Why Diagnose Dropout?
In a cohort study, participants may stop attending visits before the planned end of follow-up. The measurements after that point are missing, but the reason for their absence matters. A participant who misses visits because a clinic closed presents a different concern from one who stops attending after a deterioration in health. In either case, the data record the last observed measurement; it does not directly reveal what the participant’s later measurements would have been.
The practical task is to use what is recorded—earlier measurements, other observed history, and withdrawal reasons—to assess whether dropout could distort conclusions about outcomes after withdrawal. A pattern can raise or lower concern, but observed records alone generally cannot prove what the missing outcomes were or establish that dropout is unrelated to them.
A common classification uses three missingness assumptions. MCAR (missing completely at random) means dropout does not depend on the outcome or observed history. MAR (missing at random) means dropout may depend on the observed history, but not additionally on the unobserved outcome once that history is held fixed. MNAR (missing not at random) means dropout still depends on the unobserved outcome after conditioning on the observed history. These are assumptions about the missingness process, not labels that can usually be read directly from a withdrawal form.
In ordinary language, “informative dropout” is sometimes used broadly for any dropout associated with participant characteristics or outcomes. To be precise, dropout associated with recorded history may be explainable under MAR, while dependence on outcomes that remain unobserved after accounting for that history is MNAR. Either kind of pattern can make an analysis that simply ignores dropout misleading.
What the Observed Record Can Tell You
Begin by specifying the outcome and time point that matter. Then describe who dropped out, when they stopped providing measurements, what was measured before then, and what reasons were documented. Useful comparisons include dropout rates across baseline groups and across levels of the last observed measurement. For example, if participants with higher recent symptom scores drop out more often, the observed record supports concern that dropout is related to health history.
The interpretation must be conditional on what was actually recorded. If symptoms that predict withdrawal were repeatedly measured and included in the history, the pattern could be consistent with MAR given that history. If the relevant deterioration happened after the last measurement, or was never recorded, the observed history may not explain the dropout; MNAR is then a plausible concern. Neither conclusion follows just from the association between a prior score and dropout.
A reason such as “moved away,” “withdrew consent,” or “felt worse” is useful context, not a statistical test of the missingness assumption. Reasons may be incomplete, broad, or reported after the decision to stop. A stated health-related reason suggests a pathway linking withdrawal to health, but it does not reveal the value of the missing outcome. Conversely, an administrative reason does not guarantee MCAR: the administrative change could affect a particular clinic or participant group.
Worked Example: Dropout After High Observed Scores
Hypothetical cohort. Of 100 participants, 40 had a high symptom score at their most recent scheduled visit and 60 had a low score. Before the next visit, 12 of the 40 participants with high scores dropped out, compared with 8 of the 60 with low scores. Assess what this observed pattern suggests.
The dropout proportions are \(12/40=0.30\), or 30%, among participants with high prior scores, and \(8/60=0.1333\), or about 13.3%, among those with low prior scores. The ratio is \(0.30/0.1333\approx 2.25\). Thus, in this hypothetical cohort, dropout was about 2.25 times as frequent in the high-score group as in the low-score group.
This is evidence that dropout is associated with a measured part of the observed history. If those scores and the other relevant observed predictors are adequately represented in the analysis, a MAR assumption conditional on that history may be reasonable to consider. But the comparison does not show that MAR is true. Participants with high scores may also have had worsening symptoms after their last visit, and those later symptoms are unknown. That possibility leaves MNAR plausible. The calculation describes an observed association; it does not identify the missing scores.
