crossover analysis also relies on its specified design and model assumptions: for example, the planned treatment and period effects must be estimable, and the endpoint data must be valid under the pharmacokinetic procedures. An analysis-set decision cannot repair a design or measurement problem that invalidates the analysis.
Worked Example: Reconciling a Mock Subject Disposition
Suppose a hypothetical two-period crossover study randomizes 26 subjects. The protocol defines the primary bioequivalence set as subjects with evaluable pharmacokinetic data for both periods and no prespecified major deviation. The safety set includes all subjects who receive at least one dose. Review of the disposition record and deviation log produces the following summary.
| Disposition or deviation | Subjects | Decision under the stated rules |
|---|---|---|
| Completed both periods; no major deviation | 22 | Include in the primary bioequivalence set and safety set |
| Completed both periods; prohibited interacting medicine taken during one period | 1 | Exclude from the primary set under the prespecified major-deviation rule; retain in safety summaries |
| Completed both periods; fed before a dose despite the required fasting condition | 1 | Exclude from the primary set under the prespecified major-deviation rule; retain in safety summaries |
| Withdrew before receiving any study treatment | 1 | Exclude from the safety set and primary set; report as a randomized withdrawal |
| Withdrew after receiving the first treatment but before completing the second period | 1 | Include in the safety set; exclude from the paired primary analysis because the required two-period data are unavailable |
The disposition reconciles to \(22+1+1+1+1=26\) randomized subjects. The safety set contains 25 subjects, because 25 received at least one dose. The primary bioequivalence set contains 22: the two subjects with major deviations are excluded under the stated rule, and the two withdrawals lack the required paired data. This example depends on the hypothetical protocol’s definitions; another study’s rules could differ.
Quantifying the Effect of Justified Exclusions
For a conventional average bioequivalence assessment, the relevant pharmacokinetic endpoints are commonly analyzed on the log scale. The treatment contrast is expressed as a difference in mean log endpoint values; exponentiating that contrast gives a test-to-reference geometric mean ratio. A confidence interval is compared with the applicable acceptance limits. The precise model, endpoints, and limits must be those specified for the study.
In the next example, the hypothetical protocol prespecifies the primary set above and also asks for an inclusive analysis of all subjects with evaluable paired data. The reported estimates and standard errors are outputs from the same prespecified crossover model, applied to the respective sets. For clarity, the interval calculation uses the reported degrees of freedom and a two-sided 90% \(t\) interval. The analysis is illustrative; it does not establish a universal rule that one analysis set should replace another.
Worked Example: How Two Prespecified Exclusions Change an AUC Result
For log-transformed AUC, suppose the primary-set model output for the 22 eligible subjects is a test-minus-reference estimate of \(0.1400\) with \(SE=0.02772\) and \(df=21\). The corresponding inclusive analysis of all 24 subjects with evaluable paired data gives an estimate of \(0.1800\), \(SE=0.03782\), and \(df=23\). For this hypothetical endpoint, use acceptance limits of 80.00% to 125.0%.
For the primary set, the 90% interval on the log scale is
Exponentiating both limits gives a geometric mean ratio interval of
Both limits lie within 80.00% to 125.0%, so this endpoint meets the stated interval criterion in the prespecified primary set. This is not evidence that there is a 90% probability that the true ratio lies in this particular interval; the interval is produced by a procedure with 90% repeated-sampling coverage under its assumptions.
For the inclusive analysis, the calculation is
After exponentiation, the interval is
The inclusive interval exceeds the upper limit. The two justified exclusions therefore change the endpoint’s interval-based outcome across the two analysis sets. The appropriate report is not to select whichever result supports the desired conclusion. It is to state that the prespecified primary analysis meets the criterion, the inclusive analysis does not, identify the exclusions and their prespecified basis, and explain that the conclusion is sensitive to analysis-set membership. The bioequivalence conclusion for the study must also account for all required endpoints and the protocol’s decision rule.
The interval comparison presumes that the model and its assumptions are suitable for the data in each set, including that the planned treatment contrast is estimable and that the standard error and degrees of freedom are appropriate. Review residuals, influential observations, missingness patterns, and model diagnostics using the planned procedures. A deviation log is not a substitute for those checks. The earlier material on sensitivity analysis after protocol deviations addresses the broader role of alternative analyses; here, the central requirement is to anchor each analysis-set choice to an auditable rule.
