Discontinuation and Treatment-Policy Questions

Why Discontinuation Changes the Question, Not the Follow-Up Goal

In a randomized trial, some participants stop their assigned treatment before the outcome is measured. They may still be willing to complete assessments. If the clinical question concerns the result of assigning a treatment strategy in practice, their later outcomes remain part of the answer: stopping treatment and what follows are among the possible consequences of assignment.

This tutorial works through that question using the treatment-policy strategy. The key distinction is between an intercurrent event and a missing outcome. Discontinuation is an event after randomization; it does not, by itself, make a later outcome unobserved. Conversely, recording that a participant discontinued does not supply a week-24 outcome if that assessment was never obtained.

Definition: Let \(Z\) denote randomized assignment, with \(Z=1\) for the investigational strategy and \(Z=0\) for the comparator. Let \(D\) indicate whether assigned treatment is discontinued before the outcome time, and let \(Y\) be the outcome at a prespecified time, such as week 24. A treatment-policy outcome under assignment \(a\), denoted \(Y^a\), is the week-24 outcome that would be observed if a participant were assigned to arm \(a\), regardless of whether assigned treatment is discontinued. The participant’s subsequent course, including care received after discontinuation, contributes to that outcome.

For a higher-is-better outcome, a common treatment-policy estimand is the difference between population mean outcomes under the two randomized assignments:

\Delta_{\mathrm{TP}} = E(Y^1)-E(Y^0).

This contrast concerns assignment to the two trial strategies, including the consequences of discontinuation and subsequent care as they occur in the trial context. It is not, by itself, the effect of continuously taking the investigational treatment, nor the effect among people who would adhere to it.

What the Randomized Contrast Identifies

The basic identification argument applies when assignment is randomized, the assignment strategies and outcome are well defined, outcomes are obtained at the target time, and one participant’s assignment does not affect another participant’s outcome. Consistency means that a participant assigned to arm \(a\) has the outcome \(Y^a\) under the trial strategy actually assigned. Randomization makes assignment independent of the potential outcomes. Thus:

E(Y\mid Z=a) = E(Y^a\mid Z=a) = E(Y^a).

The first equality uses consistency; the second uses randomization. Therefore, the difference between the observed arm means estimates \(\Delta_{\mathrm{TP}}\), provided the relevant outcomes are observed for the randomized participants. In a finite randomized trial, the corresponding estimator is the difference in the two all-randomized-arm means. Its uncertainty reflects sampling variation.

Discontinuation does not invalidate this argument. It is part of the post-assignment course represented in \(Y^a\). But the argument does not say that randomization makes the people who discontinue comparable to those who continue. Discontinuation is post-randomization, so directly comparing those subgroups can introduce selection. The treatment-policy contrast instead compares the original randomized arms.

Worked Example: Including Week-24 Outcomes After Discontinuation

Consider a hypothetical randomized trial of 200 participants, with 100 assigned to each arm. The endpoint is a symptom score at week 24, measured in points; higher scores indicate better status. Every participant completes the week-24 assessment, including those who discontinued assigned treatment.

In the investigational arm, 70 participants continue assigned treatment and have a mean score of 8.6; 30 discontinue and have a mean score of 5.9. In the comparator arm, 85 continue and have a mean of 6.8; 15 discontinue and have a mean of 3.5. The all-randomized-arm means are weighted averages:

\bar{x}_{1} = \frac{70(8.6)+30(5.9)}{100} = \frac{602+177}{100} = 7.79,

\bar{x}_{0} = \frac{85(6.8)+15(3.5)}{100} = \frac{578+52.5}{100} = 6.305.

The estimated treatment-policy contrast is \(7.79-6.305=1.485\) symptom-score points in favor of assignment to the investigational strategy. It includes the measured outcomes of the 30 and 15 participants who discontinued. It does not imply that the investigational treatment itself caused a 1.485-point improvement among people who took it continuously.

For an illustrative uncertainty calculation, suppose the sample standard deviations across all 100 outcomes in the two arms are 2.4 and 2.5 points. Using the usual independent-arm standard error and a normal approximation:

SE = \sqrt{\frac{2.4^2}{100}+\frac{2.5^2}{100}} = \sqrt{0.1201} \approx 0.3466.

A 95% approximate confidence interval is \(1.485 \pm 1.96(0.3466)\), or \(1.485 \pm 0.6793\), giving \((0.806, 2.164)\) points. Under the stated trial and approximation assumptions, this interval describes uncertainty about the mean treatment-policy contrast. It is not a probability statement about where the fixed contrast lies.

Read the Post-Discontinuation Outcome in Context

An assessment after discontinuation is not a measurement of what the participant’s outcome would have been had assigned treatment continued. It is the outcome at the specified time under the course that actually followed assignment: the participant stopped, and any subsequent care or lack of additional treatment occurred. The assessment is relevant to a treatment-policy question precisely because that course is included.

The target also depends on how the trial operationalizes the outcome. The endpoint should be defined at a common time and in the same way in both arms. If a week-24 score is recorded for someone who stopped at week 10, that score is the week-24 outcome for this estimand, not an “on-treatment” score. If the endpoint is not collected after stopping, the participant’s outcome is missing; discontinuation status cannot replace it.

Worked Example: A Small Trial With Assessments After Stopping

In a hypothetical trial, six participants are randomized to each arm. A week-24 score is recorded for everyone, including those who stopped assigned treatment. The investigational-arm scores are 8, 7, 6, 5, 4, and 3; the final two participants discontinued. The comparator scores are 8, 7, 6, 5, 2, and 1; the final two discontinued.

