From an Adaptation Idea to an Executable Rule
An adaptation plan can sound clear while leaving essential decisions open. “Review the interim results and increase enrollment if needed” does not say which participants or data are reviewed, what “if needed” means, who makes the decision, or what happens if an outcome is missing. Different people could implement that sentence differently, changing the trial that is actually conducted.
A complete prespecified rule answers those questions in advance. Its purpose is not to guarantee that an adaptation is statistically appropriate; a well-written rule still needs a separate justification and evaluation. Rather, the rule makes the planned decision reproducible: the same specified information leads to the same authorized action.
A useful way to check a rule is to ask whether a person who did not help design the trial could determine, from the text alone, exactly what information to assemble and which action to take. The rule should also make clear which roles may calculate or verify results and which role has authority to decide.
Specify the Trigger, Cutoff, and Information Set
The trigger states when an adaptation review is initiated. It might be a fixed number of randomized participants reaching a specified follow-up point, a scheduled review date, or another observable event. The trigger is not automatically the same as the data cutoff: the cutoff states which data are included and the time at which the interim information is frozen for the decision.
These definitions must fit together. If a rule says that the review occurs only after every participant in a cohort has a known outcome, it cannot also rely on a branch for participants in that cohort whose outcome status is unknown at that review. If missing data are possible, the timing and status categories must allow them to occur.
The rule should define the population, time window, endpoint, and summary used in the decision. Terms such as “available data,” “adequate response,” or “high variability” are not operational unless the rule defines them. It should also specify whether later data arriving after the cutoff can change the decision; ordinarily, a frozen decision dataset prevents informal updating of the rule.
Decision Authority and Exhaustive Actions
The rule should assign responsibility precisely. For example, an independent statistician might prepare a specified summary, while an independent adaptation committee is authorized to select among the permitted actions. “The study team will decide” is weak if the team, its members, or its authority are not defined. Conversely, naming a decision-maker is not enough if that person is free to choose an action outside the prespecified options.
The available actions should cover every possible result. If a rule permits increasing enrollment when a statistic exceeds a threshold, state what happens when it is equal to the threshold and when it is below it. If the decision compares two arms, say what happens when their summaries tie. If data are missing, say whether the rule proceeds, delays, uses a defined fallback, or takes another specified action.
A compact mathematical representation helps check completeness. Let \(I\) be the information set at the cutoff and let \(g(I)\) be the action prescribed by the rule. For the rule to be operational, \(g\) must assign a permitted action to every information state that the rule allows. If a state has no action, or two incompatible actions, the protocol has a gap.
Here \(\mathcal{I}\) is the set of possible interim information states and \(\mathcal{A}\) is the set of authorized actions. This formulation is a practical completeness check, not a claim that the adaptation has desirable statistical properties. For example, \(\mathcal{I}\) must include allowed patterns of missingness, and \(g\) must define what to do for each such pattern.
Worked Example: A Blinded Sample-Size Adjustment
Hypothetical design. A trial plans to randomize 240 participants and measures a continuous primary endpoint at week 16. The protocol considers one blinded reassessment of the sample size. Write a rule that has a reachable missing-data fallback and resolves equality at its numerical boundary.
Trigger and cutoff. The review is triggered after the first 120 randomized participants have each either completed the week-16 assessment or reached the prespecified cutoff date, defined as 14 days after the last of those 120 participants reaches week 16. At that date, classify each participant as having an observed week-16 endpoint or as having no observed endpoint. Let \(U\) be the number with no observed endpoint; thus, the number with observed endpoints is \(120-U\). Because the cutoff allows an assessment to remain unobserved, \(U\) can be positive.
Information and actions. An independent statistician, without access to treatment assignments, calculates the standard deviation \(s\) of the observed week-16 endpoint values pooled across the randomized participants. If \(U>6\), retain the planned total sample size of 240. If \(U\leq 6\), retain 240 when \(s\leq 12\) endpoint units and increase the total to 300 when \(s>12\) endpoint units. The independent adaptation committee authorizes the action; the statistician reports the calculation but does not choose a different action.
