Why the Decision Is More Than a Point Estimate
A bioequivalence result is not decided by asking whether the estimated test-to-reference ratio looks close to 1. A regulatory decision asks whether the study meets the prespecified acceptance criteria using the required endpoints and analysis. The estimate and its uncertainty both matter: an estimate can lie comfortably within the acceptance limits while its confidence interval extends beyond one of them.
This tutorial uses the conventional 80–125% limits to illustrate outcome classification. Actual limits, endpoints, confidence level, and analysis must come from the applicable prespecified criteria; product-specific or jurisdiction-specific requirements can differ. The introductory material on average bioequivalence and the all-criteria rule establishes the setting: when multiple primary endpoints have required criteria, every one must satisfy its own criterion.
For the conventional average BE criterion, the estimated test-to-reference geometric mean ratio and its prespecified 90% confidence interval are assessed against the limits. Expressed as percentages, the interval must lie wholly within 80–125%, with equality at a limit treated according to the exact prespecified rule. Unless otherwise stated, examples below assume inclusive limits. Make the decision from unrounded values, then report suitably rounded values.
Three Possible Outcomes
A useful decision process starts by checking whether the criteria and the result are identifiable and valid. If they are, compare each required estimate and interval with its prespecified limit. Do not change the limits, endpoints, confidence level, or decision rule after seeing the results.
Confirm that the required endpoint, comparator, analysis, and data are available and suitable for applying the prespecified rule. If not, report that criterion as not evaluable and explain why.
For an interval-based criterion, check whether the complete required confidence interval lies within the specified limits, using unrounded values and the stated boundary convention.
Report an overall BE conclusion only if every required criterion is evaluable and met. If any evaluable required criterion is not met, the overall criteria are not satisfied. If a required criterion cannot be evaluated, the overall conclusion is not fully assessable.
The word “borderline” should prompt careful checking, not a relaxed decision rule. A confidence interval that misses a limit by a small amount still does not satisfy a criterion requiring the whole interval to be inside that limit. Conversely, proximity to a limit does not establish a clinically important difference: the regulatory classification concerns whether the specified evidential standard was met.
Worked Decisions
Worked Example: A Valid Interval That Meets the Criterion
In a hypothetical study, the prespecified conventional criterion for AUC is an estimated test-to-reference geometric mean ratio with its 90% confidence interval wholly within 80–125%. Suppose the analysis is valid and gives a ratio of 103%, with log-scale estimate \(\hat{\theta}=\ln(1.03)=0.02956\), standard error \(SE=0.0750\), and \(df=23\). For this illustration, the two-sided 90% interval uses \(t_{0.95,23}=1.714\).
On the log scale, the interval is \(\hat{\theta}\pm t_{0.95,23}SE\). Substituting the values gives:
Exponentiating the endpoints and converting to percentages gives:
Both endpoints are within 80–125%, so this AUC criterion is met. This is not, on its own, an overall BE conclusion: every other required primary criterion must also be evaluable and met.
Worked Example: A Favorable Estimate With a Borderline Failure
In a second hypothetical analysis, the estimated ratio is 90.0%, which lies within 80–125%. Its valid, prespecified 90% confidence interval is 79.8–101.5%. Assume these are unrounded values and the criterion requires the entire interval to be within the inclusive limits.
The point estimate passes the range check, but the lower confidence limit does not: \(79.8\%<80\%\). The full interval is therefore not contained in 80–125%, so the criterion is not met. Calling the result “borderline” may describe how narrowly it misses the lower limit, but it does not change the classification.
The correct interpretation is that this analysis did not demonstrate BE under the stated criterion. It is not correct to conclude from this interval alone that the true ratio is below 80%, or that the products are clinically different. The interval includes values inside the acceptance range as well as values just below it.
Worked Example: One Failed Endpoint Determines the Overall Criteria Result
A hypothetical study requires both AUC and Cmax to meet conventional interval criteria. The valid 90% confidence interval for AUC is 96–112%, while the estimate for Cmax is 118% and its 90% confidence interval is 108–128.3%. All values are in percentages.
For AUC, both 96% and 112% lie within 80–125%, so that criterion is met. For Cmax, the point estimate of 118% lies within the limits, but the upper confidence limit is \(128.3\%>125\%\). The Cmax criterion is not met.
Because both endpoints are required, the all-criteria rule means the study has not satisfied the overall BE acceptance criteria. The passing AUC result cannot offset the failing Cmax result, and the favorable Cmax point estimate cannot replace its failed interval criterion. This outcome is a failure to demonstrate BE under the stated rules, not proof that Cmax differs by a clinically meaningful amount.
Worked Example: A Required Criterion Cannot Be Evaluated
In a hypothetical study, AUC is analyzed successfully and its required interval is within its prespecified limits. However, a documented assay failure means no valid Cmax result can be produced. Suppose Cmax is also a required primary criterion.
