Why Define a While-on-Treatment Estimand?
A trial may ask what happens to symptoms during the period participants remain on assigned treatment. If a participant stops treatment, the outcomes measured afterward may no longer answer that question. A while-on-treatment estimand makes this distinction part of the target: it uses outcomes before a specified intercurrent event and excludes outcomes after that event.
This is a choice about the clinical question and outcome variable, not a rule that every post-event value is unavailable or erroneous. Such values may be collected, but they do not contribute to this particular estimand. Conversely, a pre-event outcome that was intended to be measured but was not recorded is still missing data.
The event might be permanent discontinuation of assigned treatment, initiation of rescue medication, or another event that marks the end of the period relevant to the question. The protocol must define the event operationally. “While on treatment” is not precise enough if it is unclear whether a temporary interruption, dose reduction, or a same-day assessment ends the period.
Defining the Outcome and the Event Boundary
Suppose measurements are scheduled at weeks \(4\), \(8\), and \(12\), and the intercurrent event is permanent discontinuation. Let \(T_i\) denote participant \(i\)'s event time and \(Y_i(t)\) the outcome at time \(t\). A protocol might define an individual summary \(W_i\) as the mean of scheduled postbaseline measurements strictly before \(T_i\):
where \(m_i\) is the number of scheduled measurements before the event. This is one possible outcome definition, not a universal formula for all while-on-treatment estimands. A protocol could instead specify a particular pre-event measurement or another summary of the in-treatment outcome record.
The strict inequality in this example means that a measurement at the event time is excluded. Another protocol could include a measurement if it was taken before the event on the same day. Either convention can be meaningful, but the sequence of assessment and event must be defined well enough to apply the rule consistently. If a participant discontinues at week \(8\) before the week-8 assessment, and the week-4 score is the only eligible measurement, then \(W_i\) is simply the week-4 score.
The definition also needs to cover participants with no eligible postbaseline measurement. The mean in the formula is undefined if \(m_i=0\). A complete estimand therefore requires an explicit outcome rule for that case, or a design and event definition that ensure the relevant summary exists. Any added rule must be examined carefully: assigning a value based on the event itself, for example, can change the outcome definition and introduce a composite element. It is not appropriate to silently treat an undefined summary as an ordinary missing value.
Finally, the treatment contrast must be stated. If lower scores are better, one possible contrast is the difference in population means, treatment minus control. The five attributes of a trial estimand and the distinction between estimand, estimator, and estimate provide the broader framework for stating this target precisely.
Worked Example: Calculating a Prespecified In-Treatment Summary
Hypothetical data. A trial compares an active treatment with control on a symptom score, where lower scores indicate fewer symptoms. Each participant has scheduled assessments at weeks \(4\), \(8\), and \(12\). The event is permanent discontinuation, and the protocol includes only assessments strictly before the event. For this illustration, every participant has at least one eligible postbaseline score. The protocol defines \(W_i\) as the mean of that participant’s eligible scores.
In the active-treatment group, participant A scores \(10\) at week \(4\) and \(8\) at week \(8\), then discontinues after the week-8 assessment. Both scores are before the event, so \(W_A=(10+8)/2=9\). Participant B scores \(12\) at week \(4\), then discontinues at week \(8\) before the week-8 assessment. Only the week-4 score is eligible, so \(W_B=12\).
In the control group, participant C scores \(10\) at weeks \(4\) and \(8\), with discontinuation after week \(12\); the week-12 score is also eligible if recorded, but to keep the calculation explicit, suppose the week-12 assessment was not scheduled for this participant because follow-up ended at that visit. Thus \(W_C=(10+10)/2=10\). Participant D scores \(11\) at week \(4\) and discontinues at week \(8\) before the week-8 assessment, so \(W_D=11\).
The active-group mean is \((9+12)/2=10.5\) symptom-score points. The control-group mean is \((10+11)/2=10.5\) points. The estimated active-minus-control contrast for these four participants is \(10.5-10.5=0\) points. This calculation describes the specified summaries; it does not by itself quantify sampling uncertainty or establish that the population contrast is zero.
Deriving the Population Contrast
For a two-arm trial, let \(W_i(a)\) denote the individual summary that would be defined for participant \(i\) under assigned treatment \(a\), using the event rule and outcome definition specified for that treatment. The target may be the difference in population means:
This expression follows directly from the clinical question: first define each treatment-specific outcome record through the event boundary, then summarize those records in the target population, and finally contrast the summaries. If lower scores indicate benefit, a negative active-minus-control value favors active treatment. The contrast is not automatically the effect that would have been seen had everyone remained on treatment.
With random assignment, consistent implementation of the defined treatments, and complete observation of the outcome information required by the estimand, the mean of the defined summaries in each randomized group estimates its corresponding population mean. Subtracting the group means estimates their difference. If some eligible pre-event measurements are missing, that direct calculation no longer uses complete outcome information for everyone; an analysis then needs a justified method for handling those missing values. The estimand’s exclusion of post-event outcomes does not itself supply that method.
Worked Example: Applying the Event-Time Rule to Same-Visit Measurements
Hypothetical data. Consider two participants on the same treatment. Their scores are collected at weeks \(4\), \(8\), and \(12\), whether or not they have discontinued. The protocol uses the mean of assessments strictly before discontinuation. Participant P has scores \(8\) at week \(4\) and \(7\) at week \(8\), and discontinues after the week-8 assessment. Participant Q has scores \(10\), \(4\), and \(2\) at weeks \(4\), \(8\), and \(12\), respectively, and discontinues at week \(8\) before the week-8 assessment.
