Start With the Clinical Question
An intercurrent event occurs after treatment starts and affects either the interpretation or existence of an outcome. Examples include treatment discontinuation, rescue medication, and starting another therapy. The statistical choice is not simply whether to include or exclude patients who experience such an event. It is how to define the treatment effect so that it answers a specific clinical question.
For example, a regulator, clinician, or patient might ask about the effect of assigning a treatment in ordinary practice, where some patients discontinue or use rescue medication. Another question might ask what the effect would be if rescue medication were unavailable. These questions can produce different estimands from the same trial. Choosing a strategy therefore starts with the intended interpretation, not with whichever analysis is easiest to run.
Let \(A\) denote randomized treatment assignment, with \(A=1\) for the experimental treatment and \(A=0\) for control. Let \(Y(a)\) denote the outcome under assignment \(a\), with the event handled as it would occur under that assignment. Other strategies define a different target, such as \(Y(a, E=0)\), the outcome under assignment \(a\) in a hypothetical setting where event \(E\) does not occur. The target population, treatment conditions, endpoint, and population-level summary must still be specified, as described in the earlier material on clinical estimands.
A Decision Framework for Selecting a Strategy
The five strategies differ in what they say about the event. A useful first question is: what would a decision-maker want to know if the event occurred? Should its consequences remain part of the treatment effect, should the event itself count as an outcome, or should the question instead concern a counterfactual world without it?
Specify whose decision the result will inform and what treatment choice or clinical claim the result is meant to support.
Decide whether outcomes after the event matter, whether the event is itself a meaningful outcome, or whether the question concerns a hypothetical absence of the event or a defined subgroup.
Make the event handling part of the estimand definition rather than letting a data-processing rule silently decide it.
Ask whether the required outcomes can be collected and whether the assumptions needed to estimate the chosen target are credible.
| Strategy | Question the estimand answers | Key interpretive caution |
|---|---|---|
| Treatment-policy | What is the effect of assignment when outcomes are considered regardless of the event? | Outcomes after the event must be meaningful and sufficiently observed. |
| Hypothetical | What would the effect be if a specified event did not occur? | Outcomes in the hypothetical setting are counterfactual and require credible assumptions. |
| Composite | What is the effect when the event is incorporated into the endpoint? | The event’s assigned endpoint value or category must be clinically defensible. |
| Principal-stratum | What is the effect in a subgroup defined by potential event behavior under treatment and control? | Membership is generally not observed for each person. |
| While-on-treatment | What is the effect on outcomes while participants are receiving assigned treatment? | The result concerns an on-treatment period or summary, not necessarily the overall effect of assignment. |
These strategies are not interchangeable analysis options. Each defines a different target. Randomization supports comparisons of assigned treatment, but does not automatically identify counterfactual outcomes in a no-event world or effects in latent principal strata. Even when the analysis is Bayesian, the clinical meaning of the estimand must be decided before uncertainty about it is summarized.
Worked Examples: Match the Strategy to the Question
Worked Example: Effect of Assignment Regardless of Rescue Medication
In a hypothetical randomized trial, 100 patients are assigned to each of two treatments. The endpoint is a disease-activity score at week 24, measured in points, with higher scores indicating better health. Some patients use rescue medication before week 24. The clinical question is, “What is the effect of assigning the new treatment in a setting where rescue medication may be used and its consequences matter?”
A treatment-policy strategy matches this question: use the week-24 outcome regardless of rescue use. Suppose the mean scores are 6.8 points in the new-treatment group and 4.9 points in the control group, including patients who used rescue medication. The estimated mean difference is
On this hypothetical dataset, the new-treatment group’s mean score is 1.9 points higher. This result concerns treatment assignment with rescue medication and its consequences retained in the outcome. It does not estimate what the difference would have been if nobody had used rescue medication. The interpretation also requires week-24 outcomes to be meaningful after rescue and adequate outcome data to be obtained; simply labeling the strategy treatment-policy does not resolve missing outcomes.
Worked Example: Effect in a Hypothetical No-Rescue Setting
Consider a separate hypothetical trial with 100 patients per group and a continuous week-24 outcome in points. The question is, “What would the mean treatment difference be if rescue medication were not used?” This calls for a hypothetical strategy, with the estimand defined in the setting where rescue use is prevented.
Suppose 20 patients in the new-treatment group and 30 in control used rescue medication. Among those who did not use it, the observed mean scores are 8.0 and 6.0 points, respectively. A model predicts that, had rescue use been prevented, the mean scores among rescue users would have been 5.0 points in the new-treatment group and 3.0 points in control. Standardizing to the randomized group sizes gives:
Thus the estimated hypothetical mean difference is \(7.4-5.1=2.3\) points. The arithmetic is straightforward; its causal interpretation is not automatic. It depends on the predicted outcomes being credible and on the model adequately identifying outcomes in the no-rescue setting. For example, if prognosis affects both rescue use and the outcome, an unadjusted comparison of patients who did and did not use rescue may not support those predictions. The 2.3-point contrast is therefore not an observed difference between the randomized groups.
Worked Example: Incorporate Rescue Use Into a Binary Endpoint
In a third hypothetical trial, response at week 24 is a binary endpoint. The clinical question is, “What is the effect on achieving response without rescue medication?” Define success as both being a responder and not having used rescue medication before week 24. This is a composite strategy because rescue use is incorporated into the endpoint definition.
