Why Landmark Eligibility Matters
A prediction made at a particular follow-up time applies to patients who have reached that time in a specified state. For example, a prediction made six months after treatment begins is not ordinarily meant for every patient who started treatment. It concerns patients who are still alive and free of the event at six months, with their status known at that point. Defining this group correctly is essential: including patients whose event occurred earlier, or excluding patients simply because their later follow-up is incomplete, changes who the prediction is about.
A landmark time is a prespecified time, measured from a stated time origin, at which eligibility for a prediction is assessed. The time origin might be diagnosis, treatment initiation, or study enrollment, but it must be specified consistently. A subsequent prediction interval can be written as \((L,L+h]\), where \(L\) is the landmark and \(h>0\) is the interval length. This tutorial concerns defining the landmark and the eligible risk set; it does not define a particular prediction model or risk estimand.
For a patient whose observation begins at the time origin, \(A_i=0\), so the entry condition is automatic for any nonnegative \(L\). If follow-up is delayed, the entry condition matters: someone first observed after \(L\) cannot be classified as eligible from that study’s records at \(L\). This is an observational eligibility rule, not a claim that the person was biologically event-free before entering the study.
Observed Data and Boundary Conventions
In ordinary right-censored follow-up, the observed time is \(Y_i=\min(T_i,C_i)\), and \(\delta_i=1\) indicates an observed event while \(\delta_i=0\) indicates censoring. For a patient observed from the origin, landmark eligibility can be determined from \((Y_i,\delta_i)\): the patient qualifies if \(Y_i>L\), or if \(Y_i=L\) and \(\delta_i=0\). An event recorded at \(L\) disqualifies the patient, whereas censoring at \(L\) means event-free status was observed through the landmark under the convention above.
The two indicator terms cannot both equal one. The rule treats an event at \(L\) as having occurred by the landmark and therefore excludes that patient. A censoring time equal to \(L\), by contrast, records that the patient was event-free through \(L\). If a data system records events and censoring at identical times, the event-versus-censoring tie rule must be stated; the convention here gives priority to a recorded event.
Eligibility at \(L\) does not require complete observation throughout \((L,L+h]\). A patient may be eligible at the landmark and then be censored before the end of the prediction interval. That patient’s later event status is not fully known, but their incomplete subsequent follow-up does not retroactively change their status at \(L\). This distinction is important when defining a cohort: landmark eligibility is determined using information available through \(L\), while ascertainment of what happens after \(L\) is a separate issue.
Worked Example: Applying the Landmark Rule
Suppose eight hypothetical patients are followed from treatment initiation, and the landmark is \(L=6\) months. The records below give observed follow-up time \(Y_i\) and event indicator \(\delta_i\).
| Patient | \(Y_i\) (months) | \(\delta_i\) | Eligibility at 6 months? |
|---|---|---|---|
| A | 4 | 1 | No |
| B | 6 | 0 | Yes |
| C | 9 | 1 | Yes |
| D | 5 | 0 | No |
| E | 6 | 1 | No |
| F | 8 | 0 | Yes |
| G | 7 | 1 | Yes |
| H | 3 | 0 | No |
For patient B, \(Y_B=L=6\) and \(\delta_B=0\), so the patient was censored at the landmark after being observed event-free through six months. B qualifies. For patient E, \(Y_E=L=6\) but \(\delta_E=1\), so the event occurred at the landmark and E does not qualify. Patients C, F, and G have \(Y_i>L\), so their observed records establish that they were event-free at six months. Patients A, D, and H have \(Y_i<L\), and each had an event or was censored before the landmark.
Thus the eligible set is \(\{B,C,F,G\}\), and its size is \(1+1+1+1=4\) patients. This is a count of patients eligible at the landmark, not a count of patients with fully observed outcomes over any later interval.
Why the Rule Follows from the Observation Process
The eligibility rule can be justified directly from what is observed. First suppose \(Y_i>L\). Since \(Y_i=\min(T_i,C_i)\), both \(T_i>L\) and \(C_i>L\): neither the event nor censoring has occurred by the landmark. The patient is therefore known to be event-free at \(L\). If \(Y_i=L\), the minimum is reached at the landmark. When \(\delta_i=0\), the observed endpoint is censoring rather than an event, so the patient was observed event-free through \(L\). When \(\delta_i=1\), an event occurred at \(L\), which fails the strict condition \(T_i>L\). Finally, if \(Y_i<L\), follow-up ended before the landmark, either because of an earlier event or because event-free status was no longer observed. In neither case can the patient be included as an observed event-free patient at \(L\).
These cases yield the observed-data rule above, provided the patient entered observation by \(L\). With delayed entry, \(A_i\leq L\) must be added: even a record with an event after \(L\) cannot establish eligibility at \(L\) if observation did not begin until later. The rule therefore follows from the event, censoring, and entry times together; looking only at whether \(Y_i\) exceeds \(L\) is insufficient when there is delayed entry or when an observation ends exactly at the landmark.
Worked Example: Delayed Entry Changes the Risk Set
Consider five hypothetical patients at a landmark \(L=12\) months. Their entry times \(A_i\), observed follow-up times \(Y_i\), and event indicators are as follows.
| Patient | \(A_i\) (months) | \(Y_i\) (months) | \(\delta_i\) |
|---|---|---|---|
| A | 0 | 14 | 1 |
| B | 10 | 15 | 0 |
| C | 13 | 18 | 1 |
| D | 0 | 12 | 0 |
| E | 5 | 11 | 1 |
Apply the conditions \(A_i\leq 12\) and either \(Y_i>12\) or \(Y_i=12,\delta_i=0\). Patient A satisfies \(0\leq12\) and \(14>12\), so A qualifies. Patient B satisfies \(10\leq12\) and \(15>12\), so B qualifies. Patient C has \(18>12\), but \(A_C=13>12\); the records do not establish C’s status at the landmark, so C is excluded. Patient D has \(A_D\leq12\), \(Y_D=12\), and \(\delta_D=0\), so D qualifies under the stated censoring convention. Patient E has \(Y_E=11<12\), so E is excluded because the event occurred before the landmark.
