Concept Architecture
Concept
Theoretically, Landmark Analysis is a survival analysis technique used to evaluate the association between a time-dependent variable and subsequent survival by conditioning the analysis on survival to a predefined landmark time. It was developed to reduce guarantee-time bias and immortal time bias that arise when time-dependent covariates are analysed using conventional methods. In health economics, landmark analysis is used to estimate treatment effects and prognostic relationships that inform survival models and economic evaluations.
Mathematically, landmark analysis restricts the study population to individuals who remain event-free at a specified landmark time. Survival analysis then begins at the landmark, with prognostic factors or treatment status defined according to information available at that time. Standard survival methods, including Kaplan-Meier estimation and Cox proportional hazards modelling, are subsequently applied to the restricted cohort.
In practice, investigators select a clinically meaningful landmark time before analysis, such as six or twelve months after treatment initiation. Patients experiencing the event before the landmark are excluded, while surviving patients are classified according to their status at the landmark. The resulting estimates are used to evaluate prognosis, compare treatment groups and improve long-term survival modelling for health economic analyses.
Purpose
Used to evaluate the effect of time-dependent variables while reducing guarantee-time bias and immortal time bias, supporting unbiased survival estimation and health economic evaluation.
Mathematical Formulae
Primary Formula
For t � t?:
S(t | T � t?)
where:
- t? = landmark time
- T = event time
- S(t | T � t?) = conditional survival probability after surviving to the landmark
Supporting Formulae
Cox model after the landmark:
h(t | x) = h?(t)exp(x??),?t � t?
Model parameters are estimated using:
?? = arg max L(?)
Related Mathematical Methods
- Kaplan-Meier estimator
- Cox proportional hazards model
- Time-dependent covariate analysis
- Survival analysis
- Maximum likelihood estimation
- Joint modelling
Example
An oncology trial investigates whether tumour response at six months predicts long-term survival. A landmark analysis is performed using six months as the landmark time. Patients who died before six months are excluded, while surviving patients are classified as responders or non-responders. Kaplan-Meier curves and a Cox proportional hazards model are then used to compare subsequent survival, providing estimates for long-term cost-effectiveness modelling.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =IF(A2>=180,1,0) | Identify patients eligible for the landmark analysis. |
| FILTER | =FILTER(DataRange,LandmarkFlag=1) | Create the landmark cohort for subsequent survival analysis. |
| COUNTIFS | =COUNTIFS(TimeRange,">="&LandmarkTime) | Count patients remaining at risk at the landmark time. |
| IF | =IF(Response="Yes",1,0) | Classify patients according to landmark treatment or response status. |
VBA (Optional)
Automate selection of landmark cohorts, perform repeated landmark analyses at predefined time points and generate comparative survival summaries.
Sources
- Anderson JR, Cain KC, Gelber RD. Analysis of Survival by Tumour Response and Other Comparisons of Time-to-Event by Outcome Variables.
- Dafni U. Landmark analysis at the 25-year landmark point.
- Klein JP, Moeschberger ML. Survival Analysis: Techniques for Censored and Truncated Data.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- NICE. Health Technology Evaluation Manual.
Related Concepts (3)
Library
Tools & Resources
1
survHE — Survival Analysis for Health Economic Evaluation (R package) — Gianluca Baio, R package ed., 2023 (CRAN)
An R package for fitting and comparing parametric survival models for health economic evaluation, including Bayesian estimation, and for extrapolating time-to-event data to inform cost-effectiveness models.
Software (R package)View source →
Frequently Asked Questions (6)
What is landmark analysis?
A survival technique restricting analysis to patients event-free up to a predefined time point, then examining survival from that point forward.
Source: Anderson, Cain & Gelber 1983
How does landmark analysis handle a response that develops over time?
When the effect being studied is a response that can only be assessed after some time, comparing responders with non-responders from the start of follow-up is unfair, because a patient must survive long enough to be classed a responder at all. Landmark analysis fixes a later time point, keeps only patients still event-free then, classifies them by their status at that point, and measures survival from there. This puts all patients on an equal footing at the landmark. It removes the built-in advantage of the responder group. Dafni (2011) describes this method.
Source: Dafni 2011
Why is landmark analysis used?
Landmark analysis is used to avoid immortal time bias, which arises when patients are classified by a characteristic, such as responding to treatment, that can only be determined after they have survived some period, so that responders necessarily lived long enough to respond. Comparing groups from the start would bias in favour of responders. By restricting to patients event-free at a landmark and comparing survival thereafter, landmark analysis removes this guaranteed early survival, giving a fair comparison of the groups.
Source: Anderson, Cain & Gelber 1983
How does landmark analysis avoid immortal time bias?
Landmark analysis avoids immortal time bias by choosing a fixed landmark time, including only patients still event-free at that time, classifying them by their status as of the landmark, and analysing survival from the landmark onward. This ensures that group membership is determined before the survival being compared, so no group benefits from guaranteed survival up to the landmark. Because the comparison starts after the period in which the classifying event could occur, the bias from immortal time is eliminated.
Source: Kalbfleisch & Prentice 2002
How is the landmark time chosen?
The landmark time is chosen as a point by which the classifying characteristic, such as treatment response, can be determined for most patients, balancing the need to allow the characteristic to be observed against retaining enough patients and follow-up after the landmark. Too early a landmark may misclassify patients whose status is not yet clear, while too late a landmark discards events and reduces the sample. The choice is made in advance and its influence on results may be examined.
Source: Anderson, Cain & Gelber 1983
What are the limitations of landmark analysis?
Landmark analysis discards patients who have the event before the landmark and ignores events before it, reducing the sample and the information used, and its results depend on the landmark time chosen, which is somewhat arbitrary. Classifying patients by their status only at the landmark ignores later changes. It answers a specific question, survival from the landmark among those event-free then, rather than the full survival experience. These limitations mean it is used for particular comparisons where immortal time bias is a concern.
Source: Anderson, Cain & Gelber 1983
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 21 Oct 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/landmark-analysis
- Term code
- HE-EM-SM-042
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