Introduction
In longitudinal follow-up, a patient may contribute several measurement visits and later experience an event such as death. These records are related, but they are not interchangeable. A visit tells us that the patient was observed at a particular time; a terminal event tells us that the patient reached an endpoint that ends the relevant follow-up. Confusing the two can distort both the longitudinal history and the time-to-event information.
This distinction matters especially when health status may affect monitoring. A patient whose condition worsens could be seen more often and could also face a greater risk of a terminal event. The visit history and event time may therefore be associated, yet each describes a different process. Separating them is a necessary step toward understanding how they jointly inform a patient’s course.
Three Different Records
The visit times recorded during follow-up are ordinarily those before \(X_i\). The terminal event may be observed at \(X_i\) when \(\Delta_i=1\); if \(\Delta_i=0\), follow-up ends at \(C_i\) without an observed terminal event. Thus, a patient with \(\Delta_i=0\) is not known to have avoided the event forever. The observation only establishes that the event was not recorded before censoring.
“Terminal” is relative to the endpoint and follow-up being analyzed. Death is terminal for most clinical follow-up. A first hospitalization can also be terminal if the endpoint is time to first hospitalization, even though a person may return to care afterward. The endpoint definition determines whether a subsequent clinical encounter is a recurrent visit in the same follow-up process or occurs after that process has ended.
A simple way to encode the distinction is with two counting processes. The visit count \(N_i^V(t)\) increases by one at each measurement visit up to time \(t\). The terminal-event count \(N_i^D(t)=I(T_i\leq t,\Delta_i=1)\) can increase from zero to one, but never beyond one. A visit process can have repeated jumps; a terminal-event process has at most one jump and then follow-up for that endpoint is over.
Worked Example: Separating Visit History From Event Status
Consider three hypothetical patients followed from enrollment. Patient A has measurement visits at months 1, 3, and 4, and dies at month 5. Patient B has visits at months 2, 4, and 6 and remains alive when administrative follow-up ends at month 8. Patient C has visits at months 1 and 2, is hospitalized at month 3, and hospitalization is the prespecified terminal endpoint.
For A, the visit count before the event is 3, the observed follow-up time is \(X_A=5\) months, and \(\Delta_A=1\). For B, the visit count is also 3, but \(X_B=8\) months and \(\Delta_B=0\): B’s record is censored at eight months, not evidence of an event at that time. For C, the visit count before the endpoint is 2, \(X_C=3\) months, and \(\Delta_C=1\) for the hospitalization endpoint.
The identical visit counts for A and B do not make their event records equivalent. A’s observed death time gives information about when the endpoint occurred; B’s record establishes only that no endpoint was observed through month 8. C’s hospitalization is terminal for the defined endpoint even if C later receives further care.
What Each Process Tells Us
A visit can provide a biomarker value, symptom report, examination, or other measurement of a patient’s health at that time. The sequence of visit times also describes when the patient was observed. More visits may mean more measurements, but they do not by themselves establish that health was better, worse, or unchanged between visits. The measured values and the timing of observation answer different questions.
A terminal event contributes information about the occurrence and timing of a clinically defined outcome. For an observed event, the time locates the endpoint within follow-up. For a censored record, the patient contributes event-free follow-up through the censoring time, but the later event time is unknown. Neither record is simply a summary of the number of measurement visits.
The records can be related. For example, worsening health may lead to additional visits and also be associated with a higher chance of death. Conversely, a patient who dies early has less opportunity to accumulate later visits. These possibilities make it important to keep the processes distinct before analyzing their association. They do not imply that visit frequency itself causes the terminal event.
Worked Example: Why a Censored Record Is Not a Terminal Event
Suppose, hypothetically, that terminal event times follow an exponential model with constant hazard \(\lambda=0.10\) per month. Assume right censoring is independent of the event time. For one patient observed for six months, consider two possible records: an event at month 6, or censoring at month 6 with no event observed.
Under this model, the event-time density is \(f(t)=\lambda e^{-\lambda t}\), and the event-free survival probability is \(S(t)=e^{-\lambda t}\). If the event occurs at six months, the likelihood contribution is \[ f(6)=0.10e^{-0.10(6)}=0.10e^{-0.6}\approx 0.05488 \] per month.
If the patient is censored at six months without an observed event, the event-time contribution is instead \[ S(6)=e^{-0.10(6)}=e^{-0.6}\approx 0.5488. \] The event record includes the fact that the event occurred at month 6; the censored record includes survival through month 6 but does not specify what happened afterward. These likelihood contributions are not probabilities of the two records on the same scale: the event contribution is a density, with units of inverse months, while the survival contribution is a probability.
This calculation relies on the stated exponential event model and independent censoring. It illustrates the distinction between an observed event and censoring; it does not model the timing or number of measurement visits.
A Timeline Argument for Keeping the Processes Separate
Let \(Y_i(t)=I(X_i\geq t)\) indicate that patient \(i\) is still under observation and event-free just before time \(t\), using the convention that an event at \(t\) is counted at that time. This indicator identifies when the patient contributes to the event-time risk set. It is not the visit count. A patient may have several visits while \(Y_i(t)=1\), and \(Y_i(t)\) changes to zero after the terminal event or censoring time.
