Concept Architecture
Concept
Theoretically, Progression-Free Survival (PFS) is a time-to-event endpoint measuring the duration from a predefined starting point, typically randomisation or treatment initiation, until objective disease progression or death from any cause, whichever occurs first. It is founded on survival analysis and censoring theory and is widely used in oncology to evaluate treatment efficacy before mature overall survival data become available. The concept exists to quantify the length of time during which patients remain alive without evidence of disease progression.
Mathematically, Progression-Free Survival is represented as a censored survival variable in which progression or death constitutes an event. Patients without progression or death by the analysis cut-off are right censored at their last adequate disease assessment. Survival probabilities are estimated using Kaplan-Meier methods or parametric survival models, while treatment comparisons commonly employ hazard ratios estimated from Cox proportional hazards regression.
In practice, Progression-Free Survival is calculated from the date of randomisation or treatment initiation until the earliest occurrence of objective disease progression, defined using criteria such as RECIST, or death from any cause. PFS is routinely reported in oncology clinical trials and forms a major input into health technology assessments. In health economics, PFS determines the duration of progression-free health states, influencing estimates of quality-adjusted life years, treatment costs, healthcare utilisation and incremental cost-effectiveness.
Purpose
Used to quantify the duration of survival without disease progression, supporting evaluation of oncology treatments and informing health economic models of treatment benefit.
Mathematical Formulae
Primary Formula
PFS = Tmin(progression, death) ? Tstart
where Tstart is the predefined origin of follow-up.
Supporting Formulae
Kaplan-Meier survival estimate:
?(t) = ?(1 ? d? / n?)
Hazard ratio:
HR = h?(t) / h?(t)
Hazard function:
h(t) = f(t) / S(t)
Restricted mean progression-free survival:
RMPFS = ??^� S(t) dt
Related Mathematical Methods
- Kaplan-Meier Estimation
- Cox Proportional Hazards Model
- Parametric Survival Modelling
- Log-Rank Test
- Restricted Mean Survival Time
- Survival Analysis
- Censoring
Example
A patient is randomised into an oncology trial on 1 January 2025.
Radiological disease progression is confirmed on 1 October 2026.
Progression-Free Survival:
PFS = 21 months
If another patient remains alive without progression at the data cut-off after 24 months, the observation is right censored at 24 months.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| DATEDIF | =DATEDIF(StartDate,EventDate,"m") | Calculates progression-free survival time in months. |
| MIN | =MIN(ProgressionDate,DeathDate) | Determines the first qualifying event. |
| IF | =IF(EventDate="",DATEDIF(StartDate,CutoffDate,"d"),DATEDIF(StartDate,EventDate,"d")) | Calculates survival time while accounting for censored observations. |
| COUNTIFS | =COUNTIFS(EventTypeRange,"Progression")+COUNTIFS(EventTypeRange,"Death") | Counts progression-free survival events. |
| MEDIAN | =MEDIAN(PFSRange) | Calculates observed median progression-free survival where complete observations are available. |
VBA (Optional)
VBA can automate calculation of progression-free survival times, identify censored observations and prepare datasets for Kaplan-Meier and Cox regression analyses.
Sources
- Kaplan EL, Meier P. Nonparametric estimation from incomplete observations.
- Cox DR. Regression Models and Life-Tables.
- Eisenhauer EA, Therasse P, Bogaerts J, et al. New response evaluation criteria in solid tumours: Revised RECIST guideline (version 1.1). European Journal of Cancer. 2009.
- Collett D. Modelling Survival Data in Medical Research.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Library
Publications
1
A Systematic Review of the Effectiveness of Adalimumab, Etanercept and Infliximab for the Treatment of Rheumatoid Arthritis in Adults and an Economic Evaluation of Their Cost-Effectiveness — Chen, Jobanputra, Barton, Jowett, Bryan, Clark, Fry-Smith & Burls, Vol. 10, No. 42 ed., 2006 (Health Technology Assessment (NIHR))
A landmark NIHR HTA monograph systematically reviewing the clinical effectiveness and modelling the cost-effectiveness of anti-TNF biologics (adalimumab, etanercept, infliximab) for rheumatoid arthritis using the Birmingham Rheumatoid Arthritis Model, an exemplar of HTA-body economic evaluation in a musculoskeletal disease.
Frequently Asked Questions (6)
What is progression-free survival?
A time-to-event measure defined as the time from treatment start until either disease progression or death from any cause, whichever occurs first.
Source: Latimer 2013
What two events end the progression-free survival clock?
Progression-free survival measures the time from the start of treatment until either the cancer progresses or the patient dies, whichever comes first, so those two events end its clock. It reflects how long a treatment keeps the disease from advancing, capturing benefit that can be seen sooner than overall survival, which must wait for deaths. This makes it a common trial endpoint, though a longer time free of progression does not always translate into living longer. Time until the cancer grows or the patient dies is what it captures. Latimer (2013) describes this measure.
Source: Latimer 2013
How is progression-free survival measured?
Progression-free survival is measured as the time from treatment start until the first of either disease progression or death from any cause, capturing the period without progression. So progression-free survival is measured to the first of progression or death, which is why it combines these events, since it ends when either the disease progresses or the patient dies, and measuring from treatment start until whichever occurs first gives the progression-free survival, reflecting how long the patient lives without the cancer advancing, and ending the measure at progression or death.
Source: Latimer 2013
Why is progression-free survival used?
Progression-free survival is used because it captures how long the disease is controlled without progressing, providing a measure of benefit that can be assessed sooner than overall survival, which may require long follow-up. So progression-free survival is used to measure disease control, which is why it is a common endpoint, since it reflects the period the treatment keeps the cancer from advancing and can be measured earlier than overall survival, and using progression-free survival allows a treatment's effect on delaying progression to be assessed, offering a measure of benefit that captures disease control and can be available before survival data mature.
Source: Latimer 2013
How does progression-free survival differ from overall survival?
Progression-free survival differs from overall survival in that it measures the time until disease progression or death, whichever comes first, while overall survival measures the time until death from any cause. So progression-free survival and overall survival differ in their endpoint, which is why they capture different benefits, since progression-free survival reflects how long the cancer is controlled and overall survival reflects how long the patient lives, and while overall survival is a definitive measure of survival, progression-free survival captures the period of disease control, ending at progression as well as death.
Source: Latimer 2013
What does progression-free survival reflect?
Progression-free survival reflects how long a treatment keeps the cancer from progressing, capturing the period of disease control before the disease advances or the patient dies. So progression-free survival reflects the duration of disease control, which is why it is valued, since it shows how long the treatment holds the cancer in check, and measuring the time without progression captures the benefit of delaying the disease's advance, making progression-free survival a measure of how effectively and for how long a treatment controls the cancer before it progresses.
Source: Latimer 2013
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 15 May 2026
Content version: 1.0.0
Canonical Identity
- Term code
- HE-PE-OO-018
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