What Does “While on Treatment” Target?
A treatment discontinuation can change which outcomes are relevant to a clinical question. If the question concerns symptom levels while patients are receiving assigned treatment, an outcome recorded after discontinuation may not answer it. A while-on-treatment strategy uses outcomes observed before the specified intercurrent event and does not use outcomes after that event to define the target effect. It does not, by itself, say what an outcome would have been had the patient continued treatment.
The important qualification is that a strategy for handling an intercurrent event is only one attribute of an estimand. A complete estimand also identifies the population, treatments, endpoint, and population-level summary. In particular, the summary must say how outcomes at different follow-up times and from different numbers of on-treatment participants contribute. Two analyses can both exclude post-discontinuation outcomes but target different quantities.
For example, consider a randomized trial comparing an investigational drug with control, where permanent discontinuation of assigned treatment is the event. If lower symptom scores are better, a question about symptom scores while receiving treatment might use pre-discontinuation measurements. It would not automatically target the effect of assigning treatment regardless of whether treatment is discontinued, nor the effect that would have occurred if everyone had remained on treatment. Those are different questions.
Specify the Summary, Not Just the Strategy
Let \(Y^a(t)\) denote the outcome at time \(t\) under assigned treatment \(a\), and let \(D^a(t)=1\) indicate that the participant would still be receiving that treatment, without the specified intercurrent event, at time \(t\). A possible fixed-time while-on-treatment summary is the mean outcome among participants still on treatment under each treatment:
This is a contrast between two treatment-specific on-treatment populations. The participants satisfying \(D^1(t)=1\) need not be the same people as those satisfying \(D^0(t)=1\). Thus, \(\Delta^{W}(t)\) describes the difference between the mean outcomes among those still on each treatment; it is not necessarily a treatment effect in one common group of people. This distinction matters because remaining on treatment is determined after randomization and may depend on health, response, tolerability, and treatment assignment.
A different target may summarize all eligible on-treatment visits. For scheduled times \(t_1,\ldots,t_K\), one possible person-visit-weighted mean is:
Here each eligible on-treatment visit contributes one outcome, so a participant with more on-treatment visits contributes more to the summary. A participant-weighted alternative first calculates each participant’s average of their eligible measurements and then averages those participant averages. That gives each participant equal weight, but participant averages based on different numbers or timings of measurements may still represent different parts of follow-up. The estimand must state which summary is intended.
Worked Example: A Fixed-Time On-Treatment Contrast
Hypothetical data. At week 8, a trial has 10 participants assigned to each treatment. Six control participants and four investigational-treatment participants are still receiving assigned treatment. Their mean week-8 symptom scores are 6.0 points for the control participants still on treatment and 4.0 points for the investigational-treatment participants still on treatment. Lower scores are better. Calculate and interpret the fixed-time on-treatment contrast.
The stated summary is the treatment-specific mean among those still receiving assigned treatment at week 8. Its contrast is investigational treatment minus control:
In these hypothetical data, participants still receiving the investigational treatment have a mean symptom score 2.0 points lower than participants still receiving control at week 8. This describes the two observed on-treatment groups. It does not establish that assignment to the investigational treatment reduces the week-8 mean by 2.0 points in the full randomized population: the groups remaining on treatment may differ because of post-randomization discontinuation.
The fractions remaining on treatment are \(4/10=0.40\) and \(6/10=0.60\), respectively. Those rates do not change the arithmetic of the stated conditional means, but they help show why the groups being compared may have different compositions.
Why Randomization Does Not Remove Selection After Discontinuation
Randomization supports comparisons of treatment groups before conditioning on post-randomization events. Once analysis is restricted to participants who remain on treatment, that protection need not hold. For example, suppose participants with worsening symptoms are more likely to discontinue in one arm. The remaining participants in that arm may then have milder symptoms, even if the treatments had similar effects in the full randomized population.
A short derivation makes the selection issue explicit. Let \(U\) be a baseline or evolving prognostic characteristic that affects both the outcome and the chance of remaining on treatment. For a given treatment \(a\), the distribution of \(U\) among those still on treatment is:
If the probability of remaining on treatment varies with \(U\), then \(P(U=u\mid D^a(t)=1)\) differs from the original population distribution \(P(U=u)\). If \(U\) also predicts \(Y^a(t)\), the mean among those remaining can differ from the population mean for that treatment. Because treatment can itself affect discontinuation, the selected distributions can differ between arms. This explains why randomization alone does not justify treating a comparison of on-treatment participants as a causal contrast in one shared population.
The selection does not make a conditional on-treatment estimand meaningless. It means that its interpretation must match its definition: it is a contrast between treatment-specific groups still on treatment. If the scientific question instead requires a causal contrast for a common population, the analyst must specify a different estimand and the assumptions needed to identify it.
Worked Example: Person-Visit Weighting
Hypothetical data. Lower scores are better. In the control arm, the on-treatment scores are 6, 7, and 8 at week 4, and 7 and 8 at week 8. In the investigational arm, the on-treatment scores are 4, 5, and 6 at week 4, and 5 at week 8. All outcomes after discontinuation are excluded. Calculate the person-visit-weighted means and their difference.
For control, the five eligible person-visits sum to \(6+7+8+7+8=36\). Therefore:
For investigational treatment, the four eligible person-visits sum to \(4+5+6+5=20\). Therefore:
The person-visit-weighted mean score is 2.20 points lower in the investigational arm’s on-treatment visits than in control’s on-treatment visits. This is not the same summary as a fixed-time contrast: it pools across weeks 4 and 8. It also gives more weight to participants who contribute more eligible visits. The contrast therefore depends on the distribution of follow-up visits and the on-treatment duration in each arm, as well as on the observed scores.
