Rescue Medication as an Intercurrent Event

Why Rescue Medication Changes the Target Question

In a clinical trial, rescue medication may be available when symptoms worsen or the assigned treatment is insufficient. Its use can affect a later endpoint, such as symptom improvement at week 12. It can also signal that a participant’s condition was not adequately controlled. These features make rescue use relevant to the treatment question, but they do not determine how it should be handled. Counting rescue as failure, including outcomes observed after rescue, and asking what would have happened without rescue are different choices about the estimand.

The choice should follow the clinical question and be made before looking at outcome results. For example, a treatment-policy question may concern the effect of assigning a treatment in a setting where rescue is available. A composite question may instead ask whether assignment produces improvement without needing rescue. A hypothetical question may ask about the effect if rescue had been prevented. None is simply a more or less conservative version of the others: they target different outcomes under different conditions.

For clarity, let \(A\) denote randomized treatment assignment, \(R\) indicate whether rescue medication is used before the endpoint assessment, and \(Y\) denote the endpoint, coded here so that larger values are better. Write \(Y^a\) for the outcome under assignment to treatment \(a\) in the trial setting, including its rules and availability for rescue. The notation \(Y^{a,0}\) will denote the outcome under assignment to \(a\) in a specified hypothetical setting in which rescue is not used. These outcomes need not be the same: rescue may change symptoms, and the prospect or prohibition of rescue may change clinical care.

Three Strategies, Three Questions

A treatment-policy strategy uses the endpoint as observed after assignment, whether or not rescue medication was used. It asks about treatment assignment in the setting where rescue is available under the trial’s usual rules. Rescue does not remove a participant from the target question. This strategy requires collecting the endpoint after rescue; it does not mean that rescue is irrelevant to the outcome.

A composite strategy incorporates rescue use into the endpoint definition. For instance, define success as both meeting a clinical response threshold and not using rescue. A participant who uses rescue is then classified as not a success, even if the later symptom score meets the threshold. This is one possible composite definition; the endpoint and the rule for rescue must be stated explicitly.

A hypothetical strategy targets outcomes under a specified situation in which rescue does not occur. It asks what the endpoint would have been if rescue had been prevented, while treatment assignment and other relevant conditions are defined as intended. This counterfactual outcome is generally unobserved for participants who actually use rescue, so estimating the estimand requires assumptions and a suitable model or design.

The strategies are not interchangeable. In particular, omitting participants who used rescue does not implement a hypothetical strategy. It conditions on a post-randomization event and compares selected groups whose reasons for rescue may differ between treatment arms.

Composite Endpoints: Making Rescue Part of Success

A composite strategy is useful when the clinical goal is not merely improvement, but improvement without a specified intervention that signals inadequate control. The rule must be operational. For a binary endpoint, let \(C\) indicate that the clinical response criterion is met and define success as \(Z=1\) only when \(C=1\) and \(R=0\). Thus \(Z=1\) requires both response and no rescue. Other composite rules are possible, but they can produce different results and interpretations.

Counting rescue as failure does not mean that the participant’s measured symptom score is literally set to its worst possible value. It means the analysis uses a defined composite outcome. If the endpoint is a continuous score, assigning a numerical worst score to all rescue users would be a further endpoint choice, not an automatic consequence of the composite strategy.

Hypothetical No-Rescue Outcomes and Their Assumptions

Under a hypothetical strategy, the target outcome for a participant who used rescue is the outcome that would have occurred under the specified no-rescue situation. The observed post-rescue outcome cannot simply be relabelled as that counterfactual outcome. Nor can the outcome be estimated by dropping rescue users. Randomization supports comparisons of assigned groups, but it does not randomize rescue use within each group.

A common starting point for estimation is a model for outcomes under the no-rescue condition, using relevant observed information such as baseline severity and measurements before rescue. The model must be credible for the participants and circumstances to which it is applied. Important assumptions may include correct specification of the outcome model, adequate overlap in the observed data for the histories of interest, and appropriate handling of factors that predict both rescue and later outcomes. If the model predicts no-rescue outcomes for histories rarely or never observed without rescue, the estimate relies heavily on extrapolation.

The distinction from treatment policy can be seen with a simple mixture identity. If all outcomes are observed, the mean under a treatment-policy strategy can be written as the mean among those who did not use rescue weighted by their proportion, plus the mean among those who did use rescue weighted by their proportion. This is an accounting identity, not a causal comparison of the two rescue groups.

The identity explains why excluding rescue users changes the target: it drops the second weighted component and leaves a selected subgroup. It does not establish that the subgroup mean equals the mean that would have been observed for the whole arm under no rescue. That equality would require additional assumptions, not just the displayed arithmetic.

Justification, Diagnostics, and Limitations

The key reason a no-rescue mean needs more than observed arm averages is that rescue users’ outcomes under no rescue are missing counterfactuals. For any participant who used rescue, the observed endpoint is under a rescue-including course of care, whereas the hypothetical target is under a different course of care. To replace one with the other would require equality of those outcomes, which is not generally justified. A model or other design-based information is therefore needed to connect observed data to the hypothetical target.

Several checks help identify when an analysis may be fragile:

• Check timing and definition. Specify which medicines count as rescue, the qualifying symptoms or rules, and the interval in which use is considered. Ambiguous or inconsistent recording makes all strategies difficult to interpret.
• Check outcome collection. A treatment-policy analysis needs the endpoint after rescue. If those outcomes are not collected, the intercurrent-event strategy and missing outcome data are separate issues; the treatment-policy target is not automatically recovered by analyzing only observed cases.
• Check the composite rule. Confirm that response and rescue status are both measured and that the rule is clinically meaningful. Report the component frequencies so a composite result is not mistaken for a result about response alone.
• Check the hypothetical model. Examine whether rescue users have histories comparable to participants observed without rescue, and whether predictions depend on extrapolation. Consider whether plausible alternative assumptions would materially change the estimate.
• Check post-randomization selection. A comparison restricted to participants who did not use rescue can be distorted because prognosis, symptoms, clinician decisions, and treatment assignment may all relate to rescue use.

The alternatives each have limitations. A treatment-policy effect is relevant to decisions made in a setting with rescue available, but it combines treatment effects with the consequences of rescue use under that setting. A composite effect can align with a goal of avoiding rescue, but its interpretation depends on the chosen rule and may conceal different patterns in response and rescue. A hypothetical effect may address a scientific question about outcomes without rescue, but it depends on unobserved counterfactuals and modelling assumptions. A posterior distribution or other uncertainty summary cannot correct a mismatch between the modelled quantity and the intended estimand.

Common Mistake

A practical way to prevent this mistake is to write the question in words before choosing the analysis: “assignment with rescue available,” “response without rescue,” or “outcome if rescue were prevented.” Then ensure that the endpoint definition, data collection, and assumptions all match that question.