The AUC criterion is met, but the Cmax criterion is not evaluable: there is no valid result to compare with its limits. The overall conclusion cannot be that all BE criteria were met. The appropriate report identifies the missing evaluable criterion and the reason, rather than treating the missing Cmax result as either a pass or an interval-based failure.
Not every missing value makes an endpoint unevaluable; the effect depends on the prespecified analysis and the amount and pattern of available data. Likewise, a valid but wide interval is still evaluable: if it extends outside the acceptance limits, the criterion is not met, not “not evaluable.”
Why the All-Criteria Rule Works
The logic can be stated as a short derivation. Suppose there are \(k\) required criteria and each has its own acceptance test at level \(\alpha\). The overall claim is made only when every criterion passes. Its null hypothesis is the union that at least one required criterion is outside its acceptance region; its alternative is the intersection that all required criteria satisfy their rules.
If \(H_0\) is true, at least one component null, say \(H_{0j}\), is true. A false overall claim requires passing that component test despite its null being true. Since the overall claim requires passing all tests, its probability of a false positive is no larger than the probability of falsely passing this one true component null:
This is the intersection–union logic behind requiring all primary criteria to pass; it does not mean that passing one endpoint compensates for another. The derivation assumes the component tests are each calibrated to the specified level and that the prespecified decision rule is followed. It does not permit substituting a different endpoint or decision rule after results are known.
Diagnostics, Alternatives, and Limits
Before finalizing a classification, check that the exact applicable criteria were used and that the reported interval corresponds to the specified endpoint, analysis, confidence level, and comparator. Verify that limits and estimates are on the same scale: a ratio of 0.98 corresponds to 98%, not 0.98%. Check the unrounded values if a displayed endpoint appears to equal a boundary. A value rounded to 80.0% might actually be just below or just above 80%.
A failed criterion and an unevaluable criterion need different explanations. A valid interval outside a limit is an assessable failure of the rule. Missing or invalid information may prevent assessment, but a protocol deviation, a small sample, or an inconvenient result does not automatically make a criterion unevaluable. The decision requires a reasoned assessment of whether the prespecified analysis remains valid. Report the issue and its impact rather than using “not evaluable” as a way to avoid an unfavorable result.
A simple point-estimate rule is an inadequate alternative to an interval-based criterion because it ignores uncertainty. A binary summary can also hide important distinctions: it may conflate failure to meet a rule with inability to assess it. A clear report states the result for each required criterion, the basis for its classification, and the overall consequence. The precise regulatory wording can vary, so use the applicable guidance and avoid claiming more than the criteria support.
The decision has limits. Meeting prespecified statistical criteria supports a regulatory BE conclusion under those criteria; it does not establish that every patient will have identical exposure, nor does it answer every question about clinical similarity. Not meeting a criterion means the evidential standard was not attained in that analysis; it does not establish the opposite claim. These distinctions are especially important when an interval lies close to a boundary.
Common Mistake
Wrong reasoning: “The ratio is 98%, which is inside 80–125%, so BE is accepted.” This ignores the uncertainty interval and may ignore other required endpoints. Correction: apply the complete prespecified rule to each required criterion. If the interval extends beyond a limit, that criterion is not met even when the point estimate is favorable. If required information is unavailable, report the criterion as not evaluable rather than calling it a pass.
Check Your Understanding
For each item, decide what the result supports. Then compare your reasoning with the solutions below.
- A required endpoint has a valid 90% interval of 80.0–119.0%, and the prespecified limits are inclusive 80–125%. Is the criterion met?
- A ratio estimate is 101%, but its valid interval is 76–122%. What is the criterion classification, and what conclusion should not be drawn?
- A study requires AUC and Cmax. AUC meets its criterion, while Cmax is validly estimated but its interval crosses the upper limit. What is the overall result?
- A required endpoint has no valid result because the necessary assay data are unavailable. Is that the same as a valid interval outside the limits?
- Why does a favorable point estimate not establish acceptance when the acceptance rule is based on the entire confidence interval?
Solutions. (1) Met: both endpoints of the interval lie within the inclusive limits, including the lower endpoint at 80.0%. (2) Not met: the interval extends below 80%. This does not prove the true ratio is below 80% or establish a clinically meaningful difference. (3) The overall criteria are not satisfied because one required, evaluable criterion is not met; the AUC pass does not compensate. (4) No. The endpoint is not evaluable because no valid result is available; an interval outside the limits would be an evaluable result that fails its rule. (5) The interval represents uncertainty around the estimate. Even if the estimate itself lies within the limits, an interval extending beyond a limit does not satisfy a rule requiring the whole interval to be contained within them.