Treatment-Policy Estimand With Switching Therapies

Why Switching and Missing Outcomes Are Different

In a randomized trial, participants may switch therapies after randomization. If the scientific question concerns the effect of assignment to each trial arm under the trial’s actual care setting, their outcomes after switching remain part of the answer. Switching is an observed post-randomization event; it is not, by itself, a missing outcome. By contrast, if an endpoint is not recorded, its value is missing even if the participant’s switching history is known.

This distinction matters because deleting switchers or censoring their outcomes at the time of a switch changes the question. It no longer estimates the effect of assignment under the trial’s switching and subsequent-care practices. The treatment-policy estimand keeps that assignment-based question in view. Missing outcomes then require a separate analysis, including an explicit account of assumptions about their unobserved values.

The definition presumes that the endpoint is meaningful and defined for the participants in the target population at the specified time. It also presumes that the assignment strategies and the trial setting are described well enough to interpret the outcomes they generate. Randomization supports a causal comparison of assignment strategies when assignment is implemented as planned, outcomes are defined consistently, and there is no interference between participants. The estimand is not the effect of actually receiving one therapy rather than another: switching is part of the care pathway following assignment.

For a treatment-policy estimand, outcome collection should continue after switching whenever possible. If an outcome is missing, the assignment-based estimand has not changed, but its estimation is incomplete. The assumptions used to fill in or model missing outcomes are therefore not part of the definition of the estimand. They are assumptions needed to estimate it from the available data.

Worked Example: Keep Switchers in the Assignment Groups

Estimating the Contrast When Outcomes Are Missing

A simple way to illustrate the missing-data step is to suppose a prespecified model predicts each missing week-24 outcome from observed information, such as baseline severity and earlier symptom measurements. Under a missing-at-random (MAR) assumption, the probability an outcome is missing may depend on those observed variables but does not additionally depend on the unobserved week-24 value after conditioning on them. The model must be appropriate for the outcome and observed data; MAR alone does not guarantee that a poorly specified model gives reliable predictions.

For illustration, suppose the model’s predicted mean among the 10 missing outcomes is 8.0 points in arm \(A\) and 7.5 points in arm \(B\). These are hypothetical model-based predictions, not observed means. Combining observed outcomes and predicted missing outcomes gives the following arm means:

The estimated treatment-policy contrast is \(9.26-8.31=0.95\) points in favor of assignment to \(A\). This is an illustrative completed-data calculation. In an actual analysis, uncertainty in the missing-outcome predictions must also be reflected in the standard error and interval estimate, for example by an appropriate multiple-imputation or likelihood procedure. Treating predicted values as if they were known observations generally understates uncertainty.

MNAR Sensitivity Analysis

MAR cannot generally be verified from observed outcomes alone: it concerns how missingness relates to outcomes that were not observed. A sensitivity analysis therefore asks whether conclusions change under plausible departures from the MAR predictions. One transparent approach adds an arm-specific shift, measured in outcome points, to the predicted mean among missing participants. Let \(\delta_A\) and \(\delta_B\) denote these shifts. A negative shift says that, on average, missing outcomes are worse than their MAR predictions; a positive shift says they are better.

The multiplier 0.10 is the proportion missing in each arm: shifting 10 missing outcomes by one point changes that arm’s overall mean by \(10/100=0.10\) point. If arms have different missing proportions, the two multipliers must differ. The shifts are sensitivity parameters, not values estimated from the observed outcomes. They should be justified in clinical units and explored across a range of plausible values.

The tipping value can also be derived. The estimated contrast is zero when \(0.95+0.10\delta_A-0.10\delta_B=0\). Dividing by 0.10 gives \(\delta_A-\delta_B=-9.5\) points. Thus, to make this particular point estimate zero, the missing outcomes in \(A\) must be shifted 9.5 points lower relative to their MAR predictions than the missing outcomes in \(B\). This is an algebraic tipping value for the point estimate, not a test of statistical significance. Any inferential conclusion also depends on the uncertainty calculation.

Assumptions, Diagnostics, and Alternatives

A treatment-policy analysis is most credible when the trial documents switching, treatment discontinuation, and follow-up outcomes clearly. Outcome collection after switching is especially valuable: it avoids replacing observed outcomes with assumptions simply because therapy changed. Before interpreting results, check how many participants switched in each arm, when switching occurred, whether outcomes were collected afterward, and how much outcome missingness overlaps with switching. Compare observed characteristics and earlier outcomes across participants with and without week-24 measurements. These checks can reveal data problems or sparse regions where the prediction model is extrapolating, but they cannot prove MAR.

A useful derivation clarifies why a switch is not automatically a reason to omit an outcome. If \(R=1\) indicates an observed week-24 outcome and \(R=0\) a missing one, the arm mean can be partitioned as \(E(Y\mid Z=z)=P(R=1\mid Z=z)E(Y\mid Z=z,R=1)+P(R=0\mid Z=z)E(Y\mid Z=z,R=0)\), where \(Z\) is randomized assignment. A measured outcome after switching contributes to the first term according to the participant’s randomized arm. Only the second term requires assumptions or additional information. Deleting switchers removes part of the observed data and does not recover the unobserved mean in that second term.

Different estimand strategies answer different questions. A treatment-policy strategy includes outcomes regardless of switching. A hypothetical strategy instead targets outcomes under a specified scenario in which switching did not occur; estimating it needs assumptions about outcomes under that scenario. A per-protocol or as-treated analysis groups participants by treatment received or adherence and no longer preserves the randomized comparison in the same way. These approaches are not interchangeable fixes for missing data: each targets a different question and has its own assumptions.

The treatment-policy estimate is also specific to the trial’s assignment strategies, including the switching patterns and subsequent care that arise in its setting. If switching rules or access to alternative therapies differ elsewhere, the assignment contrast need not transport unchanged. In addition, a simple shift model may not capture different MNAR departures across participant subgroups or outcome histories. Results should therefore report the MAR-based analysis, the MNAR scenarios and their rationale, and how uncertainty was calculated.

• Failure mode: Switchers have no week-24 follow-up because the analysis stops collecting outcomes at switching. The treatment-policy estimand still includes their outcomes, but they are now missing and require assumptions. Continue outcome collection where possible.
• Failure mode: A prediction model uses little information about participants who are missing, or misses important outcome-history patterns. Inspect overlap, model fit, and predictions; revise the model or acknowledge that the estimate relies on extrapolation.
• Failure mode: Sensitivity shifts are chosen without clinical interpretation. State them in endpoint units, explain why the range is plausible, and show how the contrast changes across it.
• Common mistake: “Switching means the participant no longer belongs in the assigned arm.” For a treatment-policy estimand, that is incorrect: assignment defines the comparison group, and observed outcomes after switching remain relevant. Missingness is a separate issue.