Why the Primary Question Must Stay Fixed
A sample-size re-estimation is intended to change how much information a trial collects, not what scientific claim the trial is designed to answer. This distinction can become blurred when interim results are available. A change to eligibility, the primary endpoint, the clinical margin, or the primary analysis may appear to be a practical adjustment, but it can redefine the population, outcome, or treatment effect being evaluated.
The central diagnostic is simple: if the adaptation changes what a positive or negative primary result would mean, it has changed the question. That does not make the revised question inherently unimportant. It does mean the result may no longer provide the originally planned answer, and that selecting the new question in response to interim outcomes can compromise error control and interpretation.
For example, a trial might ask whether an investigational treatment improves mean symptom score at 12 weeks among adults meeting specified eligibility criteria, compared with control. The question includes who is targeted, what is measured and when, which treatments are contrasted, and how their difference is summarized. Re-estimating a nuisance variance to increase the planned sample size can leave all of these features intact. Restricting enrollment to a subgroup because its interim treatment effect looks more favorable does not.
What Counts as Changing the Question?
Eligibility criteria define which patients the trial is designed to represent. Changing them can change the target population, particularly if the primary analysis is restricted to the newly eligible patients. An effect estimate in a biomarker-positive subgroup answers a different population-specific question from an effect estimate in the originally defined overall population. An eligibility change made for operational reasons may not always redefine the estimand, but the intended target and the analysis population must be examined rather than assumed to be unchanged.
The endpoint defines the outcome on which the treatment claim rests. Replacing a prespecified endpoint with a different measure, time point, or composite after examining interim results changes what benefit is being tested. The new outcome may be clinically meaningful, but its test is not automatically an unaltered test of the original endpoint. If multiple outcomes are examined and the most favorable one is selected, the selection can also affect the false-positive rate unless the inferential procedure accounts for it.
A margin in a noninferiority or equivalence question defines what difference is considered acceptably small. Changing that margin changes the hypothesis itself. Likewise, changing the primary analysis can change the question if it changes the analysis population, effect summary, or assumptions that connect the estimate to the target. A different estimator can sometimes target the same effect; the key is whether the target and valid inference remain the same, not whether the analysis formula looks different.
| Adaptation | Usually preserves the question when... | May change the question when... |
|---|---|---|
| Sample size | Only the planned enrollment changes; the target, endpoint, contrast, and test remain fixed. | The update is paired with a data-driven change in the target, endpoint, or decision threshold. |
| Eligibility | Operational adjustments leave the target population and primary analysis population intact. | The primary claim becomes about a selected or enriched subset rather than the original population. |
| Endpoint | A prespecified measurement detail is clarified without changing the outcome being summarized. | A different outcome or time point is promoted to primary based on interim results. |
| Margin or analysis | The prespecified threshold and estimand remain fixed, and the analysis still gives valid inference for them. | The threshold, effect measure, or analysis population is changed to favor a desired conclusion. |
Worked Examples
Worked Example: Updating a Variance Without Changing the Target
Suppose a hypothetical two-arm trial compares mean symptom-score change at 12 weeks in the originally defined population. The planned difference of interest is 5 points, the common standard deviation is initially estimated as 12 points, the allocation is equal, the test is two-sided with \(\alpha=0.05\), and target power is 90%. An interim nuisance-parameter update suggests a standard deviation of 15 points. Does increasing enrollment change the primary question?
Under the normal-approximation planning formula for two independent groups with equal variance and equal allocation, the required sample size per group is
Here \(\Delta=5\) points, \(z_{0.975}=1.960\), and \(z_{0.90}=1.282\). With the updated \(\sigma=15\) points,
Rounding up gives 190 participants per group under this approximation. The assumptions for the calculation are independent observations, equal allocation, a continuous outcome with a common variance represented by \(\sigma^2\), and a normal-approximation test. The interim estimate is being used to update a nuisance parameter, not to choose a more favorable outcome or subgroup. The 12-week endpoint, target population, treatment contrast, and test remain fixed, so this update changes the planned information, not the primary question.
Worked Example: Restricting Eligibility Changes the Target Population
In a hypothetical trial, 60% of the originally targeted population has biomarker type A and 40% has type B. The treatment’s mean benefit, defined as control mean minus treatment mean so that positive values favor treatment, is 4 points in type A and −1 point in type B. Assume these subgroup effects and population proportions are the values relevant to the planned population-level summary.
The treatment effect averaged over the original population is
If an interim review leads to restricting enrollment and the primary analysis to type A, the target effect becomes 4 points in type A, not 2 points in the original population. The two values answer different questions: the first concerns the original mixture of biomarker types, and the second concerns type A alone. The change might be scientifically defensible if the intended claim is revised and justified independently, but it is not merely a sample-size update. In particular, choosing type A because its interim result looked more favorable makes the new target data-dependent.