Interpreting Excluded Outcomes and Estimation
An outcome measured after the specified event is excluded because it is outside the while-on-treatment target, not because its value is presumed to be the same as an unobserved pre-event outcome. This differs from a hypothetical strategy, which asks about outcomes under a scenario in which the event did not occur. It also differs from a treatment-policy strategy, which uses outcomes regardless of the event to target the effect of treatment assignment in the presence of events.
Exclusion after an event does not make every pre-event measurement complete. A scheduled assessment that is missed before discontinuation is still unobserved information about an outcome that belongs to the target. Estimation then requires an appropriate approach and assumptions about that missing pre-event data. A model may also be needed when measurements are irregular or the target averages across times. A Bayesian model can quantify uncertainty about the specified estimand, but the model does not change what that estimand means.
Several checks help reveal when the analysis and target may not align:
- Compare discontinuation counts and timing across treatment groups. Large differences can change which participants contribute at later visits.
- Inspect why treatment was discontinued and whether those reasons are related to prior outcomes or prognosis.
- Report the number of participants and eligible observations contributing at each time. A mean with few remaining participants may be imprecise and represent a highly selected group.
- Check that the analysis excludes outcomes after the event but does not unintentionally discard eligible pre-event measurements.
- Verify that the fitted model’s averaging and weighting match the prespecified summary. A model-based marginal mean over the randomized population is not automatically a conditional mean among those still on treatment.
These checks diagnose interpretability and possible estimation problems; they do not convert a treatment-specific on-treatment comparison into a contrast for a common population. In particular, simply analyzing completers, carrying the last observation forward, or treating discontinuation as ordinary loss to follow-up does not define the same target. The first changes the analyzed population, the second inserts a value not specified by the while-on-treatment strategy, and the third can imply a missing-data target rather than exclusion of post-event outcomes.
How the Main Strategies Differ
The strategies differ in what the treatment effect is intended to describe, not merely in which software or model is used. The relevant question is what information after an intercurrent event means for the clinical question.
| Strategy | Role of outcomes after the event | Interpretation |
|---|---|---|
| While-on-treatment | Excluded from the target; use outcomes before the event | Outcome experience while participants remain on assigned treatment, with the summary and contributing population specified |
| Treatment-policy | Used regardless of the event | Effect of assignment to treatment, including outcomes following the event |
| Hypothetical | Target outcomes under a specified scenario in which the event does not occur | Effect that would be expected under that counterfactual scenario, requiring assumptions to estimate unobserved outcomes |
| Principal-stratum | Defines a subgroup by potential event status under treatment conditions | Effect in the specified post-randomization stratum, not simply a comparison of observed participants who remain on treatment |
The last distinction is especially important: the observed group still receiving treatment in one arm is not automatically the same group of people who would remain on treatment under the other arm. A while-on-treatment summary can be clinically useful, but it should not be described as an effect among a common subgroup unless the estimand actually defines that subgroup and the required assumptions are justified.
Worked Example: Exclusion Is Not a No-Discontinuation Scenario
Hypothetical data. A participant assigned to an investigational treatment has a symptom score of 5 points at week 4, discontinues at week 5, and has a score of 9 points at week 8 after receiving other care. For an estimand that uses the week-4 on-treatment score and excludes outcomes after discontinuation, identify the included and excluded values and distinguish the target from a hypothetical strategy.
The week-4 score, 5 points, is a pre-event outcome and is eligible for the while-on-treatment summary. The week-8 score, 9 points, is post-event and is excluded from that target. Excluding 9 does not assert that the participant’s week-8 score would have been 5, nor does it estimate what the week-8 score would have been had the participant continued treatment.
A hypothetical strategy asking about week-8 outcomes if treatment had continued would target a different quantity. The observed score of 9 is not that counterfactual score; additional modeling assumptions would be required to estimate the hypothetical outcome. The while-on-treatment strategy, by contrast, makes no such post-discontinuation prediction.
Common Pitfall
Wrong reasoning: “Because treatment was randomized, comparing the week-8 outcomes among participants who stayed on treatment gives an unbiased causal effect in the original randomized population.”
Correction: Staying on treatment is a post-randomization condition. If prognosis, response, adverse effects, or treatment assignment influences continuation, the participants who remain may be selected differently in the two arms. A conditional contrast can still answer a clearly stated on-treatment question, but it is not automatically a causal effect for the original population or a common subset. Specify the target population and summary, report who contributes, and avoid interpreting the result beyond that target.
Check Your Understanding
Answer each question using the definitions and distinctions in this tutorial. Solutions follow the questions.
- A treatment-specific week-12 mean is calculated only among participants still receiving assigned treatment. What population does each mean describe, and why may the contrast not represent a comparison in one common population?
- In a person-visit-weighted summary, one participant contributes four eligible visits and another contributes one. Which participant has more influence on the pooled mean, and what does this imply for interpretation?
- A participant discontinues at week 6. Under a while-on-treatment strategy, should a week-8 outcome be imputed as the value that would have occurred had the participant continued treatment? Explain.
- Give one diagnostic that can reveal selection or instability in a fixed-time on-treatment comparison.
Solutions. (1) The treatment-specific mean describes participants who remain on their assigned treatment in that arm at week 12. Because treatment assignment and prognosis can affect continuation, the two means can concern groups with different composition; randomization does not ensure comparability after conditioning on continuation. (2) The participant contributing four visits has four times the visit-level weight of the participant contributing one visit. The pooled mean describes eligible on-treatment visits, not an equally weighted mean across participants. (3) No. The post-discontinuation outcome is excluded from the while-on-treatment target. Predicting the outcome had treatment continued would be a hypothetical strategy. (4) Report and compare the numbers and timing of discontinuations by arm, and show how many participants contribute at week 12. Marked differences or very small remaining groups warn that the comparison may be selected or imprecise.