Apply the rule. Suppose 4 participants have no observed endpoint, so \(U=4\), and the pooled blinded standard deviation among the 116 observed values is 13.1 endpoint units. Since \(4\leq6\), the variability branch applies. Since \(13.1>12\), the prescribed action is to increase the total sample size from 240 to 300.
If instead \(s=12.0\), the rule retains 240 because equality belongs to the \(s\leq12\) branch. If \(U=7\), it retains 240 without using \(s\) to select an action. This rule is operationally explicit, but that fact alone does not establish that the reassessment preserves the trial’s error rate or has adequate power; those properties require separate evaluation under the design assumptions.
Worked Rules for Safety and Selection Decisions
Worked Example: A Safety-Based Dose-Dropping Rule
Hypothetical design. A dose-finding trial is comparing doses A and B. The protocol allows dose B to be dropped after an interim safety review. The dose-limiting toxicity (DLT) definition and its 28-day assessment window are specified elsewhere in the trial materials; for this rule, a DLT is counted only when it is confirmed using that definition.
Trigger and cutoff. Trigger the review when the first 60 randomized participants have each completed 28 days after their first dose. Freeze the safety data 14 days after the last of these 60 participants completes that window. At the cutoff, classify each participant as having a confirmed DLT or as having no confirmed DLT; an unresolved assessment is classified as unknown. Let \(U\) be the number of unknown assessments, and let \(D_A\) and \(D_B\) be the confirmed DLT counts among participants assigned to doses A and B.
Authority and exhaustive actions. The independent safety committee makes the decision. If \(U>3\), continue both doses while resolving the assessments; do not drop a dose at this review. If \(U\leq3\), drop dose B and stop assigning participants to it when \(D_B\geq8\) and \(D_A<8\). If \(U\leq3\) and both counts are at least 8, stop enrollment to both doses pending a new safety review. In all other cases with \(U\leq3\), continue both doses. These branches assign an action even when either count is exactly 8.
Apply the rule. Suppose \(U=2\), \(D_A=5\), and \(D_B=8\). Since \(2\leq3\), use the count branches. Here \(D_B\geq8\) and \(D_A<8\), so the committee drops dose B. If the counts were \(D_A=8\) and \(D_B=8\), the rule would instead stop enrollment to both doses. The equality case is not left to individual interpretation.
Worked Example: Selecting a Dose for Expansion With a Tie Rule
Hypothetical design. A trial compares low and high doses and plans to expand one dose based on a binary response assessed at day 28. The selection rule must state its denominator, missing-data branch, minimum response threshold, and tie action.
Trigger and cutoff. Trigger the review after the first 40 randomized participants have each reached day 28. Freeze the data 14 days after the last of these participants reaches day 28. At the cutoff, a participant is evaluable if the day-28 response is recorded; otherwise the response is unknown. Let \(U\) be the number of unknown responses. For each dose, calculate the response proportion as the number of recorded responses divided by the number of evaluable participants assigned to that dose.
Authority and actions. An independent statistician calculates the two proportions, and the independent adaptation committee authorizes the action. If \(U>4\), do not select a dose at this review and enroll 10 additional participants per dose before repeating the same review rule. If \(U\leq4\) and the larger of the two response proportions is below 0.20, stop expansion for insufficient observed response. Otherwise expand the dose with the larger response proportion. If the two proportions are equal, expand the low dose. Thus a proportion of exactly 0.20 meets the expansion threshold, and equality between doses is resolved explicitly.
Apply the rule. Suppose there are 2 unknown responses. Among the evaluable participants, the low dose has 6 responses among 19 participants and the high dose also has 6 among 19. The proportions are
Since \(U=2\leq4\), the selection branch applies. Both proportions exceed 0.20, and they are equal, so the prescribed action is to expand the low dose. The tie rule is necessary even though the observed data happen to give a simple comparison.