For P, both week \(4\) and week \(8\) are before the event, so \(W_P=(8+7)/2=7.5\) points. For Q, only week \(4\) is strictly before the event, so \(W_Q=10\) points. The mean of these two summaries is \((7.5+10)/2=8.75\) points.
The week-8 score of \(4\) for Q is excluded because the event occurred before that assessment. Q’s week-12 score of \(2\) is also excluded because it was recorded after discontinuation. Those values were collected, but neither belongs to the defined while-on-treatment summary. If the event and assessment were recorded only as occurring “at week 8,” without their order, the inclusion rule could not be applied unambiguously.
How This Strategy Differs from Alternatives
| Strategy | Role of post-event outcomes | Question represented |
|---|---|---|
| While-on-treatment | Excluded from the target outcome | What is the treatment contrast for outcomes during the defined on-treatment period? |
| Treatment-policy | Included, regardless of the event, when relevant and collected | What is the effect of assignment when outcomes are considered regardless of the event? |
| Hypothetical | The target concerns outcomes under a specified hypothetical condition, such as if the event had not occurred | What would the contrast be under that hypothetical condition? |
| Composite | The event is incorporated into the outcome definition | What is the effect on an outcome that includes the event? |
These strategies answer different questions; one is not a general-purpose correction for another. In particular, excluding post-event outcomes is not the same as estimating the outcome that would have occurred had participants continued treatment. That latter question requires a hypothetical target. Nor does a while-on-treatment contrast automatically describe the treatment effect among a special group who would remain on treatment under either assignment; that is a different target.
Worked Example: Why Different Strategies Can Give Different Contrasts
Hypothetical data. Suppose a symptom score is measured before discontinuation and again at week \(12\) for everyone, including those who discontinued. Lower scores are better. In the active group, participant A has a while-on-treatment summary of \(6\) points and a week-12 score of \(12\); participant B has a summary of \(8\) and a week-12 score of \(10\). In the control group, participant C has a summary of \(8\) and a week-12 score of \(9\); participant D has a summary of \(10\) and a week-12 score of \(11\). The post-discontinuation week-12 scores are available for participants who discontinued.
The while-on-treatment mean is \((6+8)/2=7\) points for active treatment and \((8+10)/2=9\) points for control. The active-minus-control contrast is \(7-9=-2\) points. Under this outcome definition, the active group’s mean symptom score during the defined on-treatment period is \(2\) points lower.
For comparison, a treatment-policy contrast using the week-12 scores is \((12+10)/2-(9+11)/2=11-10=1\) point. It points in the opposite direction because it uses a different outcome definition and includes outcomes after discontinuation. The two calculations do not contradict one another: they summarize different targets. Neither calculation alone establishes a causal mechanism for the observed difference.
Diagnostics, Limitations, and Common Pitfalls
A while-on-treatment estimand can be useful when the scientific question is explicitly limited to the period on treatment. Its interpretation nevertheless depends on careful specification and appropriate analysis. Review the event and outcome definitions against the trial’s actual data collection, including the timing of assessments, temporary interruptions, and the recording of events. Check how many participants have no eligible measurements, how many required pre-event measurements are missing, and whether inclusion rules are applied consistently across treatment groups.
- Do not confuse exclusion with missingness. An outcome after the event is excluded by the target definition. A required measurement before the event that was not observed remains missing.
- Do not use “last observed value” without a rule. The last value may be at the event visit, before it, or after it. Specify which observations qualify and how the summary is calculated.
- Do not interpret the contrast as an effect among people who would stay on treatment. The participants contributing observed in-treatment data can differ between arms because treatment assignment may affect event occurrence and timing.
- Do not hide undefined summaries. If some participants have no eligible outcome, an estimand based on a within-person mean needs an explicit rule for them before estimation.
A further limitation is that a summary such as the mean of all eligible scores can depend on the assessment schedule and the duration of time on treatment. Participants with longer exposure may contribute more measurements, even though the formula above gives each participant one summary before averaging across participants. Other summaries answer different questions and must be prespecified. Changing the summary after seeing the event pattern can change the target.
Check Your Understanding
Answer each question using the definitions and rules in this tutorial. Solutions follow.
- A participant has scores \(9\) at week \(4\) and \(7\) at week \(8\), and discontinues after the week-8 assessment. Under a strict-before-event rule, what is the mean of the eligible scores?
- A participant discontinues at week \(8\) before the week-8 assessment. The week-4 score is \(13\). What is the defined mean if week \(4\) is the only eligible assessment?
- Explain why a week-12 outcome collected after discontinuation is excluded from a while-on-treatment target but a missing week-4 outcome before discontinuation is still a missing-data issue.
- In a study, the while-on-treatment mean is \(5\) points for active treatment and \(7\) points for control, with lower scores better. What is the active-minus-control contrast, and how should its direction be interpreted?
- Why does a while-on-treatment contrast not automatically represent the treatment effect among people who would remain on treatment under either assignment?
Solutions. (1) Both scores are strictly before discontinuation, so the mean is \((9+7)/2=8\) points. (2) The only eligible score is week \(4\), so the mean is \(13\) points. (3) The week-12 value occurs after the event and is outside the defined target; the week-4 value is part of the target but was not observed, so it must be handled as missing data. (4) The contrast is \(5-7=-2\) points. The active-treatment mean is \(2\) points lower for the specified while-on-treatment outcome; because lower scores are better, this direction favors active treatment. (5) The treatment arms can have different event patterns, and the people contributing in-treatment outcomes need not be the same type of people in each arm. The while-on-treatment target does not restrict the population to those who would remain treated under either assignment.