Defining Intermediate Outcomes in Time-to-Event MAMS

Why an Intermediate Outcome Needs a Precise Definition

In a time-to-event multi-arm multi-stage (MAMS) design, a treatment arm may be assessed using information available before the final event endpoint is sufficiently observed. The outcome used for that assessment is an intermediate outcome: a prespecified measure recorded at an earlier point or over an earlier window, with a stated role in the design, such as informing which arms continue. It is not automatically the trial’s primary endpoint, a substitute for that endpoint, or evidence that an arm improves it.

Calling something “early response” or “the interim measure” is not a complete definition. A usable definition states exactly what is recorded, when it is recorded, for which participants, and how the resulting data enter the design. Those details prevent a score measured at one visit from being silently treated as the same outcome as a score measured at another, or a measure in a subset from being described as if it represented the full randomized population.

A complete definition should answer four questions. Measure: what event, score, response, or laboratory value is recorded, including its scale and scoring direction? Time: at what visit or during which window is it assessed, and what is the time origin? Population: which randomized participants are intended to contribute, and what happens if measurement is unavailable? Role: how is the measure used in the design, and what is it not being used to establish?

Specify the Measure, Time, Population, and Role

The measure must be operational, not just a clinical label. “Improvement” does not say which instrument is used, what change counts, or whether improvement is determined by a participant, clinician, or laboratory assay. A definition should identify the instrument or event criteria, units or categories, scoring rule, and direction in which values are interpreted. If a binary outcome is derived from a score, the threshold and whether equality meets the threshold should be stated.

Time specification requires a time origin and a visit or window. For example, “at week 6 after randomization” identifies a target time; “the lowest score recorded during the first 6 weeks” defines a different measure. If the measure is collected within a window, specify how observations in that window are selected or summarized. A measurement date should not be replaced by a vague phrase such as “early in treatment.”

The population definition should state whether the intended population is all randomized participants, participants who start assigned treatment, or another explicitly defined group. The choice matters: restricting the definition to participants with an observed measurement can change who is represented, especially if missingness or early events differ across arms. State in advance how unavailable measurements and events before the scheduled assessment are handled. Do not silently remove participants from the denominator or assign them an outcome without a prespecified rule.

Finally, describe the measure’s design role narrowly. If it contributes to an arm-selection decision, say so. Do not imply that selection based on an intermediate outcome demonstrates benefit on the final endpoint. Defining that role is different from specifying how arms are selected or evaluating whether the intermediate measure predicts or captures effects on the final endpoint.

A Simple Notation for Keeping the Outcomes Separate

Let \(T_i\) denote participant \(i\)’s time from a stated origin to the event specified by the final endpoint. Let \(I_i(t_I)\) denote that participant’s intermediate measure at a prespecified assessment time \(t_I\). The intermediate measure need not be binary: it could be a score, a response indicator, or a laboratory value. The notation emphasizes that a measure at \(t_I\) and an event time \(T_i\) are different data items, even when both relate to the same disease process.

For example, if the final endpoint is time to death, a participant who responds by day 28 and dies on day 80 can have both \(I_i(28)=1\) and \(T_i=80\) days. The response does not replace, delay, or redefine the death time. Likewise, a participant alive at the end of follow-up has an observed follow-up duration and may be censored for the final endpoint; that censoring status does not by itself define their response or score at an earlier scheduled visit.

This distinction can be expressed by defining an intermediate binary outcome as an indicator of a specified event by a specified time. If \(R_i\) denotes whether participant \(i\) meets stated response criteria, then the day-28 response is \(I_i(28)=1\) when the criteria are met by the day-28 assessment, and \(I_i(28)=0\) otherwise under the protocol’s rule. The final endpoint remains \(T_i\), measured from its own time origin to its own event. The two definitions can be applied to the same participant without conflating their meaning.

Justification: Why the Time and Population Are Part of the Outcome

A measurement cannot be interpreted independently of when it is defined. Consider a binary response indicator \(I_i(t)\) that equals 1 if participant \(i\) meets response criteria by time \(t\), and 0 otherwise under a specified rule. Changing \(t\) changes the event being counted. A participant who first meets the criteria on day 35 contributes 0 to a day-28 response definition but may contribute 1 to a day-42 definition. Therefore, these are not interchangeable labels for one outcome.

The population is equally fundamental. If the intended population is all randomized participants but the reported proportion is calculated only among those with observed scans, the denominator is the observed subset. In the binary example, that denominator is \(35\), not \(40\). The observed-subset proportion is exactly \(18/35\); it is not automatically the proportion that would have been observed in all 40 under complete assessment. The target population and the analysis rule must therefore be stated separately from the arithmetic used to summarize available data.

These points justify a basic design discipline: define the intermediate outcome before using it, and define the final time-to-event endpoint independently. Otherwise, apparently simple choices about visit timing, eligibility, or missing observations can change the quantity being compared across arms without changing its name.

Diagnostics, Alternatives, and Limitations

A definition should be checked for operational consistency before the measure is used. Useful questions include:

• Would two trained assessors apply the measurement and scoring rules to the same record and obtain the same value?
• Is the assessment time or window stated relative to a common origin, and is the window feasible across arms?
• Are the denominator, participants who experience an event before assessment, and missing measurements addressed explicitly?
• Does the protocol use one instrument, assay, and scoring direction across arms and sites, or document a justified harmonization rule?
• Can the data system distinguish “not assessed,” “not applicable,” and a genuine negative or zero value?

If the answers are unclear, the problem is not repaired by adding a more elaborate statistical analysis. Ambiguous scoring, inconsistent visit windows, or undocumented denominators mean that the intended outcome may not have been measured consistently. These are design and data-quality failures, and should be reported as such rather than hidden by relabeling the measure.

The principal alternative is to base decisions on the final time-to-event endpoint itself, using the event information available at the relevant analysis. That keeps the decision measure aligned with the final endpoint but may provide less mature event information at an early stage. An intermediate outcome may provide an earlier measure, but it answers a different measurement question. A baseline covariate is another distinct type of variable: it is measured before treatment and may describe or adjust for participants, whereas an intermediate outcome is measured after treatment begins and has a stated design role. Neither should be confused with the final event-time endpoint.

A precisely defined intermediate outcome has important limitations. It can be measured reliably and still fail to reflect treatment effects on the final endpoint. Its early timing may leave out later benefits or harms, and its observed values may depend on who remains available for assessment. Defining the outcome is necessary for interpretable design and reporting; it does not, by itself, establish its prognostic value, surrogacy, or suitability for selecting arms.

Common Mistakes

• Using only a label. “Early response” leaves the criteria, assessment time, population, and missing-data rule unspecified. Write the operational definition instead.
• Changing the denominator without saying so. A proportion among observed participants is not automatically a proportion among all randomized participants. Name the denominator and report unavailable assessments.
• Treating the intermediate measure as the final endpoint. A day-28 response or week-6 score does not become a time-to-event endpoint because it is used at a stage decision.
• Claiming more than the role supports. Use of a measure for arm selection does not prove that it predicts or substitutes for the final endpoint.
• Leaving early events undefined. State what happens when the final event occurs before the scheduled intermediate assessment; otherwise, participants may be handled inconsistently.