Rescue Medication Changes the Question, Not Necessarily the Outcome Record
Suppose participants in a randomized trial may take rescue medication if their symptoms become difficult to manage. Rescue use is an intercurrent event: it occurs after treatment assignment and can affect how the outcome should be interpreted. It is not, by itself, a missing outcome. A participant may take rescue medication and still provide the scheduled outcome measurement. Whether that observed measurement belongs in the analysis depends on the clinical question the estimand is intended to answer.
For example, an investigator might ask whether assignment to a new treatment improves symptoms in the trial setting where rescue medication is available. Another investigator might ask what the treatment effect would have been if nobody had used rescue medication. A third might define success to require both adequate symptom control and no rescue use. These are different questions, so their estimands can differ even when they use data from the same trial.
The estimand attributes still need to be specified: the population, treatment conditions, variable, intercurrent-event strategy, and population-level summary. Here, focus on how the strategy changes the variable or treatment contrast. A treatment contrast might be the difference in mean outcome, or the difference in success proportions, depending on the chosen variable.
Three Strategies, Three Clinical Questions
Let \(A\) denote randomized treatment assignment, and let \(Y\) be a scheduled outcome measured at a specified time. For illustration, suppose higher scores indicate better functioning and the outcome is measured in points. Let rescue medication be permitted under the trial protocol.
Under a treatment-policy strategy, the outcome is the scheduled score whether or not rescue medication was used. The contrast compares the mean outcomes under assignment to each treatment in the trial setting, including the consequences of rescue use as it occurs there. Under a hypothetical strategy, the target is instead the outcome that would be observed under each treatment assignment in a scenario where rescue medication is not used. Under a composite strategy, rescue use becomes part of the endpoint itself. For example, a participant could be classified as a success only if they do not use rescue medication and reach a prespecified score threshold.
This expression describes a treatment-policy contrast in a randomized trial when outcomes are available for the relevant participants. In potential-outcome terms, it compares the mean outcomes under assignment to treatment 1 and treatment 0, with rescue use handled as it occurs under each assignment. It is not the effect of treatment in a world where rescue is prohibited.
Here \(Y^{a,\mathrm{no\ rescue}}\) denotes the outcome that would occur under assignment \(a\) in the specified no-rescue scenario. This outcome is counterfactual for participants who actually used rescue medication. It generally cannot be calculated by simply deleting those participants from the data.
For a composite example, define \(Z=1\) when a participant has not used rescue medication by the outcome time and has a score of at least 75 points; otherwise define \(Z=0\). A contrast in \(P(Z=1)\) asks about the probability of meeting this combined success definition. Other composite definitions are possible, but the rule must be set out clearly and justified for the clinical context.
Worked Example: Treatment Policy With Observed Post-Rescue Scores
Worked Example: Treatment Policy With Observed Post-Rescue Scores
Consider a hypothetical randomized trial of 200 participants. The outcome is functioning at week 12, measured from 0 to 100 points, with higher scores better. Rescue medication is permitted. All participants have a week-12 score, including those who used rescue medication.
In the treatment group, 30 participants used rescue and their mean score was 70; 70 did not use rescue and their mean score was 80. In the control group, 50 used rescue and their mean score was 65; 50 did not use rescue and their mean score was 72. We calculate the overall mean in each group, retaining the post-rescue outcomes.
Treatment group: The weighted mean is \( (30\times70+70\times80)/100=(2100+5600)/100=77.0 \) points.
Control group: The weighted mean is \( (50\times65+50\times72)/100=(3250+3600)/100=68.5 \) points.
Contrast: \(77.0-68.5=8.50\) points. In this hypothetical trial, the mean week-12 score under assignment to treatment was 8.50 points higher than under assignment to control in the setting where rescue medication was available and used as observed. This calculation describes the treatment-policy contrast; by itself it does not establish statistical significance or prove that treatment caused the difference.
The weighted calculation follows from partitioning each randomized group into participants who did and did not use rescue. If \(R\) indicates rescue use, the mean outcome in an assignment group is \(E(Y\mid A=a)=P(R=1\mid A=a)E(Y\mid A=a,R=1)+P(R=0\mid A=a)E(Y\mid A=a,R=0)\). The two rescue-pattern proportions sum to one, so this expression averages over the group as randomized rather than describing only one post-randomization subgroup.
Worked Example: A Hypothetical No-Rescue Contrast
Worked Example: A Hypothetical No-Rescue Contrast
Use the same hypothetical trial setting, but now ask: what would the mean week-12 score have been if rescue medication had not been used? Assume, purely for illustration, that a prespecified model using baseline information and the observed outcome history predicts a mean of 79 points under treatment with no rescue and 71 points under control with no rescue. These are model-based predictions for the full randomized groups under the stated scenario, not the observed means from the previous example.
The hypothetical contrast is \(79-71=8.00\) points. Under the model and the no-rescue scenario, the predicted mean score is 8.00 points higher under treatment than under control.
The arithmetic is simple, but the counterfactual prediction is not supplied by the observed data alone. The model must make assumptions that permit prediction for participants whose outcomes under no rescue were not observed. Those assumptions should be stated and assessed; a model-generated value is not automatically identified merely because software produces it. This example illustrates the contrast, not a proof that the assumed predictions are correct.
The hypothetical question must also be clinically coherent. For example, “no rescue at any time” differs from “no rescue before week 4,” and an intervention that prevents rescue could itself affect outcomes differently from merely withholding medication. The scenario needs enough detail to define which outcome is being targeted.
