Missingness After Treatment Discontinuation

Discontinuation Is Not the Same as Missingness

When a participant stops taking assigned treatment, two things may happen: the treatment exposure changes, and later outcome measurements may or may not be collected. These are separate events. A participant can discontinue treatment but continue scheduled assessments; another can discontinue and also stop attending visits. Treating both situations as the same data status obscures what outcome the analysis is trying to summarize.

The distinction matters particularly for a treatment-policy question: what is the outcome under assignment to a treatment strategy when participants may discontinue and receive subsequent care as they otherwise would? For such a question, an outcome measured after discontinuation can be relevant. If it is not collected, the outcome is missing; discontinuation itself does not supply its value. This tutorial focuses on that distinction, rather than on choosing an estimator for the treatment-policy effect.

Definition: Treatment discontinuation means that a participant stops the assigned treatment. Study withdrawal means that the participant stops participating in some or all study procedures. An unobserved outcome is an outcome value at a specified time that is not available for analysis. Discontinuation can occur with or without study withdrawal, so it does not by itself determine whether a later outcome is observed.

Let \(A_i\) denote participant \(i\)'s randomized assignment, with \(A_i=1\) for the experimental strategy and \(A_i=0\) for the comparator. Let \(D_i=1\) indicate discontinuation of assigned treatment before the target assessment and \(D_i=0\) otherwise. Let \(R_i=1\) if the target outcome is observed and \(R_i=0\) if it is not. The outcome \(Y_i\) is the value at that target assessment. For a treatment-policy question, the outcome remains relevant after discontinuation, provided the outcome is still defined and can be measured.

These indicators describe different things. \(D_i\) concerns treatment exposure; \(R_i\) concerns availability of the outcome. In particular, \(D_i=1, R_i=1\) is possible: the participant stopped assigned treatment, but the outcome was collected. Likewise, \(D_i=1, R_i=0\) is possible: treatment stopped and the scheduled outcome was not obtained.

Which Question Does Follow-Up Answer?

The earlier material on Missing Data Within a Defined Estimand emphasizes that missing-data decisions follow the target question. Here, suppose the target is the mean outcome under each assigned strategy when discontinuation and subsequent care are allowed to occur. Write \(Y_i^a\) for participant \(i\)'s outcome at the target time under assignment strategy \(a\), allowing treatment discontinuation and subsequent care as specified by that strategy. The arm-specific target mean is \(\mu_a=E(Y_i^a)\), and a mean-difference contrast is \(\mu_1-\mu_0\).

For this treatment-policy target, the value after discontinuation is part of the outcome being summarized. Continuing assessment after treatment stops therefore helps observe outcomes relevant to the target. By contrast, a while-on-treatment question concerns outcomes during treatment exposure; an assessment after discontinuation may not answer that question. The same participant and measurement can thus be relevant to one question and outside the defined outcome window for another.

An outcome can be missing even when the participant remains in the study, for example if a visit is missed or a particular test is not completed. Conversely, a participant may stop assigned treatment but permit a brief outcome assessment or remote follow-up. Trial protocols should therefore record treatment status, study participation, and outcome availability separately rather than using one “discontinued” flag for all three.

Participant status before target time	Target outcome observed?	What it means for a treatment-policy question
Still taking assigned treatment	Yes	Outcome is available under the assigned strategy.
Stopped assigned treatment	Yes	Post-discontinuation outcome is available and contributes to the target summary.
Still taking assigned treatment	No	Outcome is missing despite continued treatment.
Stopped assigned treatment	No	Post-discontinuation outcome is missing; stopping treatment does not determine its value.

A Decomposition Shows What Is Missing

The target mean can be separated according to whether the endpoint was observed. This identity clarifies why outcome collection after discontinuation matters and why the observed participants alone may not answer a treatment-policy question.

\mu_a =E(Y_i^a\mid R_i^a=1)P(R_i^a=1) +E(Y_i^a\mid R_i^a=0)P(R_i^a=0).

The identity follows by partitioning the population into the disjoint groups \(R_i^a=1\) and \(R_i^a=0\). In the expectation of \(Y_i^a\), multiply by the two group indicators and take expectations:

\begin{aligned} E(Y_i^a) &=E\{Y_i^a I(R_i^a=1)\}+E\{Y_i^a I(R_i^a=0)\}\\ &=P(R_i^a=1)E(Y_i^a\mid R_i^a=1) +P(R_i^a=0)E(Y_i^a\mid R_i^a=0). \end{aligned}

Here \(I(\cdot)\) is an indicator: it equals 1 when the condition is true and 0 otherwise. The first conditional mean is informed by observed outcomes. The second is the mean among participants whose outcomes are missing. Without further assumptions or information, the observed data do not reveal that second mean. The problem is especially visible when missing outcomes occur after discontinuation, but the identity applies to missing outcomes for any reason.

