Landmark Analysis: Fixing Immortal Time Bias

Landmark analysis is a specific design fix for immortal time bias: pick a fixed time point after cohort entry (the landmark), restrict the analysis to subjects who are still alive and under follow-up at that point, and classify their exposure using only what was known at the landmark, then start the survival clock there. It does not explain what immortal time bias is or why it inflates apparent drug effects — see immortal time bias: how it inflates drug effects and how to correct it for the mechanism. This guide is the applied companion: how to actually build a landmark analysis, how to choose the landmark time defensibly, what it costs you, and a worked simulation showing the correction in action.

The two moves that define a landmark analysis

A landmark analysis makes exactly two changes to how a cohort is analyzed, relative to the naive whole-follow-up design that creates immortal time bias:

Restrict the analysis population to landmark survivors. Any subject who died, was lost to follow-up, or otherwise left the cohort before the landmark time is dropped from this analysis entirely — not censored at the landmark, excluded.
Classify exposure at the landmark, and start the clock there. A subject counts as “exposed” only if they had already started the drug (or met whatever the exposure definition is) by the landmark date. Follow-up time and events are then counted starting from the landmark, not from cohort entry.

Both moves matter. Restricting to survivors alone does not fix the bias if exposure is still classified using information from after the landmark; classifying at the landmark without restricting the population still lets pre-landmark deaths contaminate one arm’s person-time. Together, they guarantee that by the time either group’s clock starts, its exposure status is already a known, fixed fact — the condition immortal time bias violates.

Why this actually removes the bias

Immortal time bias exists because a subject’s eventual exposure status gets credited across a stretch of follow-up during which that status was not yet knowable — effectively guaranteeing survival for part of the “exposed” person-time. A landmark analysis removes the guarantee by construction: nobody’s group assignment reaches back before the landmark, and nobody who died before the landmark can contribute immortal time to either arm, because they are not in the analysis at all. The trade-off is visible in that same sentence — the technique buys unbiasedness by discarding real information (every event before the landmark, and any exposure switching after it in the simplest version), which is why it is a deliberate, disclosed design choice rather than a free fix.

A worked example: naive analysis vs. landmark analysis

The numbers below come from a simulated cohort, not real patient data, generated so every figure is independently reproducible: 20,000 simulated subjects, each given a true event (death) time drawn from an exponential distribution with an identical hazard for every subject (0.0020/day) — meaning the simulated drug has, by construction, zero true effect on survival — and a separate, independent time-to-drug-initiation drawn from an exponential distribution with hazard 0.0100/day, capped at a 730-day (2-year) administrative end of follow-up. Because the true hazard is identical for everyone, the honest answer for any correctly specified comparison is a hazard ratio of 1.00.

Naive “ever-treated” analysis (the immortal-time-bias setup: a subject who ever received the drug within follow-up is credited as exposed for their entire follow-up period, from cohort entry):

Group	Deaths	Person-days	Death rate per 1,000 person-days
Ever treated (naive)	11,931	7,425,197	1.61
Never treated	3,375	281,313	12.00

Naive hazard ratio (ever-treated vs. never-treated): 0.134 — on its face, an apparent 87% reduction in mortality. The true effect is zero. The entire apparent benefit is immortal time: subjects only make it into the “ever treated” group by first surviving long enough to receive the drug, and that guaranteed survival gets counted as drug-attributable time.

Landmark analysis at day 90: restrict to the 16,646 subjects still alive at day 90 (3,354 died before the landmark and are excluded), classify each as exposed or unexposed based on whether they had started the drug by day 90, and count events and person-time starting from day 90:

Group (status at day 90)	Deaths	Person-days (from landmark)	Death rate per 1,000 person-days
Exposed at landmark	7,109	3,628,380	1.96
Unexposed at landmark	4,843	2,435,876	1.99

Landmark hazard ratio: 0.985 — correctly close to the true null of 1.00, and correctly nowhere near the naive analysis’s spurious 87% apparent benefit. The gap between 0.134 and 0.985 is the entire size of the artifact the naive design manufactured; the landmark analysis did not shrink a real effect, it removed a fabricated one. (Simulation parameters and the deterministic-seed generator used to produce every number above are stated in full so the result can be independently re-run.)

