Three Different Questions About Follow-Up
A longitudinal record can be incomplete in more than one way. A patient might be seen unusually often because symptoms worsen; the patient might attend a visit but not provide a blood sample; or the patient might withdraw and have no further study visits. These situations can all leave an irregular or incomplete sequence of measurements, but they describe different features of data collection.
The key is to ask, in order: When did a visit occur? Was the measurement recorded at that visit? Did follow-up stop? Visit timing concerns the observation schedule. Item nonresponse concerns a measurement that was not obtained despite a visit or other measurement opportunity. Dropout concerns the end of a participant’s ongoing study follow-up. They can occur together, but none is simply another name for the others.
The definition of \(R_{ij}\) is tied to a particular measurement. A participant can attend a visit and have one measure recorded but another unavailable. Conversely, if no visit takes place, the absence of a measurement at that time is not automatically item nonresponse: there may have been no measurement opportunity at all. A study may still store an empty value for that occasion, but the data-management code does not by itself identify the reason.
The word informative describes a relationship between a process and relevant outcome information. Visit timing is outcome-dependent when the timing or frequency of visits is associated with the outcome’s current or evolving history. Item nonresponse is outcome-related when the chance that a measurement is recorded depends on outcome information. Dropout is outcome-related when leaving follow-up is associated with outcome information. These relationships are separate questions; evidence for one does not establish another.
A Record-Level Way to Separate the Processes
Consider the data for one participant over a follow-up period. The visit record says whether and when visits occurred. At each relevant measurement opportunity, the availability record says whether the measure was obtained. The follow-up record says whether participation continued or ended. Keeping these records distinct prevents an analyst from interpreting every gap in a measurement series as the same kind of missingness.
The distinction can be expressed as a probability identity. Write \(V\) for a visit pattern, \(R\) for measurement-availability indicators, and \(Y_{\mathrm{obs}}\) for the values actually recorded. The chain rule gives:
This is a factorization of a joint distribution, not an independence assumption. It separates three questions: what visit pattern occurred; which measurements were recorded given the opportunities; and what the observed values were given that pattern and availability. A dropout record adds information about when ongoing follow-up ceased, and can affect which later visits or measurement opportunities could occur. The identity does not imply that these processes are independent, nor that the observed records alone reveal their dependence on unobserved outcomes.
Worked Example: Outcome-Triggered Visits With Complete Measurements
In a hypothetical study, a participant is scheduled for assessments at weeks 4, 8, and 12. A symptom flare prompts extra visits at weeks 6 and 10. At all five visits, the biomarker is measured. The participant remains in follow-up through week 12.
Visit timing. There are five visits, including two additional visits prompted by a symptom flare. The schedule is not simply the planned schedule: visit timing is related to the clinical history that prompted the extra assessments. This is a feature of the visit process.
Measurement availability. All five measurements are recorded, so the availability indicators for this biomarker are \(R_{ij}=1\) at each visit. There is no item nonresponse for this measure in the described record.
Dropout. The participant completed follow-up as planned, so no dropout is described. The classification is therefore outcome-related visit timing, complete measurement recording, and no dropout. Having more observed measurements does not mean the participant’s underlying outcome was sampled at a fixed or outcome-independent schedule.
Worked Example: A Visit Occurs but One Measurement Is Missing
In a hypothetical study, 20 scheduled visits take place. At 16 visits, both the symptom score and a blood biomarker are recorded. At four other visits, the participant attends and completes the symptom score, but the blood sample is unusable. The participant continues follow-up.
For the blood biomarker, the number of recorded values is \(16\), and the number of measurement opportunities is \(20\). The observed completion proportion is
Thus, the biomarker is recorded at 80% of these visits, and is unavailable at four visits despite attendance. This is item nonresponse for the blood biomarker. It is not dropout, because follow-up continues, and the four instances are not missed visits, because the participant attended them. The record does not establish why the samples were unusable or whether unobserved biomarker values are related to sample availability.
Worked Example: A Missed Visit Followed by Dropout
In a hypothetical study with monthly planned visits, a participant attends at months 1 and 2, misses the planned month-3 visit, and contacts the study team at month 4 to withdraw. The biomarker is recorded at both attended visits.
The month-3 record indicates a missed planned visit: there was no observed visit then. It does not, by itself, establish item nonresponse at an attended visit. The withdrawal at month 4 marks dropout, so no later study visits are expected under the participant’s continued follow-up. The two available biomarker measurements were recorded at the visits that did occur.
