Concept Architecture
Concept
Relapse-Free Survival (RFS) is the length of time from a defined starting point, typically treatment initiation or surgical resection, until disease recurrence or death from any cause, whichever occurs first. It is a recognised time-to-event endpoint widely used in oncology and other chronic disease research to evaluate the durability of treatment benefit following curative-intent therapy. In health economics, relapse-free survival provides an important measure of clinical effectiveness for estimating long-term outcomes and informing cost-effectiveness models.
Mathematically, Relapse-Free Survival is represented by the survival function, which estimates the probability of remaining alive without disease recurrence beyond a specified time. The survival function is estimated using non-parametric methods such as the Kaplan?Meier estimator or modelled using parametric and semi-parametric survival models. Hazard ratios are commonly used to compare relapse-free survival between treatment groups.
In practice, relapse-free survival is measured by prospectively following patients from the defined baseline until documented relapse, death or censoring. Clinical trials estimate relapse-free survival curves, median relapse-free survival and survival probabilities at specified time points. Health economic evaluations use these estimates to populate partitioned survival models, Markov models and survival extrapolations.
Purpose
Used to quantify the duration of survival without disease recurrence, evaluate treatment effectiveness, compare interventions in clinical trials and provide survival inputs for health economic modelling.
Mathematical Formulae
Primary Formula
S(t) = P(T > t)
Supporting Formulae
Kaplan?Meier estimator:
?(t) = ?(1 ? d? / n?)
Hazard Ratio:
HR = h?(t) / h?(t)
Related Mathematical Methods
- Kaplan?Meier estimation
- Cox proportional hazards model
- Log-rank test
- Parametric survival modelling
- Restricted Mean Survival Time
- Partitioned survival modelling
Example
A clinical trial follows 500 patients after curative surgery for colorectal cancer. After three years, the Kaplan?Meier estimate of relapse-free survival is 0.78, indicating that 78% of patients remain alive without documented disease recurrence. This survival curve is subsequently extrapolated for use in a cost-effectiveness model comparing alternative adjuvant therapies.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =IF(OR(C2="Relapse",C2="Death"),1,0) | Creates the event indicator for survival analysis. |
| MIN | =MIN(RelapseDate,DeathDate,CensorDate)-StartDate | Calculates observed relapse-free survival time. |
| MEDIAN | =MEDIAN(B2:B501) | Summarises observed relapse-free survival times. |
| COUNTIFS | =COUNTIFS(C:C,"Censored") | Counts censored observations for reporting. |
VBA (Optional)
Automate calculation of relapse-free survival summaries and preparation of survival datasets for statistical analysis and health economic modelling.
Sources
- Kaplan EL, Meier P. Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association. 1958.
- Cox DR. Regression Models and Life-Tables. Journal of the Royal Statistical Society Series B. 1972.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
1
Economic Evaluation in Clinical Trials — Glick, Doshi, Sonnad & Polsky, 2nd Edition ed., 2015 (Oxford University Press)
Practical guidance on conducting cost-effectiveness analyses alongside controlled trials, covering trial design, measurement of costs and quality-adjusted life years, handling censored and missing data, and reporting stochastic uncertainty. Volume 4 in the Handbooks in Health Economic Evaluation series.
BookView source →
Frequently Asked Questions (6)
What is relapse-free survival?
A time-to-event measure defined as the time from treatment completion until disease recurrence or death, used for curative-intent treatments.
Source: Latimer 2013
What does relapse-free survival measure after curative treatment?
For a treatment given with the aim of cure, relapse-free survival measures the time from completing treatment until the disease returns or the patient dies, whichever comes first. It captures how long patients stay both alive and free of their disease, which is the goal of curative therapy, and it can register a treatment's benefit earlier than overall survival, since relapse usually precedes death. Its meaning depends on how relapse is defined and detected. It tracks durable freedom from disease. Fleming and DeMets (1996) discuss such endpoints.
Source: Fleming & DeMets 1996
How is relapse-free survival measured?
Relapse-free survival is measured from a defined starting point, typically the completion of curative-intent treatment, until the first occurrence of disease recurrence or death, with patients who remain relapse-free and alive at the end of follow-up censored at their last assessment. Survival analysis methods, such as the Kaplan-Meier estimator, are used to estimate it, handling censoring appropriately. Regular follow-up to detect recurrence is needed. Because it combines recurrence and death, relapse-free survival captures both events, and its measurement depends on consistent monitoring for relapse.
Source: Latimer 2013
Why is relapse-free survival used?
Relapse-free survival is used because, for curative-intent treatments, the key question is how long patients remain free of the disease returning, and this measure captures that directly, combining recurrence and death into a single endpoint reached sooner than overall survival. It allows the effectiveness of curative treatment in preventing relapse to be assessed and compared. Because avoiding recurrence is the goal of curative therapy, relapse-free survival is a relevant and meaningful endpoint, though its relationship to overall survival is considered when interpreting it.
Source: FDA 2018
How does relapse-free survival differ from overall survival?
Relapse-free survival measures the time from treatment completion until recurrence or death, capturing how long patients stay free of relapse and alive, while overall survival measures time until death from any cause regardless of recurrence. Relapse-free survival includes recurrence as an event and so occurs earlier, allowing earlier assessment, whereas overall survival is definitive but requires longer follow-up. A treatment may improve relapse-free survival without necessarily improving overall survival, so the two provide complementary information, with relapse-free survival focusing on preventing the disease returning.
Source: Latimer 2013
What are the limitations of relapse-free survival?
The limitations of relapse-free survival arise because it combines recurrence and death, which differ in severity, into one endpoint, so a difference may be driven by recurrence without a survival benefit, and detecting recurrence depends on the intensity and consistency of follow-up, which can affect the measure. Its relationship to overall survival must be considered, and definitions of recurrence can vary. These limitations mean relapse-free survival is defined clearly with consistent monitoring and interpreted alongside overall survival and the clinical importance of avoiding recurrence.
Source: Latimer 2013
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 10 Nov 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-ES-CO-064
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