Choosing the landmark time

The landmark date is a real analytic decision with a real trade-off, not an arbitrary cutoff:

Too early, and most subjects who would eventually be exposed have not started treatment yet at the landmark — the “exposed” group at that point is small, underpowered, and may not represent the population of interest.
Too late, and real early events get discarded along with the bias — every death before the landmark is excluded from the analysis entirely, which both loses statistical power and can distort the estimate if early events are not occurring at random with respect to eventual exposure.

The standard mitigation, described in Urania Dafni’s widely cited methodological review of the technique, is to pre-specify a landmark time based on clinical or substantive reasoning (a known typical time-to-treatment window, a protocol-defined visit) and then run the same analysis across a small set of alternative landmark times as a sensitivity analysis — if the qualitative conclusion holds across a reasonable range, the specific landmark choice is not driving the result. Choosing the landmark after looking at where the data make the effect look strongest is a form of the same data-dependent-decision problem immortal time bias itself illustrates, and should be disclosed if it happens.

What landmark analysis costs you

Landmark analysis is not a strictly-better replacement for a correctly specified time-varying exposure model — it is a simpler, more transparent alternative with real limitations:

Discarded early events. Every death, dropout, or other early departure before the landmark is excluded, not analyzed — a real loss of information and statistical power, and one that can bias the estimate if early attrition correlates with the exposure being studied.
A single snapshot of exposure. The simplest version of the method (used above) freezes exposure status at the landmark and ignores later switching — a subject who starts the drug on day 200 is analyzed as “unexposed” for the whole post-landmark period. Extensions exist (repeated/“super” landmarking at multiple time points, or combining a landmark restriction with a time-varying Cox model after the landmark) but add back some of the complexity landmarking was meant to avoid.
The answer is conditional. A landmark analysis answers “among those who survived to day X, does exposure status at day X predict the outcome?” — a real, well-posed question, but a narrower one than “does starting this drug at any point improve survival from cohort entry,” and the two should not be presented as interchangeable.

Landmark analysis vs. a time-varying Cox model

Both are legitimate corrections for immortal time bias and both appear routinely in the pharmacoepidemiology and oncology literature; they are not competing claims about what the truth is, they are different ways of asking the question. A time-varying Cox model uses every subject’s full follow-up and lets exposure status change over time within the model itself, which preserves statistical power and answers the whole-cohort question — at the cost of requiring the dataset restructured into start-stop intervals and the proportional-hazards assumption checked. Landmark analysis trades some of that power and scope for a design that is easier to explain, easier to audit, and does not depend on a modeling assumption holding across the full follow-up period. A well-designed study sometimes reports both as a form of internal replication: if the time-varying model and a landmark sensitivity analysis agree, that materially strengthens confidence in the result reported for the hazard ratio.

Reporting a landmark analysis

State, explicitly, in the methods section: the landmark time and the reasoning behind it, how many subjects were excluded for not surviving to the landmark, exactly how exposure was defined at the landmark (a single snapshot, or something more elaborate), and the range of alternative landmark times tested in sensitivity analysis. A landmark analysis that reports only the single chosen cutoff, with no sensitivity range and no accounting of how many early events were dropped, does not give a reader enough information to judge whether the landmark choice is doing quiet work on the result.

Frequently asked questions

Is landmark analysis the same thing as immortal time bias?

No — immortal time bias is the problem (a design flaw that manufactures a spurious protective effect); landmark analysis is one specific fix for it. See immortal time bias for the mechanism.

How do you choose a landmark time?

Pre-specify it based on clinical or substantive reasoning (a typical treatment-initiation window, a protocol-defined visit), then test a small range of alternative landmark times as a sensitivity analysis rather than relying on a single cutoff chosen after seeing the data.

Does landmark analysis discard real data?

Yes, deliberately. Every subject who did not survive to the landmark is excluded from that analysis. This is the trade-off that removes the bias, not a side effect to be minimized away — it should be reported, including how many subjects were excluded.

Is landmark analysis better than a time-varying Cox model?

Neither is categorically better — they answer slightly different questions and make different assumptions. A time-varying model uses full follow-up and preserves power but requires start-stop data restructuring and a proportional-hazards check; a landmark analysis is simpler and easier to audit but answers a narrower, conditional question and discards pre-landmark events. Some studies report both.

Where does the landmark method come from?

The approach traces to Anderson, Cain, and Gelber’s 1983 paper on analyzing survival by tumor response in Journal of Clinical Oncology, and was formalized as a general methodological tool in later reviews, notably Dafni’s 2011 tutorial in Circulation: Cardiovascular Quality and Outcomes.

Landmark Analysis: The Practical Fix for Immortal Time Bias