The classification is a missed visit followed by dropout, with no stated item nonresponse. If the participant had attended month 3 but declined the biomarker test, that would instead add item nonresponse for the biomarker. The distinction rests on the event recorded, not merely on the empty cell in a biomarker table.
Why the Distinction Matters
Analyses of longitudinal outcomes can be distorted if they treat the observed measurements as though they came from a common fixed schedule when visit timing is related to outcome history. For example, patients with worsening symptoms might be measured more often. A dataset that counts every measurement equally may then give greater representation to periods or participants with more frequent monitoring. This concern is about how observations are selected over time; it does not require that any value be missing at an actual visit.
Item nonresponse raises a different issue: among measurement opportunities, the observed values may not represent all values that would have been obtained. Dropout raises another: after follow-up ends, later measurements are unavailable because participation has ceased. The earlier material on informative dropout addresses consequences and sensitivity to dropout; here the essential point is to avoid labeling a visit process as item nonresponse or treating an isolated unavailable measurement as dropout.
A practical comparison is:
| Feature | Question asked | Example record |
|---|---|---|
| Visit timing | When, or how often, did observation visits occur? | An extra visit follows worsening symptoms. |
| Item nonresponse | At a measurement opportunity, was this particular value recorded? | The participant attends but the blood sample is unusable. |
| Dropout | Did ongoing study participation end before planned follow-up ended? | The participant withdraws and has no further study visits. |
These distinctions help identify the relevant data and the questions an analysis must address. They do not, on their own, determine which statistical method is appropriate or prove that a process is informative. Determining dependence on outcomes that were not observed is especially difficult: a recorded visit reason or a measured symptom may help characterize the process, but the absence of a recorded outcome cannot generally reveal its own value.
Diagnostics and Common Misclassifications
Begin with the planned visit calendar, actual visit dates, measurement-level availability indicators, and documented follow-up status. Compare planned and actual times, identify which measures are absent at attended visits, and record when and why follow-up ended when that information exists. These checks can expose coding errors, such as a missed visit being entered as a missing assay or a participant who withdrew being left with apparent future scheduled observations.
Useful summaries include the number and spacing of actual visits, the proportion of attended visits with each measure recorded, and counts of participants who discontinue follow-up. Compare these summaries across observed histories such as prior symptom levels, while recognizing that observed associations do not establish dependence on an unobserved current value. Reasons documented for extra visits, unavailable samples, or withdrawal can clarify classification, but may be incomplete or measured imperfectly.
- Mistake: “A missing value means the participant missed the visit.” Correction: the participant may have attended, with the particular measure unavailable. Check attendance and measurement records separately.
- Mistake: “More measurements mean more complete follow-up.” Correction: more visits describe the observation schedule. They do not guarantee that every measurement was recorded or that follow-up was noninformative.
- Mistake: “A missed visit is dropout.” Correction: a participant can miss one visit and return later. Dropout refers to cessation of ongoing participation, not a single gap.
- Mistake: “A pattern in observed data proves the process depends on the true, unobserved outcome.” Correction: observed records can show associations with recorded history, but dependence on unobserved outcomes requires assumptions or additional information.
The labels also have limits. A participant may have outcome-related extra visits, an unavailable assay at one attended visit, and later dropout. Classification should preserve all three facts rather than force the record into one exclusive category. Planned study closure is not dropout merely because measurements stop; it is the end of the observation window. The data should make clear which follow-up ended early and which ended as planned.
Check Your Understanding
For each question, identify the relevant feature and compare your reasoning with the solutions.
- A participant attends every scheduled visit, but a questionnaire is blank at two of them. Is this a missed visit, item nonresponse, or dropout?
- A patient has extra visits after worsening symptoms, with the biomarker recorded at every visit and follow-up continuing. Which feature is outcome-related in the description?
- Of 30 attended visits, a measure is recorded at 27. Calculate the observed recording proportion and state what it describes.
- A participant misses one visit, returns at the next, and later completes the study. Is the initial missed visit dropout?
- Why does an association between extra visits and recorded symptom history not, by itself, establish dependence of visit timing on the unobserved current outcome?
Solutions. (1) Item nonresponse for the questionnaire: the participant attended, but that measure was not recorded. (2) Outcome-related visit timing: extra visits follow worsening symptoms. The description indicates no item nonresponse for the biomarker and no dropout. (3) The proportion is \(27/30=0.90\), or 90% of attended visits with the measure recorded; it does not describe visit frequency or dropout. (4) No. The participant returned, so the record shows a missed visit, not cessation of follow-up. (5) The observed symptom history is not the unobserved current outcome. An association with the recorded history does not identify how visits relate to a value that was not measured.