Check the Rule for Reachability and Ambiguity
A practical review should test both the wording and the possible data states. Count categories should partition the relevant participants: for example, observed event, observed no event, and unresolved status. Their counts should add to the cohort size. If the rule defines every participant as having one of two known statuses by the cutoff, a fallback based on too few classified participants is unreachable. If such a fallback is intended, the cutoff must allow unresolved statuses and the rule must define their treatment.
A short completeness audit can be made before the rule is finalized:
- Can the trigger be identified from records and dates?
- Does the cutoff define exactly which observations are eligible?
- Are every population, endpoint, time window, denominator, and summary measure defined?
- Is each possible result assigned to one and only one permitted action?
- Are boundary equality, ties, and missing or delayed information addressed?
- Is it clear who calculates, verifies, and authorizes the decision?
A decision table can be easier to audit than a paragraph when several conditions interact. A narrative rule is still acceptable if its branches are mutually exclusive and exhaustive. In either form, the rule should not rely on an undefined phrase such as “clinical judgment” to fill a gap. If expert judgment is intentionally part of the decision, specify who exercises it, what information they may consider, the allowed options, and how the decision is recorded.
Common Pitfalls, Alternatives, and Limits
| Approach | Strength | Risk to address |
|---|---|---|
| Free-form narrative | Can explain the rationale and context in readable language | May leave thresholds, equality, or missing-data cases implicit |
| Decision table or algorithm | Makes branches and actions easy to inspect | Can omit context or fail to cover an allowed information state |
| Discretionary review | Can respond to circumstances not captured by a simple threshold | May not be reproducible unless authority, scope, and permitted actions are bounded |
A common mistake is to equate “prespecified” with “complete.” For example, “At 120 participants, review the event count; if the data are insufficient, keep the original sample size” is still ambiguous. It does not define “insufficient,” the status categories used to count participants, or whether unknown outcomes can exist at the cutoff. The correction is to define those categories and thresholds and check that the fallback is attainable under the specified timing.
Another mistake is to assume a complete rule automatically controls error rates or protects against bias. It does not. The rule determines what the trial will do; its statistical consequences depend on the design, data-generating assumptions, analysis, and decision process. Earlier material on conditional error and strong error control provides relevant concepts for evaluating adaptive decisions, but precise wording is not a substitute for that evaluation. Similarly, a rule cannot remove operational risks such as late data, inconsistent endpoint coding, or unauthorized access to interim information. Those risks need practical safeguards and clear responsibilities.
Check Your Understanding
For each question, identify the rule-writing issue and compare your answer with the solutions below.
- A rule reviews the first 80 participants only after each has a known event or non-event status. It says to retain the planned sample size if fewer than 76 participants have a known status. Is this fallback reachable as written? How could the rule be repaired?
- A blinded reassessment retains the planned sample size when \(s\leq10\) and increases it when \(s>10\). What action is specified when \(s=10\)?
- A dose-selection rule chooses whichever of two response proportions is larger but says nothing about equal proportions. What must be added?
- Why should a rule distinguish the statistician who calculates a summary from the committee authorized to choose an action?
Solutions. (1) No. If all 80 participants have one of the two known statuses, the known-status count is 80, so it cannot be fewer than 76. To make a missing-data fallback reachable, define a cutoff at which some statuses may remain unknown, count known and unknown statuses separately, and specify the action when the unknown count crosses a stated threshold. Alternatively, remove the unreachable fallback. (2) Retain the planned sample size, because equality is included in \(s\leq10\). (3) Specify a deterministic tie action, such as choosing the lower dose, or state another permitted action and who makes it. (4) Separating calculation from authority prevents a report of a summary from being mistaken for an authorized decision and makes responsibility for the adaptation clear.