The eligible set is \(\{A,B,D\}\), with size \(1+1+1=3\). Omitting the entry-time condition would incorrectly include C. That error would treat follow-up after the landmark as evidence about the patient’s earlier event-free status.
Eligibility Is Not the Same as Complete Outcome Follow-Up
Suppose the prediction interval is \((L,L+h]\). A patient can qualify at \(L\) but be censored shortly afterward, leaving the event status over the full interval unknown. Conversely, requiring every patient to remain observed until \(L+h\) would select patients using future follow-up, rather than defining eligibility solely from information available at the landmark. These are different sets with different meanings.
Worked Example: Landmark Eligibility Versus Horizon Observation
Let \(L=4\) months and \(h=3\) months, so the interval of interest is \((4,7]\). Five hypothetical patients have follow-up from the origin.
| Patient | \(Y_i\) | \(\delta_i\) | Eligible at 4 months? | What is known after 4 months? |
|---|---|---|---|---|
| A | 4 | 0 | Yes | Censored at landmark; no later status observed |
| B | 4 | 1 | No | Event at landmark |
| C | 5 | 0 | Yes | Censored one month after landmark |
| D | 7 | 1 | Yes | Event at the end of the interval |
| E | 8 | 0 | Yes | Observed event-free through the interval |
The eligible patients are A, C, D, and E, so the eligible count is \(1+1+1+1=4\). Patient B is excluded because the event occurred at \(L=4\). Among the eligible patients, C’s status through month 7 is unknown because censoring occurred at month 5. A has no follow-up after the landmark, so A’s status over the interval is also unknown. D had an event at month 7, which falls in \((4,7]\), while E was observed event-free beyond month 7. Thus only D and E have fully observed status through the interval in this example; that does not change the count of four eligible patients.
Diagnostics, Alternatives, and Limitations
Before using a landmark risk set, check the records and the definition rather than relying on a single software-generated count. Confirm the time origin and units; verify that event and censoring indicators are coded consistently; inspect observations at exactly \(L\); and, when entry is delayed, confirm that entry times are compared with \(L\). A useful audit is to classify each excluded record as an event before or at \(L\), censoring before \(L\), or entry after \(L\). Unexpected counts in any category may reveal a coding or time-scale error.
- Including earlier events. A patient with \(Y_i<L\) and \(\delta_i=1\) is not event-free at the landmark. Counting that patient confuses the original cohort with the landmark-eligible cohort.
- Treating censoring as an event. A patient censored before \(L\) is not known to have had the event, but is also not known to be event-free at \(L\). The patient cannot be included as an observed eligible patient under this rule.
- Dropping everyone censored after \(L\). Later censoring does not erase eligibility already established at \(L\). It affects what can be learned about subsequent outcomes, not whether the patient qualified at the landmark.
- Ignoring exact-time conventions. An event at \(L\) and censoring at \(L\) have different meanings here. State how tied records are handled and apply the rule consistently.
- Ignoring delayed entry. A patient who enters after \(L\) cannot be assigned observed event-free status at \(L\) using follow-up that begins later.
A landmark approach describes a population selected at a specified follow-up time. It differs from making a prediction for the original cohort at baseline: patients who have already experienced the event are not eligible for a prediction conditional on reaching the landmark event-free. It also differs from simply analyzing only patients whose follow-up happens to extend to the end of a later horizon; that restriction uses subsequent observation and can discard otherwise eligible patients. Joint-model-based prediction is a further alternative that uses the longitudinal and event processes together, rather than defining predictions through a landmark cohort. These approaches answer different questions, and the eligible set alone does not determine which approach is preferable.
Landmarking has limitations. Results depend on the chosen time origin and landmark, and a different \(L\) can produce a different eligible population. Eligibility also selects patients who remain event-free until \(L\), so conclusions for that group should not be presented as conclusions for all patients at baseline. Finally, eligibility does not solve later censoring or missing covariate information. Those issues require methods and assumptions beyond the construction of the risk set.
Check Your Understanding
Use the boundary and entry conventions in this tutorial. Each question is followed by its solution.
- At \(L=5\), a patient has \(Y=5\) and \(\delta=1\). Is the patient eligible? Solution: No. The event occurred at the landmark, and eligibility requires \(T>L\).
- At \(L=5\), another patient has \(Y=5\) and \(\delta=0\). Is the patient eligible if entry was at month 0? Solution: Yes. The patient was censored at the landmark after being observed event-free through \(L\), and \(A=0\leq5\).
- At \(L=8\), a patient entered at month 9 and had an observed event at month 12. Should the patient be in the observed eligible set at month 8? Solution: No. Although the event was after month 8, entry was later: \(A=9>8\). The study does not establish the patient’s status at the landmark.
- At \(L=6\), a patient has \(Y=10\) and \(\delta=0\). Is the patient eligible at 6, and is their status necessarily known through month 12? Solution: The patient is eligible because \(Y=10>6\). Their status through month 12 is not known from these data: censoring occurred at month 10, before that horizon.