Worked Example: Rescue Use as Part of a Composite Endpoint
Worked Example: Rescue Use as Part of a Composite Endpoint
Suppose the trial instead defines success at week 12 as both no rescue use and a functioning score of at least 75 points. In the hypothetical treatment group, 70 participants did not use rescue, and 56 of them reached the score threshold. In the control group, 50 did not use rescue, and 30 of them reached the threshold. Participants who used rescue are failures under this prespecified composite, regardless of their score.
Treatment success proportion: \(56/100=0.560\), or 56.0%.
Control success proportion: \(30/100=0.300\), or 30.0%.
Risk difference: \(0.560-0.300=0.260\), or 26.0 percentage points. The treatment group had a 26.0-percentage-point higher proportion meeting this combined definition of success in this hypothetical sample. The interpretation is about the composite endpoint, not about the mean score alone.
This definition makes rescue use count against success, but it does not imply that rescue is clinically harmful in every circumstance. The composite is meaningful only if the threshold and the rule for rescue use reflect a defensible clinical judgment. A different threshold or a different rule could change the estimated contrast and the question answered.
Assumptions, Diagnostics, and Failure Modes
Randomization supports comparisons by assigned treatment, but it does not make the three strategies interchangeable. The treatment-policy interpretation requires a clear description of the trial setting and a well-defined outcome under each assignment, including the rescue medication rules. If outcomes are missing, the treatment-policy estimand still calls for the outcome after rescue; additional assumptions and methods are needed to address the unobserved measurements.
A hypothetical strategy requires more than randomization. In addition to defining the no-rescue scenario, analysis generally relies on assumptions about how the unobserved no-rescue outcomes can be predicted from recorded information. Predictions may be especially fragile if few participants avoid rescue in important baseline or outcome-history groups. This is a practical warning about limited information and extrapolation, not a claim that any particular model resolves the problem.
A composite strategy requires an explicit, clinically defensible endpoint rule. Check that rescue use is defined consistently, including the relevant medication, timing, and circumstances, and that the score threshold and time point are prespecified. Report the composite in a way that lets readers understand how its components contributed; a single success proportion can hide whether a difference arose mainly from rescue use or from the score threshold.
Useful diagnostics include checking rescue frequency by randomized group, the timing and recorded reasons for use, outcome availability before and after rescue, and whether the endpoint definition was applied consistently. Markedly different rescue rates may be clinically important and may make the treatment-policy contrast differ substantially from a no-rescue contrast. If many post-rescue scores are absent, distinguish the event itself from the missing measurements and examine whether the missingness pattern differs by treatment and rescue history. No diagnostic can establish the truth of an untestable counterfactual assumption, but these checks can reveal where conclusions depend heavily on it.
| Strategy | What is included in the question? | Interpretation of contrast |
|---|---|---|
| Treatment policy | Scheduled outcome regardless of rescue use | Difference under treatment assignment in the setting where rescue is available |
| Hypothetical | Outcome under a defined no-rescue scenario | Difference predicted if the specified scenario applied |
| Composite | Outcome rule that incorporates rescue use | Difference in the probability or summary of meeting the combined endpoint |
These strategies are alternatives for defining the clinical question, not interchangeable corrections for a defective analysis. In particular, comparing only participants who did not use rescue does not generally estimate a hypothetical no-rescue effect: rescue use occurs after randomization and can be related to prognosis. Restricting the analysis to that subgroup changes who is compared and can undermine the protection randomization provides.
Common Pitfall and Key Takeaway
Wrong reasoning: “A participant took rescue medication, so their outcome should be treated as missing or excluded; the remaining participants show the treatment effect without rescue.” This confuses an intercurrent event with missing data and conditions on a post-randomization event.
Correction: First decide which estimand answers the clinical question. For a treatment-policy question, retain observed outcomes after rescue. For a hypothetical no-rescue question, define the counterfactual scenario and justify how its outcomes are predicted. For a composite question, state how rescue changes the endpoint. In every case, an outcome that was not recorded remains missing and must be addressed as such; rescue use alone does not make an observed score missing.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A participant uses rescue medication but provides the scheduled outcome score. Is that score necessarily missing? Which strategy would ordinarily retain it without changing the outcome definition?
- In a trial, the treatment-policy mean is 74 points and the control mean is 69 points, with higher scores better. Calculate the contrast and state its interpretation in context.
- Why does removing all participants who used rescue not, in general, estimate the effect that would occur if nobody used rescue?
- A composite defines success as no rescue use and a score of at least 80. A participant uses rescue and scores 90. How is this participant classified under the stated rule?
- Name one important assumption or limitation of a hypothetical no-rescue analysis.
Solutions. (1) No. The outcome is observed; a treatment-policy strategy ordinarily retains it in the scheduled outcome regardless of rescue use. (2) \(74-69=5\) points. The treatment-policy mean is 5 points higher under treatment assignment than under control assignment in the setting where rescue is available, assuming the means represent the stated trial population and outcomes. (3) Rescue is post-randomization and may be related to prognosis, so the no-rescue subgroup can differ between assigned groups; simply excluding rescuers does not create the counterfactual outcomes they would have had without rescue. (4) Failure, because the rule requires both no rescue and a score of at least 80. (5) The analysis must define a coherent no-rescue scenario and rely on assumptions that permit prediction of counterfactual outcomes for participants who used rescue; sparse information can make those predictions especially uncertain.