Worked Decisions at the Boundary
Some deviations are less clear-cut than a missed period or a documented major dosing violation. The most defensible approach is to ask what the rule says about the affected endpoint and whether the data remain interpretable, not whether the observed value appears unusual. A low concentration is not, by itself, proof of a dosing deviation; nor is an unusually high concentration automatically grounds for exclusion.
Worked Example: A Missed Sample Near \(C_{\max}\)
In a hypothetical study, one subject completes both periods and has otherwise valid dosing and sample records. In the test period, a scheduled sample near the expected peak is missed. The protocol states that a \(C_{\max}\) value is unevaluable if a specified critical peak-window sample is absent, but that the AUC may remain evaluable when the remaining sampling schedule satisfies the prespecified AUC rule.
Decision for \(C_{\max}\). The missing sample meets the stated criterion for an unevaluable \(C_{\max}\) in that period. If the primary \(C_{\max}\) analysis requires evaluable values in both periods, this subject is excluded from that endpoint’s paired analysis.
Decision for AUC. The AUC rule is checked separately. If the available samples satisfy its requirements, the subject can contribute to the AUC analysis. Excluding the subject from both endpoints merely because one peak-window sample is missing would not follow the stated endpoint-specific rules.
Documentation. Record the missed sample, its timing, the applicable rule, and the endpoint-specific decision. Do not replace the missing value with an invented concentration or remove the subject from an endpoint for which the data remain valid under the protocol.
Diagnostics, Reporting, and Common Pitfalls
Several checks help detect inconsistent analysis-set decisions. Reconcile the randomized, treated, completed, and analyzed counts. Confirm that every exclusion has a recorded subject-level reason and a cited rule. Check that endpoint-specific counts agree with the actual availability and validity of the required period data. Compare the primary and inclusive results using the same model specification where that comparison is meaningful. Unexpected changes in estimates or standard errors should prompt a check of data handling, model inputs, and membership—not an undocumented change to the rule.
For transparency, report the number of subjects in each set, the number and reasons for exclusions, endpoint-specific evaluability where relevant, the analysis method, and the estimated treatment ratio with its confidence interval. Describe discrepancies between the primary and inclusive analyses in context. If a deviation is discovered after unblinding or after results are reviewed, disclose that timing and explain how the decision was made; do not present a post hoc rule as if it had been prespecified.
A common mistake is to remove an influential subject because that subject makes the interval fail, then describe the reduced-set result as the primary result. The correction is to apply the prespecified criteria without regard to the subject’s treatment contrast, report the required primary analysis, and show a justified alternative analysis when appropriate. Conversely, retaining a subject whose data fail a prespecified endpoint-validity rule simply to preserve sample size is also incorrect.
Analysis-set comparisons have limitations. A result that changes after exclusions may reflect the subjects’ influence, a changed sample size and precision, or both. It does not prove that the excluded subjects were “wrong,” that the inclusive analysis is automatically preferable, or that the primary result is invalid. Likewise, passing a criterion in one set does not erase a conflicting result in another set. The interpretation depends on the prespecified primary analysis, the rationale for deviations, and the complete bioequivalence decision rule.
Check Your Understanding
Answer each question using the decision principles and calculations in this tutorial.
- A subject received one dose and then withdrew before the second crossover period. If the safety set includes everyone dosed and the primary analysis requires evaluable data from both periods, which set includes the subject?
- A subject has a missed sample that makes \(C_{\max}\) unevaluable under the protocol, but the AUC remains evaluable. Must the subject be excluded from both endpoint analyses?
- In a primary-set analysis, the estimated log treatment contrast is 0.100 and its 90% interval is \([0.040,\;0.160]\). What is the exponentiated interval to three significant figures, and does it lie within 80.00% to 125.0%?
- An inclusive analysis fails the interval criterion, while the prespecified primary analysis passes after two subjects are excluded for documented major deviations. What should the report say?
Solutions. (1) The subject belongs in the safety set because at least one dose was received, but not in the paired primary analysis because the second-period data are unavailable. (2) No. Apply the rules separately: exclude the subject from the \(C_{\max}\) analysis if required, but retain the subject for AUC if its evaluability rule is satisfied. (3) Exponentiation gives \([\exp(0.040),\exp(0.160)]=[1.041,\;1.174]\), or \([104.1\%,\;117.4\%]\). Both limits are within the stated bounds. (4) Report both results, the prespecified basis for each exclusion, and that the endpoint conclusion differs by analysis set. Do not replace the primary result with the inclusive result or hide the discrepancy.