The distinction follows directly from what the records mean. A visit at time \(V_{ij}\) adds one observation opportunity, so it increments \(N_i^V(t)\). An event at time \(T_i\) establishes the endpoint and removes the patient from the event-free risk set, so it increments \(N_i^D(t)\) once. Censoring ends observed risk-set contribution without an event jump. Treating these as a single count would erase whether an observed time was a measurement, an endpoint, or the end of observation.
Specify the event that ends the analysis follow-up, such as death or first hospitalization.
List measurement visit times and the measurements made at those visits, up to the end of observed follow-up.
Store \(X_i\) and \(\Delta_i\) separately from the visit history, so an event time is not mistaken for a visit or a censoring time.
Worked Example: Visit Counts Do Not Replace Event Follow-Up
Four hypothetical patients are followed for at most six months. Patient A has visits at months 1, 2, and 4 and dies at month 5. Patient B has visits at months 1, 3, and 5 and is administratively censored at month 6. Patient C has visits at months 2 and 4 and dies at month 4.5. Patient D has visits at months 1, 2, 3, 4, and 5 and is administratively censored at month 6.
The total visit count is \(3+3+2+5=13\). The total observed person-time is \(5+6+4.5+6=21.5\) months, and two terminal events are observed. The crude event rate is therefore \[ \frac{2\text{ events}}{21.5\text{ person-months}}=0.09302\text{ events per person-month}. \]
That crude rate is only a descriptive calculation; it does not adjust for patient differences or establish a causal effect. Its purpose here is to show that event information uses event counts and time at risk, whereas the visit total describes measurement opportunities. Patient D has the most visits but no observed event during follow-up, while C has fewer visits and an event. A visit count alone cannot recover event times, censoring status, or time at risk.
Diagnostics, Alternatives, and Limitations
Before analysis, inspect patient timelines and check that each record has a coherent endpoint definition, event status, and sequence of visit times. In particular, verify that visits do not appear after the terminal time for the same endpoint. If a visit and event share a recorded timestamp, follow the study’s time-ordering convention; decide whether the measurement was taken before the event, at the event, or is not a valid pre-event measurement. An unresolved tie can change which observations are treated as available before the endpoint.
Check that administrative study end and loss to follow-up are coded as censoring rather than as terminal events. Also check that the endpoint indicator has at most one event per patient. If a proposed endpoint can recur, such as repeated hospital admissions, it is not terminal in that analysis unless the endpoint has been defined as time to the first occurrence.
| Representation | Information preserved | What it can lose or misstate |
|---|---|---|
| Separate visit history and event record | Measurement times, repeated values, event time, and censoring status | Requires clear endpoint and time-ordering rules |
| Visit count alone | Number of recorded visits | Visit timing, measured values, event timing, and censoring status |
| Event status alone | Whether an event was observed | Event time and the amount of event-free follow-up |
A common mistake is to treat death as ordinary dropout because both stop future measurements. The reasoning is that neither patient has later biomarker values, so both should be coded as missing follow-up. The correction is that death is an observed terminal outcome when it is the endpoint; dropout is generally a non-event ending of observation. Death both ends the opportunity for future measurements and supplies event-time information. Treating it as ordinary censoring discards that information and changes the question being analyzed.
Another mistake is to use the last visit as if it were the event time. The last visit is the time of the last recorded measurement, not necessarily the time of death or another endpoint. If the patient is alive but lost to follow-up then, the endpoint time is censored at that point; if an event is later observed, its recorded time is the event time. Likewise, more frequent visits do not necessarily indicate worse health: monitoring practices, access to care, and clinical status can all affect observation.
The separate records are a foundation, not a complete model for their dependence. A simple event-time analysis may describe the terminal endpoint while a longitudinal analysis describes measured trajectories, but analyzing them separately may not account for relationships among health, visit timing, and event risk. Conversely, combining records without distinguishing their meanings can create incorrect risk sets or count an event as a measurement visit. The appropriate analysis depends on the scientific question and assumptions about observation, censoring, and the relationship between the processes.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A patient has visits at months 1 and 4 and is alive when follow-up ends at month 7. What are \(X_i\) and \(\Delta_i\), and what does the record establish?
- Why is a first hospitalization a terminal event in one analysis but potentially a recurrent event in another?
- Two patients each have three visits. One dies at month 5; the other is censored alive at month 5. Why are their event records not equivalent?
- A patient dies at month 3, but a data file lists a measurement visit at month 5. Give one issue that must be checked before analyzing the records.
Solutions. (1) \(X_i=7\) months and \(\Delta_i=0\). The record establishes that no event was observed through month 7, not that the patient never experienced the event afterward. (2) The endpoint definition controls the classification: time to first hospitalization ends at the first admission, whereas an analysis of repeated admissions treats each admission as a possible recurrence. (3) The first record contains an observed event time; the second contributes event-free follow-up through month 5 but has no observed event. Equal visit counts do not change that distinction. (4) Check for a recording error, an endpoint or time-origin mismatch, or whether the month-5 record belongs to follow-up after the defined terminal endpoint. Under the stated endpoint and time origin, a post-death measurement cannot be an ordinary later visit.