Survival modelling for HTA
A cost-effectiveness model is only as defensible as the survival curves under it. We help you choose, fit and justify the survival model behind a health technology assessment. That covers the extrapolation beyond the trial, cure and relative-survival models, the uncertainty the economic model needs, and the answers when a reviewer pushes back.
Built by the people who wrote the methods and the software. One of us co-authored NICE DSU TSD 21, and the merlin family is our own work.
What a reviewer will test
A trial follows patients for a few years, and a cost-effectiveness model needs their whole lifetime. Mean survival is the area under the whole curve, so when the curve has not reached zero by the end of follow-up, much of that area lies beyond the data. Models that fit the trial equally well can imply very different lifetimes, and the choice can move the result more than any other assumption in the analysis.
Is the tail plausible?
An extrapolated hazard that falls below the general population's has patients dying more slowly than their peers. Modelling the excess hazard on top of general-population mortality, as relative survival does, keeps it realistic.
Cure, or no cure?
A plateau is an assumption that the data can support only with long follow-up. A cure model and a standard model that fit the trial alike can extrapolate to very different lifetimes.
How the treatment effect carries on
A hazard ratio that is constant for ever is itself an assumption. Whether to model each arm separately, and what happens if the effect wanes, are choices to state and to test.
How uncertain is it?
The uncertainty in the survival model belongs in the probabilistic sensitivity analysis of the cost-effectiveness model, beside the uncertainty about which model is right.
From a second opinion to the whole analysis
Most engagements are one of these, or a few of them together.
Review an extrapolation
A methods review of the survival modelling in a draft submission: the candidate models, how they were compared, what each implies beyond follow-up, and whether the choice is justified. Right when you want a second opinion before it goes to the agency.
Fit and compare the candidates
Standard parametric, flexible parametric (Royston–Parmar), cure and relative-survival models, fitted in the merlin family and compared on fit and on what each implies beyond the data. Where only a publication is available, our Kaplan–Meier reconstruction tool rebuilds patient-level data from the published curve.
Multi-state and partitioned survival
Survival and multi-state structures for the economic model, with the transition hazards estimated in one coherent framework. Try the partitioned survival explorer.
Uncertainty for the economic model
Parameter uncertainty carried through to the probabilistic sensitivity analysis, and the structural uncertainty of the model choice shown as scenarios.
Answering reviewers
The written justification of the model choice, and the sensitivity and scenario analyses a reviewer asks for, prepared with the people who built the models.
Teaching your team
The models taught hands-on, in our flexible parametric survival analysis course or as bespoke in-house training.
The people who wrote the methods and the software
The expertise behind this work is published and open to inspection.
NICE DSU TSD 21
One of us co-authored the NICE Decision Support Unit's technical support document on flexible methods for survival analysis, which covers flexible models for survival beyond the standard parametric ones, including cure models.
The merlin family
merlin fits the flexible parametric, cure and relative-survival models. pendragon, in development, builds multi-state cost-effectiveness models on top of them, and morgana adds Bayesian uncertainty. The family is our own work.
Published methods
Papers our team has co-authored include a framework for estimating quality-adjusted life-years with joint models, natural history modelling for Duchenne muscular dystrophy and its effect on cost-effectiveness decisions, and adjusting survival estimates for treatment switching.
Selected publications
- Rutherford MJ, Lambert PC, Sweeting MJ, Pennington B, Crowther MJ, Abrams KR, Latimer NR. NICE DSU Technical Support Document 21: flexible methods for survival analysis. NICE Decision Support Unit, 2020. doi:10.15131/shef.data.33849118
- Crowther MJ, Gasparini A, Ekberg S, Felizzi F, Gallagher E, Paracha N. A framework for the estimation of quality-adjusted life-years using joint models of longitudinal and survival data. Medical Decision Making, 2026. doi:10.1177/0272989x261477224
- Broomfield J, Abrams KR, Crowther MJ, Guglieri M, Latimer NR, Rutherford MJ. Evaluating the impact of different natural history modeling methods on cost-effectiveness decisions: a case study in Duchenne muscular dystrophy. MDM Policy & Practice, 2026. doi:10.1177/23814683261447231
- Latimer NR, Abrams KR, Lambert PC, Crowther MJ, Wailoo AJ, Morden JP, Akehurst RL, Campbell MJ. Adjusting survival time estimates to account for treatment switching in randomised controlled trials – an economic evaluation context. Medical Decision Making, 2014. doi:10.1177/0272989x13520192
Engagements that fit the problem
Expert advisory
Hours to days. A focused conversation or short review: a second opinion on an extrapolation, a sanity check on an approach, or direction before you commit to an analysis.
Project engagement
Weeks to months. Scoped to a defined deliverable, such as the survival modelling for a submission, with a named expert team, an agreed scope and milestones, and reproducible code and documentation.
Ongoing support
Continuous access across several submissions a year, where the relationship compounds.
The method, in the open
Primers, worked examples and tools on the problems above. Nothing needs an account.
What are cure models?
What a cure model is, mixture and non-mixture models, a worked example of how a cure model and a Weibull extrapolate, and what a plateau does not prove.
What is relative survival?
What relative survival and net survival measure, how life tables give the expected survival, the main estimators, and when to use them.
Relative survival analysis
How excess mortality is estimated against general-population life tables, and a worked analysis with code.
Probabilistic sensitivity analysis and survival models
Implementing probabilistic sensitivity analysis in survival-analysis contexts, with code — relevant for health-economic modelling.
Reconstruct & extrapolate a KM curve
Turn a published Kaplan–Meier curve back into patient data, then extrapolate it out to a lifetime horizon.
Partitioned survival analysis explorer
Progression-free and overall survival in; state occupancy, QALYs, ICER and a cost-effectiveness plane out, including the curve-crossing pitfall.