Why the Missing Outcomes Cannot Be Recovered From Dropout Rates
A simple mean calculation shows why even a clear dropout pattern does not determine the cohort’s outcome. Suppose a fraction \(p\) of participants has an observed outcome, with mean \(\bar{Y}_{\text{obs}}\). Let \(\bar{Y}_{\text{mis}}\) be the mean outcome the participants who dropped out would have had at the target time. The full-cohort mean is a weighted average of those two group means:
Subtracting \(\bar{Y}_{\text{full}}\) from the observed-participant mean gives \(\bar{Y}_{\text{obs}}-\bar{Y}_{\text{full}}=(1-p)(\bar{Y}_{\text{obs}}-\bar{Y}_{\text{mis}})\). This follows by substituting the weighted-average expression and collecting terms. Therefore, the difference between the observed-participant mean and the full-cohort mean depends on how the missing participants’ mean compares with the observed participants’ mean. The dropout proportion alone cannot supply that missing quantity.
Worked Example: Same Observed Mean, Different Missing Outcomes
Hypothetical cohort. At a target visit, 90 of 100 participants have an observed score with mean 4.0 points. Ten participants dropped out. Compare two possible assumptions about their unobserved scores.
Here \(p=90/100=0.90\) and \(\bar{Y}_{\text{obs}}=4.0\). If the ten missing scores had mean 6.0 points, then \(0.90(4.0)+0.10(6.0)=3.60+0.60=4.20\) points for the full-cohort mean. If instead their mean had been 2.0 points, the calculation would be \(0.90(4.0)+0.10(2.0)=3.60+0.20=3.80\) points.
Both calculations use the same observed data, but produce different full-cohort means because the missing outcomes differ. The values 6.0 and 2.0 are hypothetical possibilities, not estimates from these records. The example demonstrates the limit of diagnosis: observed data can show who dropped out and what their earlier measurements were, but cannot by themselves select the true mean among their unobserved scores.
Worked Classification Problems
Worked Example: Withdrawal After a Documented Deterioration
Hypothetical cohort. A study records a health score at each visit. Participants with a sharp decline at one visit are more likely to withdraw before the next visit. The decline and a clinician’s assessment of worsening health are recorded before withdrawal. Classify the concern.
First, the pattern is not consistent with MCAR as a working description: withdrawal rates differ according to observed health history. The recorded decline provides information that could explain who is more likely to withdraw.
If the analysis conditions on the decline and the other relevant recorded history, this pattern could be MAR: within the same observed history, withdrawal would not additionally depend on the unobserved next score. However, that last condition cannot be confirmed solely from the pattern described. If an unrecorded deterioration between visits further increases withdrawal, MNAR remains possible. The recorded reason and prior decline are valuable diagnostic evidence, but neither reveals the next score.
Worked Example: Administrative Closure of One Clinic
Hypothetical cohort. A study follows 200 participants at two clinics. All 20 participants at Clinic B stop contributing measurements when that clinic closes. The closure date and clinic are recorded; there is no indication that participants withdrew because of their health. What is the most careful classification?
The dropout is not MCAR across the entire cohort, because clinic membership predicts dropout: every participant at Clinic B is affected, while Clinic A participants are not. But clinic and closure date are observed. If these variables are included in the relevant history, and withdrawal has no additional dependence on unobserved outcomes after conditioning on that history, the pattern is compatible with MAR. A closure reason makes health-driven dropout less immediately concerning, but it does not prove that assumption. For example, if Clinic B participants had different unrecorded health trajectories, those outcomes would remain a concern.
The key distinction is that an external reason can explain a dropout pattern without making the pattern MCAR. The diagnosis must account for how dropout relates to the observed cohort structure as well as to health history.
Worked Example: A Study Endpoint Is Not Ordinary Dropout
Hypothetical cohort. In a study of time until hospitalization, 6 of 60 participants are hospitalized and stop attending routine measurement visits. Another 4 participants withdraw without a hospitalization. Should all 10 be classified as dropouts?
No. For the hospitalization analysis, the 6 hospitalizations are observed events, not missing event outcomes: they are the endpoint the study is tracking. They may end routine measurement collection, but that does not turn the event itself into dropout. The other 4 participants have withdrawn before a recorded hospitalization and may have missing subsequent measurements or event follow-up, depending on the study records. Their withdrawal requires a separate assessment.