Suppose 54 of 100 patients assigned to the new treatment meet this definition, compared with 41 of 100 assigned to control. The success proportions are
The estimated risk difference is
or 13 percentage points. The interpretation is a difference in the proportion meeting the combined success definition—not a 13-point difference in response alone. The endpoint rule is appropriate only if treating rescue use as failure reflects the clinical question. If rescue is acceptable and outcomes after rescue matter, this composite may answer the wrong question even though its calculation is clear.
Worked Example: A Latent Principal Stratum Is Not an Observed Subgroup
Suppose a trial asks about the treatment effect among patients who would not discontinue treatment under either assignment. This is a principal-stratum question: the target group is defined by potential discontinuation behavior under both treatment and control. Membership depends on two potential outcomes for each patient, only one of which can be observed.
For illustration, suppose a model targeting this latent group estimates mean scores of 6.4 points under the new treatment and 5.2 points under control. Its estimated contrast is \(6.4-5.2=1.2\) points. This is an effect among patients who would remain on treatment under either assignment, not an effect among those observed to remain in whichever arm they happened to receive. Those observed groups can differ because assignment may affect discontinuation and because patients’ prognoses may differ. The model-based contrast also depends on assumptions that permit inference about the unobserved principal-stratum membership; randomization alone does not reveal that membership.
Justifying a Hypothetical Contrast
The standardization in the no-rescue example follows from the target definition. For each randomized group, the hypothetical mean is the average of that group’s outcomes under the specified no-rescue condition. Partition the group by whether rescue was observed, and write the mean as the weighted average of the two subgroup means:
For patients who did not use rescue, observed outcomes may inform the first conditional mean if the observed outcome corresponds to the no-rescue condition. For patients who did use rescue, the second conditional mean is counterfactual: their outcomes under no rescue were not observed. A model, assumptions, and relevant baseline information are needed to estimate it. This decomposition explains why the hypothetical contrast is not obtained by merely deleting rescue users: deletion changes the target population and does not supply their outcomes under the hypothetical condition.
Diagnostics, Limitations, and Common Mistakes
No single diagnostic certifies that a strategy is right. Instead, look for a mismatch between the question, the event handling, and the data available. Check whether outcomes after events were collected, how many participants experienced the event in each group, whether predictions rely heavily on extrapolation, and whether the endpoint’s event rule is understandable to clinicians and patients. For a principal-stratum target, ask whether the identifying assumptions are scientifically plausible and how sensitive the result is to them. For an on-treatment target, check whether outcome collection and the definition of the on-treatment period align with the intended interpretation.
A common mistake is to say, “Discontinuers are not relevant, so exclude them and compare the patients who remained on treatment.” That comparison is not automatically a while-on-treatment estimand, and it is not generally a randomized comparison: remaining on treatment is a post-randomization condition that can depend on treatment and patient prognosis. The correction is to define the target first. If the question concerns outcomes while receiving treatment, specify an appropriate on-treatment summary and its interpretation; do not assume that excluding participants creates an unbiased answer.
Another mistake is to select a hypothetical strategy because the event is inconvenient to analyze. A no-event estimand makes a claim about a counterfactual setting and can be difficult to identify from trial data. Conversely, a treatment-policy strategy is not always preferable simply because it preserves randomization: outcomes after an event must still be clinically meaningful and available. The earlier material on while-on-treatment estimands gives that strategy’s interpretation in greater depth; for selection, the essential distinction is that its target is confined to outcomes during treatment, rather than outcomes regardless of event or outcomes in a hypothetical world without it.
Each approach has limitations. Treatment-policy effects may combine pharmacologic effects with downstream consequences of events. Hypothetical effects depend on unobserved counterfactual outcomes. Composite effects depend on the chosen endpoint rule, and different rules can change the clinical meaning. Principal-stratum effects concern a latent group that may be hard to identify. While-on-treatment effects do not, by themselves, describe the full consequences of assigning treatment. If no strategy directly answers the decision question, the remedy is to refine the question and estimand—not to overstate what a convenient analysis means.
Check Your Understanding
For each situation, identify a suitable strategy and explain the target. Solutions follow the questions.
- A trial asks about the effect of assignment when patients may stop treatment, and outcomes after stopping remain clinically relevant and are collected. Which strategy fits?
- A decision-maker asks what the treatment effect would be if a particular rescue therapy were unavailable. Which strategy fits, and what is its main inferential challenge?
- A trial defines success as symptom improvement without hospitalization. Hospitalization is counted as failure. Which strategy is being used?
- Why is comparing only participants who remained on treatment not automatically a valid randomized comparison?
- A question concerns patients who would avoid a specified event under either randomized assignment. Why is that group not directly observed?
Solutions. (1) Treatment-policy: the comparison retains outcomes regardless of stopping, matching the question about assignment with consequences included. (2) Hypothetical: it targets a no-rescue setting; outcomes under that condition for patients who used rescue are counterfactual and require assumptions or modeling. (3) Composite: hospitalization is incorporated into the success definition as failure. (4) Remaining on treatment is determined after randomization and may depend on assignment and prognosis, so the selected groups need not retain the comparability created by randomization. (5) Each person’s behavior under both assignments cannot be observed: only the outcome under the assigned condition is seen, so membership in the defined principal stratum is latent.