Defining Delayed Feedback in Adaptive Trials

Why Timing Needs Precise Definitions

In an adaptive trial, treatment assignment and the information used to make later assignments do not necessarily occur at the same time. A participant may be randomized today, complete a scheduled assessment weeks later, and have that result verified and made available to the allocation system still later. The time between these events matters: at an allocation decision, some participants may have outcomes available while others are still being followed or their results are being processed.

A useful description therefore needs more than the statement that an outcome is “delayed.” It should identify the starting point, what event counts as feedback, and the status of an outcome at a specified time. The definitions here establish that timing vocabulary without prescribing how a trial should adapt while outcomes are unavailable.

The time origin for \(D_i\) is allocation, not study opening, enrollment of the first participant, or the start of a calendar month. Its endpoint is operational: feedback occurs when the relevant information is available to the allocation process, not merely when a biological event occurs or a value is first written in a source record. If an outcome is never made available, a completed feedback time—and hence a finite completed-outcome delay—is not observed. The trial may still record when the outcome became known to be unavailable.

These times should be understood on one consistent clock, such as date and time in a specified time zone, or elapsed time from a common study origin. If the study records only dates, it may be possible to describe delay only in whole days. Precision in the recorded timestamps cannot compensate for an unclear definition of when feedback is considered complete.

Pending, Missing, and Censored Are Different Statuses

A participant’s outcome status is relative to a particular decision time \(t\), as well as to the protocol’s endpoint and data-collection rules. A value that is unavailable today may be pending, but a later review may establish that it was not obtained. The labels describe different facts; they are not interchangeable names for an empty data cell.

Pending is a temporary status of an outcome that is still awaited; missing describes a value not obtained; censoring describes what has been learned about an incompletely observed outcome. In a time-to-event study, for instance, a participant who has not yet had an event at an interim review may still be under follow-up. That participant’s event time is unresolved, not automatically missing or censored. If follow-up ends without observing the event, the record may instead be right-censored at the last observation time, subject to the study’s endpoint and censoring definitions.

For a fixed-time endpoint, an assessment scheduled for a future date is ordinarily pending before that date. If the assessment window passes and the value cannot be obtained, the endpoint may be classified as missing under the trial’s rules. Censoring is not a universal synonym for “not observed”: it is particularly meaningful when a valid partial observation, such as event-free follow-up through a known time, is available. A trial’s endpoint and analysis plan determine the appropriate description.

Worked Example: Separating Measurement From Feedback

Classifying Status at a Decision Time

A status label should be assigned using information available at the decision time and the trial’s documented expectations. One can express the basic timing condition for an awaited complete outcome as \(A_i\leq t<F_i\), but that inequality alone is not enough to establish that an outcome is pending: it also matters whether the outcome remains expected. Conversely, an empty value at \(t\) does not establish that it is missing if follow-up is ongoing.

For a hypothetical allocation review, suppose four participants have been assigned before the review. One has a verified endpoint already delivered to the allocation system. A second completed the assessment yesterday, but the laboratory has not yet released the result and still expects to do so. A third missed the assessment window, and the site has confirmed that the value cannot be recovered. A fourth is in a time-to-event study, remains under scheduled follow-up, and has not yet had the event. The appropriate descriptions at the review are:

• The first participant’s complete outcome is available.
• The second participant’s complete outcome is pending feedback.
• The third participant’s endpoint is missing under the stated collection facts.
• The fourth participant’s event time is unresolved during ongoing follow-up; it is not automatically missing or censored at this review.

The final case illustrates why an observed status should include the endpoint type and the follow-up history. If follow-up later stops at a known event-free time, the record may be censored at that time. If follow-up continues, no censoring time has yet occurred. In either case, an adaptive-trial report should not compress those distinct states into a single count of “unavailable outcomes” without defining what that count includes.

Worked Example: Statuses in a Hypothetical Review

A Short Justification for Keeping the Clocks Separate

Suppose an endpoint is measured at \(M_i\), then takes \(L_i\) units of time to be validated, transferred, and released for allocation. Under a simple sequential record of these events, \(F_i=M_i+L_i\), so:

The first term, \(M_i-A_i\), is the allocation-to-measurement lag. The second, \(F_i-M_i\), is the post-measurement feedback lag. Their sum is the allocation-to-feedback delay. This identity explains why recording only the endpoint assessment date can understate the time during which the allocation system lacks that result. It also shows why the terms should not be used as synonyms: a long delay may arise from late assessment, slow processing, or both.

Operational Checks and Common Alternatives

Before summarizing delay, specify which outcome is being timed, what event starts the clock, and what event ends it. In a protocol with several endpoints, feedback for one endpoint does not imply that all outcomes for the participant are available. Similarly, a preliminary value available to clinicians may not be available to, or permitted for use by, the allocation system. The relevant \(F_i\) must match the intended use.

Useful checks include comparing allocation, assessment, verification, and system-release timestamps; checking that recorded feedback does not precede allocation; and reviewing cases where an outcome is labeled pending long after its assessment window. Such cases may reflect a genuine processing backlog, a missed visit, or a status field that was never updated. A summary of observed delays among completed outcomes should also be described as such: it does not, on its own, describe the outcomes that remain pending or were never obtained.

These definitions also clarify alternatives in design descriptions. A fixed design can make assignments without using accumulating outcome feedback, so a participant’s feedback time need not determine another participant’s assignment. An adaptive design may use available feedback at later allocation decisions, but the mere fact that outcomes arrive at different times does not specify how those decisions are made. A protocol might instead schedule reviews at set times or organize assignments in groups. Those are different operational choices; they do not change the meaning of \(A_i\), \(F_i\), or the status labels.

Limitations of a Single Delay Summary

A mean or median of completed \(D_i\) values can summarize observed allocation-to-feedback delays, but it cannot fully describe timing when some outcomes are still pending or never observed. Completed outcomes may have shorter or longer delays than unresolved ones; the completed cases alone do not establish the distribution of all eventual delays. Nor does a delay summary explain why feedback was late. A timestamp is a description of timing, not an explanation of the process that produced it.

Finally, delay is endpoint-specific and trial-specific. A day-30 measurement, a time-to-event outcome, and a laboratory-confirmed binary outcome can have different meanings of measurement and completion. Reporting the starting event, the feedback event, the time units, and how pending, missing, and censored records were classified makes a delay description interpretable and reproducible.