This distinction matters because treating an observed event as if it were ordinary loss to follow-up confuses an outcome with a missing outcome. For longitudinal measurements after hospitalization, measurements may indeed be unavailable; that is a different missing-data question from whether the hospitalization event was observed.
Diagnostics, Comparisons, and Limits
A useful diagnosis combines several checks rather than relying on one test or one reason code. Compare dropout proportions by baseline characteristics and prior measurements; inspect whether the last observed scores change as dropout approaches; summarize timing and recorded reasons; and check whether key health or treatment history is absent near withdrawal. A strong association with observed history indicates that a complete-case analysis may select a different group from the cohort. Little observed association is reassuring only about the measured variables and available sample; it cannot rule out dependence on unobserved outcomes.
| Working assumption | What dropout may depend on | What the diagnosis can establish |
|---|---|---|
| MCAR | Neither observed history nor the outcome | Rarely verified from observed data alone; an external mechanism may make it plausible. |
| MAR | Observed history, but not additionally the missing outcome after conditioning on it | Observed patterns can identify useful predictors, but cannot confirm the condition for missing outcomes. |
| MNAR | The missing outcome even after conditioning on observed history | Health-related reasons may raise concern, but the missing outcomes are not observed to verify the dependence. |
These assumptions are not interchangeable with a judgment that dropout is “good” or “bad.” Under MAR, dropout can be strongly related to measured health history and still be explainable using that history in an appropriately specified analysis. Under MNAR, the observed record does not contain enough information to determine the missing-outcome relationship without additional assumptions or information. The introductory material on sensitivity to unobserved outcomes treats how conclusions can be examined under alternative assumptions; diagnosis here identifies why that issue arises.
Dropout also differs from irregular visit timing. A participant who continues in the study but attends visits at changing times is not necessarily a dropout; they may still provide outcomes. Conversely, a participant can stop contributing measurements even if the scheduled visit times were regular. Keep the reason for a missing outcome distinct from the timing of an observed visit.
Common Mistakes
- Calling a withdrawal reason proof of a missingness assumption. “Moved away” may suggest an administrative cause, but does not establish MCAR. Consider whether the reason is related to clinic, participant history, or unrecorded health.
- Calling any association with prior outcomes MNAR. If dropout depends on a recorded prior score, that dependence may be accounted for under MAR conditional on the score. MNAR concerns additional dependence on an outcome that remains unobserved after conditioning on observed history.
- Assuming similar observed means settle the question. Participants who remain and those who leave may have similar last recorded means but different outcomes afterward. Similar observed history cannot reveal the missing values.
- Counting a recorded event as dropout. An endpoint that is observed is not a missing endpoint merely because it ends routine follow-up.
Check Your Understanding
For each problem, identify the most defensible conclusion from the stated information.
- In a hypothetical cohort, participants with higher recorded symptom scores are more likely to miss the next visit. Does this alone establish MNAR?
- A clinic closes and all participants receiving care there stop attending. Why is this not necessarily MCAR?
- Of 80 participants, 60 have observed target scores with mean 5 points. What full-cohort mean results if the missing 20 would have averaged 8 points?
- In a study of time to hospitalization, a participant is hospitalized and then has no routine follow-up score. Is the hospitalization itself dropout?
Solutions. (1) No. The association is with an observed score and may be compatible with MAR conditional on that score and relevant history; it does not establish whether the missing outcome has an additional role. (2) Clinic predicts dropout, so the pattern is not MCAR across the full cohort. It may be compatible with MAR conditional on clinic and relevant history, but that condition is not proven by the closure reason. (3) The observed fraction is \(60/80=0.75\), so the full-cohort mean is \(0.75(5)+0.25(8)=3.75+2.00=5.75\) points. (4) No. Hospitalization is an observed event endpoint; the subsequent routine score may be unavailable, but that is separate from whether the event was observed.