Worked Example: Relaxing a Noninferiority Margin Changes the Hypothesis
Consider a hypothetical noninferiority trial with treatment difference \(\theta=p_T-p_C\), where \(p_T\) and \(p_C\) are event probabilities and lower values are better. The estimated difference is \(\hat{\theta}=-0.08\), with \(SE=0.03\). The original noninferiority margin is \(M=0.05\), so the hypotheses are \(H_0:\theta\leq -0.05\) and \(H_a:\theta>-0.05\).
The test statistic at the original boundary is
For a one-sided test at \(\alpha=0.025\), the critical value is approximately 1.960. Since \(-1.00\) is not greater than 1.960, these data do not establish noninferiority using the original margin.
If the margin were changed to \(M=0.15\), the null boundary would instead be \(-0.15\), giving
That statistic exceeds 1.960, so the same estimate would pass this one-sided test at the stated level under the wider margin. But the wider margin permits a larger loss in efficacy; it is a different clinical standard and a different hypothesis. Selecting it after observing interim data to obtain a favorable result is not an innocuous way to revise sample size.
Why Data-Driven Changes Are Risky
An interim result is uncertain. If it is used to select a subgroup, endpoint, margin, or analysis that looks favorable, the final test is no longer simply the prespecified test applied to new data. Even when the final sample is larger, selection based on interim outcomes can make estimates optimistic and can raise the probability of a false-positive claim. The direction and size of the distortion depend on the adaptation and the inferential procedure; a larger sample does not itself correct it.
A useful formal check is to write down the target before and after the proposed change. For a mean treatment effect, one possible expression is
where \(Y_T\) and \(Y_C\) denote outcomes under treatment and control and \(P\) denotes the target population. Changing \(P\) changes the conditional population over which the effect is defined. Changing the outcome \(Y\), time point, or effect summary changes another part of the target. If the proposed adaptation changes any of these, the team should not describe it as only a sample-size update.
This check does not imply that every change to an analysis method changes the estimand. For example, a prespecified covariate-adjusted estimator may target the same treatment contrast as an unadjusted estimator, if its assumptions and analysis plan support that interpretation. But changing to a different analysis population, choosing covariates because they improve the interim result, or switching effect measures can alter the target or the validity of the inference. The distinction requires a clear statement of the estimand and a justification for the method.
A Practical Review and Its Limits
Name the target population, outcome and time point, treatment contrast, effect summary, and primary hypothesis or threshold.
Specify which eligibility rule, endpoint, margin, analysis population, or analysis method would change, and which interim information motivates it.
Ask whether the same positive result would support the same claim in the same population under the same clinical standard. If not, the primary question has changed.
Consider whether selection using interim data affects error rates, bias, or interpretation, and whether the chosen procedure is valid for the adaptation.
The main alternative is to keep the original primary question and use interim information only for an adaptation that preserves it, such as an appropriately designed nuisance-parameter-based sample-size update. If emerging evidence suggests that a different population or outcome deserves study, that can motivate a separately justified question or a future study. In some settings, an adaptive design can incorporate broader changes while maintaining valid inference, but this requires an appropriate design and analysis; merely labeling a change “adaptive” does not establish validity.
The review also has limits. It can identify that the scientific target has changed, but it cannot decide whether a revised target is clinically worthwhile or whether a particular adaptive inferential method controls error. Those judgments require clinical justification and statistical evaluation of the design’s operating characteristics. A change made for feasibility may also affect representativeness even if the primary analysis population is nominally unchanged, so the implications for interpretation should be stated.
Common Pitfall
Correction: Restriction changes the target population if the primary claim is now about that subgroup. It can also select a favorable effect based on noisy interim data. A sample-size increase can improve precision for a fixed target, but it cannot make a changed target equivalent to the original one or erase the consequences of data-driven selection.
A reliable report distinguishes the action from its scientific meaning: state whether enrollment alone changed or whether the population, outcome, margin, or primary analysis changed as well. The primary question is preserved only when the intended claim and its inferential basis remain intact.
Check Your Understanding
For each question, identify whether the proposed change preserves the primary question and explain why.
- A trial updates its assumed outcome variance using interim data and increases enrollment, while retaining the original eligibility criteria, endpoint, treatment contrast, and test. What has changed?
- Interim results look stronger in patients with a particular marker, so the sponsor proposes to make that group the sole target of the primary claim. What is the key consequence?
- In a noninferiority trial, the observed difference is near the original margin. The team proposes a wider margin after reviewing the interim estimate. Why is this not just a sample-size adjustment?
- A prespecified covariate-adjusted analysis replaces an unadjusted estimate, but both target the same treatment contrast in the same population. Does a different formula alone prove the question changed?
Solutions. (1) The planned sample size changes, while the specified target and test remain fixed; this can preserve the question if the update and inference are valid. (2) The target population changes from the original population to the marker-defined subgroup, and selection based on interim results can affect inference. (3) The margin defines the noninferiority boundary and therefore the null hypothesis; widening it changes the clinical standard and hypothesis. (4) No. A different estimator can target the same effect. The analyst must verify that the target, assumptions, analysis population, and valid inferential procedure remain appropriate.