Composite Estimands for Treatment Discontinuation

Why Put Discontinuation Into the Outcome?

If participants discontinue assigned treatment, a trial must specify how that event relates to the outcome it aims to compare. A composite strategy makes discontinuation part of the outcome definition. For example, a participant may count as a treatment failure if they discontinue before the endpoint visit, even if their later clinical outcome is known. The resulting contrast answers a question about a combined outcome, not solely about clinical response among participants who remain on treatment.

This choice is relevant in adaptive trials because adaptations can change allocation, follow-up, or other features of trial conduct. The estimand remains interpretable only if its target population, treatment conditions, event handling, outcome definition, and summary are kept explicit. In particular, changing the rule for discontinuation partway through a trial can change what the treatment contrast means.

Specify the Composite Before Estimating It

A useful specification states which discontinuations count, when they count, and exactly how they enter the endpoint. “Discontinuation” alone is not sufficiently precise. A protocol should say whether discontinuation includes stopping all assigned treatment, switching treatment, or stopping for particular reasons; whether the event must occur before the endpoint time; and whether a participant who restarts treatment is still classified as having discontinued. It should also state how discontinuation is combined with the clinical outcome.

For a binary endpoint, one straightforward definition is success only if the participant meets the clinical response criterion and has not discontinued by the endpoint time. If \(D=1\) denotes discontinuation by that time and \(R=1\) denotes clinical response, define composite success as \(Z=1\) when \(D=0\) and \(R=1\); otherwise \(Z=0\). For a continuous measure, a rule might assign a specified low value to discontinuation. That value must have a defensible interpretation on the outcome scale.

The composite endpoint is not the same thing as a missing-data rule. A recorded discontinuation can be incorporated into the endpoint even when the clinical outcome after discontinuation is unavailable. But if a participant does not discontinue and their endpoint assessment is missing, the composite may still be missing: the protocol needs a separate plan for that case. Nor does a composite rule imply that the clinical outcome after discontinuation is irrelevant for every possible estimand. It means that the chosen endpoint has defined that event as part of its outcome.

A Binary Composite: Definition and Interpretation

Let \(a\) denote a randomized treatment condition. Let \(D^a\) indicate whether a participant would discontinue assigned treatment by week 12 under that condition, and let \(R^a\) indicate whether they would meet the response criterion by week 12. Define \(Z^a=1\) if \(D^a=0\) and \(R^a=1\), and \(Z^a=0\) otherwise. The population-level estimand may be the risk difference in composite success:

Here \(Z^1\) and \(Z^0\) refer to the composite outcomes under the two treatment conditions in the fixed target population. A positive \(\Delta_Z\) means a higher probability of meeting the combined success definition under treatment 1. It does not, by itself, isolate a treatment effect on the clinical response criterion.

The relationship to response and discontinuation can be shown directly. Because composite success requires both no discontinuation and response, the multiplication rule for probabilities gives:

Thus, the composite success probability depends on both the probability of remaining on assigned treatment and the response probability among those who do not discontinue. The second factor is a conditional probability, not automatically a causal treatment effect among a comparable group: who discontinues may differ between treatment conditions. The composite contrast avoids defining the target as a comparison restricted to observed non-discontinuers, but it combines distinct ways of achieving or failing the endpoint.

Other Composite Scales

A composite need not be binary. It can retain more information by assigning a value or rank to discontinuation, provided the rule is defined in advance and the resulting scale is interpretable. If higher values represent greater benefit, for example, a protocol could assign a low score to discontinuation and compare mean scores. That estimate describes the average of the constructed composite score; it is not an estimate of the mean clinical outcome that would have been observed had everyone continued treatment.

Composite time-to-event endpoints use a related idea: the event can be defined as the first occurrence of discontinuation or a clinical event such as worsening. The event definition must specify which components count and how their timing is handled. A time-to-first-event summary then concerns time until any qualifying component, not time until clinical worsening alone.

Assumptions, Diagnostics, and Comparisons

The numerical calculations above require correctly applied endpoint rules, valid ascertainment of the events and outcomes that define the composite, and an analysis consistent with the randomized comparison. The Wald calculations additionally use a large-sample approximation. If endpoint status is missing, a separate missing-data approach and its assumptions are needed; missingness must not be silently treated as discontinuation or as composite failure. The causal interpretation of the randomized treatment contrast also relies on the trial's design and conduct supporting comparison of the assigned treatment conditions in the target population.

Diagnostics should begin with the event and endpoint records, not only the final treatment contrast. Check event timing against the specified window, reasons for discontinuation, whether restarting treatment changes classification, and whether every participant can be assigned a composite outcome. Tabulate each composite component by treatment group. For a score-based endpoint, inspect how many observations receive the assigned discontinuation value and whether that value is at the intended end of the scale. If a composite is based on first events, confirm that event order is recorded well enough to classify the first qualifying event.

The main alternatives differ in their target. A treatment-policy estimand uses outcomes regardless of discontinuation when those outcomes are defined and available; it answers a question about treatment assignment in the presence of subsequent events. A hypothetical estimand targets a specified scenario in which the event did not occur. A composite estimand instead counts the event through the outcome rule. A while-on-treatment approach focuses on outcomes during treatment exposure and raises distinct questions about outcomes after treatment stops. These approaches should not be treated as interchangeable sensitivity analyses: changing strategy changes the question.

A composite can be attractive when discontinuation is itself clinically important, when it represents lack of tolerability or efficacy, or when assigning success despite discontinuation would be misleading for the decision at hand. Its limitations follow from that same construction. The contrast can be driven by different components in different treatment groups; components may differ substantially in severity; and an assigned score or failure rule can be arbitrary if not clinically justified. A single summary can hide those differences, so component results and the full endpoint definition should accompany it.

In an adaptive trial, changing allocation does not by itself require redefining a composite endpoint. But a change to the event window, discontinuation rule, or assigned score can change the estimand. If an adaptation makes such a change necessary, the resulting endpoint definitions and the populations or stages to which they apply must be stated clearly; a pooled estimate cannot be assumed to represent one unchanged composite without justification.