Interpreting Recorded Reasons For Withdrawal

What a Recorded Reason Can Tell You

When a participant leaves a longitudinal study, a recorded explanation such as “burden,” “relocation,” or “worsening symptoms” can help investigators understand how withdrawal occurred. It can suggest plausible stories about why later outcomes are missing. But a reason is a report or classification of the withdrawal, not a direct observation of outcomes that were never collected. The distinction matters: the wording of a reason does not establish whether the missingness mechanism is MAR or MNAR.

For a visit at time \(t\), let \(D_t=1\) mean that a participant withdraws before the outcome at that visit is obtained, and let \(D_t=0\) mean that the participant does not withdraw then. Let \(O_t\) denote information recorded by the time of withdrawal, such as baseline covariates and previously observed outcomes. Let \(U_t\) denote outcomes that remain unobserved after withdrawal. A recorded reason, \(Q_t\), is an explanation or category entered for a withdrawal. Depending on the study, it may come from a participant, a clinician, or an administrative record.

In a simplified setting, missingness is MAR relative to the specified observed information when, conditional on that information, withdrawal does not additionally depend on the unobserved outcomes. It is MNAR when withdrawal still depends on unobserved outcomes after conditioning on the specified observed information. As emphasized in the earlier material on why mechanism labels depend on the conditioning set, these labels are relative to a stated set of information, not properties conveyed by a word on a withdrawal form.

This expression is a conceptual condition: it does not say that every measured association between withdrawal and observed history must be absent. Nor does a reason category settle whether \(U_t\) matters. For example, “worsening symptoms” might refer to symptoms already recorded in \(O_t\), or to a worsening known to the participant but not recorded before withdrawal. Those possibilities have different implications for the missingness mechanism.

Read the Reason as Evidence About a Story, Not a Verdict

A reason can narrow the set of plausible explanations. “Relocation” may suggest an external disruption that has little to do with a participant’s future outcome. “Burden” may reflect observed appointment demands, or unrecorded fatigue that also predicts future health. “Worsening symptoms” may describe an already observed change, a current outcome collected at withdrawal, or a deterioration that would otherwise have been measured later. The category alone usually does not distinguish these possibilities.

The quality and timing of the reason matter. Check who supplied it, when it was recorded, how categories were defined, whether multiple reasons could be selected, and how often the reason was unknown. A category assigned retrospectively by study staff may not mean the same thing as a participant’s own explanation. A single “primary reason” can also compress several concurrent causes. These are not minor clerical details: they affect what the recorded reason supports.

Reasons are often observed only for participants who withdraw. Therefore, a reason category should not automatically be treated as a covariate available for all participants at all visits. If a formal analysis conditions on reasons, its definition and timing must be represented appropriately. In particular, recording a reason after withdrawal does not turn an unobserved later outcome into an observed one.

Compare Reasons With What Was Observed Before Withdrawal

A useful next step is to examine whether the recorded reasons align with information already available. For instance, compare reason categories across levels of the last observed symptom measure, or describe withdrawal by previously recorded adverse events. This can show whether a proposed account is consistent with the observed record. It cannot show whether the same account also depends on an unobserved current or future outcome.

A Justification for Caution

The limitation is not merely that reason categories may be imperfect. Even if a reason is recorded consistently, the observed records can be compatible with different distributions of outcomes after withdrawal. Consider participants with the same observed history \(O_t\) and the same recorded reason \(Q_t\). In one possible full-data account, their unobserved outcomes \(U_t\) follow the same distribution as outcomes among comparable participants who remain observed. In another, participants who withdraw have systematically worse unobserved outcomes. If \(U_t\) is never measured for those who withdraw, both accounts can produce the same observed histories, withdrawals, and reason counts.

The reason counts alone therefore cannot distinguish the two accounts. Formally, the observed data for a withdrawn participant include the withdrawal and recorded information, but not \(U_t\). Summing over possible unobserved outcomes leaves the same observed record compatible with different conditional distributions of \(U_t\). A narrative reason supplies useful context, but does not supply the missing outcome values needed to choose between those distributions.

The sum illustrates the information loss when \(U_t\) is unobserved; for continuous outcomes it is an integral instead. Different full-data distributions can yield the same observed distribution after this marginalization. Consequently, reason labels cannot, by themselves, verify MAR or establish MNAR.

Practical Checks, Alternatives, and Limits

Before using reasons to inform an analysis, check whether the categories are exhaustive, mutually exclusive, and consistently applied. Report the denominator for every percentage, retain an unknown or unreported category rather than silently omitting it, and distinguish participant-reported reasons from staff-assigned codes. Where possible, record multiple reasons and preserve the date and source of each report. These checks improve the description but do not convert it into a test of MAR or MNAR.

Reason summaries and the earlier diagnostic tables for dropout by observed history serve related but different purposes. A reason summary describes how withdrawals were recorded as occurring. A history-based table describes how observed characteristics or outcomes relate to subsequent response. Neither alone identifies dependence on outcomes that remain unobserved. If important uncertainty remains, sensitivity analysis can make alternative assumptions about the missing outcomes explicit and assess whether conclusions change. That approach addresses uncertainty rather than pretending the reason label has resolved it.

A common mistake is to reason, “The participant withdrew because of relocation, so missingness is MAR,” or “The reason was worsening symptoms, so missingness is MNAR.” The correction is to ask what information the reason refers to, whether that information was observed before withdrawal, and whether withdrawal could still depend on unobserved outcomes after conditioning on the stated observed information. A plausible explanation is a useful starting point for assumptions, not proof of those assumptions.