If follow-up continues after discontinuation, more of those post-discontinuation outcomes can be directly observed, reducing the portion of the target mean that must be inferred from missing data. Continued collection does not guarantee that every outcome is observed, nor does it automatically remove all bias. It does, however, avoid making treatment discontinuation itself a reason for an outcome to be unavailable.

Worked Example: Separating Discontinuation From Endpoint Availability

Consider a hypothetical trial with 100 participants assigned to each strategy. In each arm, 20 participants discontinue assigned treatment before the target visit. In the experimental arm, 17 of those 20 have the target outcome collected; in the comparator arm, 8 of 20 have it collected. Assume all 80 participants per arm who did not discontinue also have the outcome observed.

In the experimental arm, the post-discontinuation collection rate is \(17/20=0.850\), or 85.0%. The post-discontinuation missingness rate is \(3/20=0.150\), or 15.0%. There are \(80+17=97\) observed endpoints out of 100, so overall endpoint availability is 97.0%.

In the comparator arm, the post-discontinuation collection rate is \(8/20=0.400\), or 40.0%. The post-discontinuation missingness rate is \(12/20=0.600\), or 60.0%. There are \(80+8=88\) observed endpoints out of 100, so overall endpoint availability is 88.0%.

The same discontinuation count—20 in each arm—coexists with substantially different endpoint availability. The figures describe data collection, not the outcomes of people whose endpoints are missing. They do not establish that either arm has better outcomes after discontinuation.

Observed Means Need Not Equal the Target Means

A simple numerical example shows the consequence of using only observed outcomes. Suppose the endpoint is a symptom score in points, with lower scores indicating fewer symptoms. In a hypothetical trial, each arm has 8 participants. All missing endpoints follow treatment discontinuation. In the experimental arm, 6 observed scores sum to 42 points and 2 scores are missing. In the comparator arm, 7 observed scores sum to 56 points and 1 score is missing.

Worked Example: Available Endpoints Versus the Treatment-Policy Summary

The observed experimental-arm mean is

\bar{y}_{1,\mathrm{obs}}=\frac{42}{6}=7.00\text{ points}.

The observed comparator-arm mean is \(56/7=8.00\) points. Thus the observed-participant contrast is \(7.00-8.00=-1.00\) point, with a lower observed mean in the experimental arm.

For illustration only, suppose the two missing experimental scores would have been 10 and 12 points, and the one missing comparator score would have been 9 points. If those values were known, the full-arm means would be

\bar{y}_{1}=\frac{42+10+12}{8}=8.00,\qquad \bar{y}_{0}=\frac{56+9}{8}=8.125.

The corresponding full-arm contrast is \(8.00-8.125=-0.125\) point, not \(-1.00\) point. The illustration does not reveal the actual missing scores: they were supplied only to show how the target summary could differ from the available-outcome summary. When scores are genuinely missing, the observed-participant contrast alone does not determine the full treatment-policy contrast.

If all participants instead continued outcome follow-up after discontinuing treatment, these endpoint values could be recorded, assuming participants completed the assessment. Treatment discontinuation would still have occurred, but the target outcomes would be available for this summary.

Design, Diagnostics, and Failure Modes

Follow-up after discontinuation is a design choice as well as an analysis issue. A protocol can specify that treatment may stop while outcome assessments continue, with collection by clinic visit, telephone, electronic questionnaire, or another suitable mode. The method must preserve the outcome's meaning and timing. It should also respect consent, participant burden, safety procedures, and the possibility that some participants decline further contact.

Specify the target question.
State whether the target outcome includes assessments after treatment discontinuation or is restricted to a defined on-treatment period.

Keep event and observation records distinct.
Record when treatment stopped, whether study participation continued, and whether each scheduled outcome was collected.

Summarize follow-up by treatment status.
Report how many discontinued and, among them, how many had each later outcome observed, preferably by randomized arm and time point.

Describe what remains unobserved.
Give the amount and timing of missingness and the recorded reasons. A missingness pattern is information about data availability, not a substitute for the unobserved outcomes.