The investigational mean is \((8+7+6+5+4+3)/6=33/6=5.5\). The comparator mean is \((8+7+6+5+2+1)/6=29/6\approx4.833\). Thus, the treatment-policy estimate is \(5.5-4.833\approx0.667\) score points.

If an analyst instead kept only participants who continued assigned treatment, the means would be \((8+7+6+5)/4=6.5\) and \((8+7+6+5)/4=6.5\), giving a contrast of zero. That calculation answers a different, selected-subgroup question. It is not a substitute for the randomized treatment-policy comparison, and the difference between the two answers does not establish that discontinuation caused a particular change.

When Discontinuation Is Followed by Missing Outcomes

A treatment-policy target can be defined even when some outcomes are missing, but the target’s definition does not make those outcomes observed. The complete-outcome randomized comparison above identifies the target under its stated conditions. If follow-up is incomplete, estimating the same target requires additional assumptions or information; simply averaging observed outcomes does not generally recover the all-randomized-arm mean.

Worked Example: Why Discontinuation Counts Do Not Fill In Missing Scores

Suppose a hypothetical trial has 20 participants per arm and a week-24 score bounded between 0 and 10. In the investigational arm, 18 scores are observed with mean 7, while two scores are missing. In the comparator arm, 16 scores are observed with mean 6, while four are missing. The observed score totals are \(18(7)=126\) and \(16(6)=96\).

Without assumptions about the unobserved scores beyond the 0-to-10 scale, the investigational all-participant mean could range from \((126+2(0))/20=6.3\) to \((126+2(10))/20=7.3\). The comparator mean could range from \((96+4(0))/20=4.8\) to \((96+4(10))/20=6.8\). Consequently, the treatment-policy contrast could range from \(6.3-6.8=-0.5\) to \(7.3-4.8=2.5\) points under these bounds.

The observed-case difference is \(7-6=1\) point, but it is not identified as the all-randomized treatment-policy contrast by these data alone. Knowing that some participants discontinued does not reveal their missing week-24 scores. The wide range here illustrates why outcome collection after discontinuation matters; it does not prescribe a particular missing-data model.

Choosing and Checking the Question

A treatment-policy question is useful when the decision concerns assignment to a strategy in a setting where participants may stop treatment and continue to receive outcome follow-up. Its meaning is tied to the trial’s procedures and subsequent-care context. Different strategies target different questions, rather than serving as interchangeable ways to calculate one universal effect.

Question or strategy	How discontinuation is handled	What the contrast concerns
Treatment policy	Use outcomes at the target time regardless of discontinuation.	Assignment strategies, including the consequences of stopping and subsequent care.
While on treatment	Define the outcome summary using the period while assigned treatment is taken.	Outcomes during treatment, rather than the same fixed-time treatment-policy outcome.
Hypothetical	Target outcomes under a specified scenario in which discontinuation does not occur.	A scenario-dependent contrast, not the observed post-discontinuation course.
Composite strategy	Incorporate the event into the outcome definition.	A contrast in a variable that combines clinical outcome and event information.

Before interpreting a result, check that the analysis has not quietly changed the question. In particular, verify that participants are grouped by randomized assignment, the outcome time is consistent, and assessments after discontinuation are included when observed. Also report how many participants discontinued in each arm and how many target-time outcomes were obtained. These counts help readers assess implementation and follow-up; they do not, on their own, determine the treatment-policy effect.

Several warning signs point to a mismatch. An analysis that removes everyone who discontinued, or reassigns participants according to treatment received, no longer gives the straightforward randomized treatment-policy comparison. An analysis that calls all post-discontinuation outcomes “missing” discards observed information and confuses an event with an unobserved value. Finally, a treatment-policy result should not be described as the effect of continuous treatment: it averages over the post-assignment experiences occurring under each randomized strategy.

Common pitfall: “Participants who stopped treatment were no longer part of the treatment comparison, so their later outcomes should be excluded.” This reasoning changes the target and conditions on a post-randomization event. For a treatment-policy question, retain their observed outcomes in their randomized arms. If a later outcome was not collected, treat it as missing rather than as a consequence that can be inferred from the discontinuation record.

Key takeaway: A treatment-policy contrast compares outcomes under randomized assignment while allowing discontinuation and its subsequent consequences to occur. Its interpretation depends on collecting the target outcome after discontinuation; defining the estimand does not, by itself, solve missing follow-up.

Check Your Understanding

Answer each question, then compare with the solutions below.

A participant assigned to the investigational arm stops treatment at week 8 but provides the planned week-24 score. Should that score contribute to a treatment-policy analysis? Explain.
In a randomized trial, the mean week-24 score is 6.2 in the investigational arm and 5.4 in the comparator arm, with higher scores better. State the estimated treatment-policy contrast and interpret it.
Why is comparing only participants who continued assigned treatment not generally the same as comparing the randomized arms?
Some participants discontinue, and their week-24 outcomes are not collected. Does the treatment-policy definition imply that their outcomes are observed or that an all-participant mean is identified?

Solutions. (1) Yes. The observed score is the target-time outcome under the course following assignment, which includes discontinuation. (2) The estimate is \(6.2-5.4=0.8\) score points. Assignment to the investigational strategy is associated with a mean week-24 score 0.8 points higher in this trial’s target population; the contrast includes post-discontinuation outcomes and is not automatically an effect of continuous treatment. (3) Continuation is determined after randomization, so restricting to continuers selects subgroups that need not retain the comparability created by randomization. (4) No. A target can be defined when outcomes are missing, but its mean is not generally identified from the observed outcomes alone; additional assumptions or information are needed.