Concept Architecture
Concept
Theoretically, the Partitioned Survival Model is a state-transition modelling framework that estimates the proportion of patients occupying mutually exclusive health states directly from survival curves. It is founded on partitioned survival analysis and survival modelling rather than transition probability estimation. The model exists to evaluate disease progression and treatment outcomes when overall survival and progression-free survival data are available, making it particularly suited to oncology and other chronic diseases.
Mathematically, the model partitions the patient population into health states using survival functions. Overall survival defines the proportion of patients who remain alive, progression-free survival defines the proportion who remain alive without disease progression, and the proportion in the progressed disease state is obtained as the difference between the two survival functions. Long-term outcomes are generated by integrating state occupancy over time.
In practice, partitioned survival models are implemented by fitting parametric survival models to observed overall survival and progression-free survival data, extrapolating these curves over the required time horizon and calculating state occupancy at each model cycle. Costs, utilities and adverse events are then assigned to each health state to estimate lifetime costs, quality-adjusted life-years and incremental cost-effectiveness. Partitioned survival models are widely used in health technology assessment, particularly for oncology interventions.
Purpose
Used to estimate health-state occupancy directly from survival curves, supporting cost-effectiveness analysis when progression-free and overall survival data are available.
Mathematical Formulae
Primary Formula
Progressed Disease(t) = OS(t) ? PFS(t)
where:
OS(t) = overall survival function
PFS(t) = progression-free survival function
Supporting Formulae
Progression-Free(t) = PFS(t)
Dead(t) = 1 ? OS(t)
QALYs = ??? ? U? ? P?(t) dt
Costs = ??? ? C? ? P?(t) dt
where:
U? = utility associated with health state i
C? = cost associated with health state i
P?(t) = proportion of patients in health state i at time t
T = time horizon
Related Mathematical Methods
- Parametric Survival Model
- Kaplan-Meier Estimator
- Partitioned Survival Analysis
- Area Under the Curve Approach
- Quality-Adjusted Life-Year (QALY)
- Maximum Likelihood Estimation
- Incremental Cost-Effectiveness Ratio (ICER)
Example
An oncology model evaluates a new immunotherapy using three health states: progression-free, progressed disease and death. At 24 months:
PFS(24) = 0.46
OS(24) = 0.68
The proportion of patients in the progressed disease state is:
Progressed Disease = 0.68 ? 0.46 = 0.22
The proportion of patients who have died is:
Dead = 1 ? 0.68 = 0.32
These state occupancies are multiplied by state-specific costs and utilities to calculate lifetime costs and QALYs.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =B2-C2 | Calculate the proportion of patients in the progressed disease state. |
| SUMPRODUCT | =SUMPRODUCT(B2:D2,$H$2:$H$4) | Calculate expected costs or utilities across health states. |
| EXP | =EXP(-((A2/$B$1)^$B$2)) | Generate extrapolated survival probabilities from fitted survival models. |
| SUM | =SUM(E2:E241) | Calculate total discounted costs or QALYs over the model horizon. |
VBA (Optional)
Automate partitioned survival calculations, survival extrapolation and generation of lifetime cost-effectiveness results across multiple treatment strategies.
Sources
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- Hoyle MW, Henley W. Improved Curve Fits to Summary Survival Data: Application to Economic Evaluation of Health Technologies. BMC Medical Research Methodology. 2011.
- Latimer NR. Survival Analysis for Economic Evaluations Alongside Clinical Trials: Extrapolation with Patient-Level Data. Medical Decision Making. 2013.
- NICE. Health Technology Evaluation Manual.
- ISPOR-SMDM Modeling Good Research Practices Task Force Reports.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes.
Related Concepts (4)
Library
Publications
1
NICE DSU Technical Support Document 19: Partitioned survival analysis as a decision modelling tool — Woods, Sideris, Palmer, Latimer & Soares, TSD 19 ed., 2017 (NICE Decision Support Unit (University of Sheffield))
Guidance on the partitioned survival (area-under-the-curve) modelling approach widely used in oncology cost-effectiveness analysis, contrasting it with state-transition models and setting out its assumptions, strengths and limitations.
Media
1
Partitioned Survival Analysis vs Markov Models — Health Economics Explainer — Mtech Access (Hannah Gillies), 2023 (Mtech Access)
An expert explainer video summarising the NICE DSU guidance on partitioned survival analysis versus Markov models — their use in HTA, strengths, limitations and recommendations for cost-effectiveness modelling.
VideoView source →
Tools & Resources
2
hesim — Health Economic Simulation Modeling and Decision Analysis (R package) — Devin Incerti & Jeroen P. Jansen, R package ed., 2024 (CRAN)
A modular, computationally efficient R package for building and analysing health economic simulation models — cohort state-transition, partitioned survival, and individual-level continuous-time models — with fast individual-patient simulation and PSA via C++.
Software (R package)View source →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 a partitioned survival model?
An oncology modelling technique estimating the proportion of a cohort in each health state using separately fitted survival curves for different endpoints, rather than modelling transitions.
Source: Woods et al. 2020
How does a partitioned survival model use separate survival curves?
A partitioned survival model, common in cancer evaluation, derives the share of patients in each health state directly from separately fitted survival curves rather than from transition probabilities. The proportion alive comes from an overall survival curve, the proportion alive and free of progression from a progression-free curve, and the difference between the two gives the proportion alive with progressed disease. State membership is read off the curves at each time. It does not model movement between states explicitly. Woods and colleagues (2017) describe this structure.
Source: Woods et al. 2017
How does a partitioned survival model work?
A partitioned survival model works by fitting survival curves to endpoints such as overall survival and progression-free survival, then partitioning the cohort into health states using the areas under and between these curves: the progression-free proportion is given by the progression-free survival curve, the dead proportion by one minus overall survival, and the progressed proportion by the difference between overall and progression-free survival. The state proportions over time follow directly from the curves, without modelling transition probabilities between states.
Source: Woods et al. 2020
How does a partitioned survival model differ from a state-transition model?
A partitioned survival model derives state occupancy directly from separately fitted survival curves for endpoints, whereas a state-transition model, such as a Markov model, represents movement between states through transition probabilities. The partitioned approach uses the curves without modelling transitions, making it simple and closely tied to trial endpoints, but it treats the endpoint curves independently. The state-transition approach models the underlying process of moving between states, which can better capture structural relationships but requires estimating transitions.
Source: Woods et al. 2020
What are the advantages of partitioned survival models?
Partitioned survival models are advantageous in oncology because they use the survival endpoints, overall and progression-free survival, that trials commonly report, fitting them directly and requiring fewer assumptions about the disease process than a transition model. They are relatively simple to build and align closely with the trial evidence. This makes them a common and convenient approach for cancer cost-effectiveness analysis, where the relevant endpoints are available and mapping them to states is straightforward.
Source: Woods et al. 2020
What are the limitations of partitioned survival models?
Partitioned survival models fit the endpoint curves independently, so they do not enforce the structural relationships a transition model would, and the separately extrapolated curves can imply implausible state occupancy, such as a progressed proportion that behaves unrealistically, especially in extrapolation. They rely on the endpoint curves and their independent projection, which may not cohere. Because of these concerns, guidance recommends comparing partitioned survival models with state-transition models and scrutinising the plausibility of the extrapolated state proportions.
Source: Woods et al. 2020
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 25 Sep 2026
Content version: 1.0.0
Canonical Identity
- Term code
- HE-EM-SM-063
Stable URI · Machine-readable · Resolvable · CC BY 4.0