Useful diagnostics include a table crossing discontinuation status with endpoint availability, counts of missed visits by time since discontinuation, and summaries of recorded reasons for non-collection. Comparing observed characteristics of participants with and without follow-up can flag differences that matter for analysis. However, no diagnostic using only observed information can verify the values of outcomes that were never measured. A high follow-up rate is reassuring about coverage, but it does not prove that the remaining missingness is harmless.

A common failure is to code every participant who discontinues treatment as having a missing outcome. This misclassifies those who stop treatment but complete later assessments. The correction is to define discontinuation and outcome availability separately, and to use the actual endpoint records to determine which outcomes are observed.

The converse failure is to assume that a treatment-policy question is automatically answered by the observed post-discontinuation outcomes. Participants may still lack measurements, and the observed post-discontinuation group may differ from the group with missing outcomes. Collection improves direct evidence but does not, by itself, establish that observed participants represent everyone with the target question.

Comparing the Main Data-Collection Choices

Choice	What it provides	Main limitation
Continue outcome collection after treatment stops	Direct measurements relevant to a treatment-policy question, including outcomes during subsequent care.	Some outcomes may still be missed; continued contact requires planning and participant agreement.
Stop outcome collection at treatment discontinuation	Outcomes up to discontinuation, which may suit a question explicitly limited to that period.	For a treatment-policy question, post-discontinuation outcomes are unavailable and must not be treated as if discontinuation defined the target.
Collect only selected post-discontinuation measures	Some information on later outcomes while reducing burden or focusing on essential endpoints.	Uncollected target outcomes remain missing; the limited schedule may not answer every outcome question.

The choice is not between “discontinuation” and “missing data” as mutually exclusive explanations. Discontinuation is an event affecting treatment exposure; missingness describes whether an outcome was observed. For a treatment-policy question, the most direct design is generally to seek the target outcome even when assigned treatment has stopped. If that is infeasible, the analysis must acknowledge which outcomes were not observed and what assumptions or additional information are needed to address them. The introductory material on Overlaps Missing Data (C38) gives broader background on missing-data concepts; the focus here is the specific separation of treatment discontinuation from later outcome collection.

Key takeaway: Discontinuing assigned treatment does not make a later outcome undefined or automatically missing. First define whether that outcome belongs to the target question; then determine whether it was actually observed. Collection after discontinuation can inform a treatment-policy question, while non-collection leaves an outcome-data problem rather than changing the event into an outcome value.

Worked Example: Checking a Follow-Up Plan

In a hypothetical study, 120 participants are assigned to one treatment strategy. By the target visit, 24 have stopped assigned treatment. Among those 24, 18 complete the target assessment. Of the 96 who have not stopped treatment, 90 complete it. Calculate the endpoint availability and explain what the counts say.

There are \(18+90=108\) observed outcomes among 120 participants, so overall availability is \(108/120=0.900\), or 90.0%. Among those who discontinued, availability is \(18/24=0.750\), or 75.0%; the remaining \(24-18=6\), or 25.0%, lack the target measurement. Among those who did not discontinue, availability is \(90/96=0.9375\), or 93.8% to one decimal place.

The figures show lower measured follow-up among those who discontinued, but they do not show whether their missing outcomes were better or worse. If the target is a treatment-policy outcome, those six outcomes are still unobserved target outcomes. The event count cannot be substituted for their symptom or clinical measurements.

Check Your Understanding

Answer each question, then compare your reasoning with the solutions below.

In a treatment-policy question, a participant stops assigned treatment but completes the scheduled endpoint visit. Is the endpoint missing? Explain.
Among 30 participants who discontinued, 21 provide the target assessment. What are the post-discontinuation collection and missingness rates?
Why does the available-outcome mean not necessarily equal the treatment-policy target mean?
A protocol stops all outcome collection at treatment discontinuation. What distinction should be made when reporting this decision?

Solutions. (1) No. Treatment stopped, but the target outcome was collected, so \(D_i=1\) and \(R_i=1\). (2) Collection is \(21/30=0.700\), or 70.0%; missingness is \(9/30=0.300\), or 30.0%. (3) The missing participants contribute to the target population, but their outcomes are not represented in the available-outcome mean; their mean may differ from the observed participants' mean. (4) State that discontinuation ends outcome collection, then note that post-discontinuation target outcomes are consequently unavailable. Do not describe treatment discontinuation itself as the missing outcome or assume the outcome is irrelevant without first specifying the target question.