Parametric survival distributions
EasyHTA fits parametric survival models using maximum likelihood estimation via the flexsurv package (Jackson, 2016). Seven distributions are supported: all six recommended by NICE DSU Technical Support Document 14 (Latimer, 2011), plus the gamma. For the reconstruction step that precedes model fitting, see The Guyot algorithm.
Supported distributions
| Distribution | Parameters | Hazard shape | Typical use in HTA |
|---|---|---|---|
| Exponential | rate | Constant | Useful as a baseline or sensitivity model; appropriate when a constant hazard is plausible. |
| Weibull | shape, scale | Monotone increasing, monotone decreasing, or constant (exponential as a special case) | Commonly used and frequently selected in oncology HTA; simple and supports monotone hazards. |
| Log-normal | meanlog, sdlog | Unimodal: initial increase followed by later decline | Appropriate when a unimodal hazard is plausible (early rise, later decline). |
| Log-logistic | shape, scale | Decreasing if shape ≤ 1; unimodal if shape > 1 | Heavier tails than log-normal, so long-tail behaviour must be justified. |
| Gompertz | shape, rate | Monotone increasing, monotone decreasing, or constant (shape > 0, < 0, or = 0) | Can represent exponentially changing hazards; background mortality should be assessed or incorporated separately rather than implicitly absorbed. |
| Gamma | shape, rate | Monotone increasing if shape > 1, monotone decreasing if shape < 1, constant if shape = 1 (exponential as a special case); tends to a constant hazard in the tail | Less commonly selected in HTA than the Weibull, and its asymptotically constant hazard should be justified against the plausible long-term hazard. Nested within the generalised gamma. |
| Generalised gamma | mu, sigma, Q | Flexible; nests Weibull, gamma, and log-normal as special cases | Useful flexible reference model; nested special cases can be compared via constrained likelihood comparisons where statistically valid. |
Model selection
EasyHTA computes AIC and BIC for all fitted models. Lower values indicate better fit relative to model complexity. AIC and BIC are internal fit diagnostics against the observed data only; they do not validate the plausibility of the extrapolated tail. Model choice should also weigh hazard plausibility, external evidence, and uncertainty in the extrapolated period.
Parameter estimation
All models are fitted by maximum likelihood estimation. The full variance–covariance matrix is included in the Excel export, supporting propagation of correlated parameter uncertainty in downstream probabilistic sensitivity analyses (PSA), provided the parameter scale (flexsurv estimates positive parameters on the log scale), ordering, and any back-transformations are handled correctly by the receiving model.
TSD14 alignment
- All six standard distributions recommended in TSD14 are available, alongside the gamma
- Model comparison outputs include log-likelihood, AIC, and BIC
- Visual inspection overlays (fitted curves vs the reconstructed KM) are shown in the model-fitting results views
- The variance–covariance matrix is exported for PSA use
- Analysis metadata (run date, reconstruction method) is recorded in the
Metadatasheet of the Excel export - For complex hazards, non-proportional hazards, cure assumptions, or situations where background mortality materially affects extrapolation, analysts should also consider methods discussed in NICE DSU TSD21 alongside TSD14
References
Guyot P, Ades AE, Ouwens MJNM, Welton NJ (2012). Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan–Meier survival curves. BMC Medical Research Methodology, 12, 9. doi:10.1186/1471-2288-12-9
Jackson C (2016). flexsurv: A Platform for Parametric Survival Modeling in R. Journal of Statistical Software, 70(8), 1–33. doi:10.18637/jss.v070.i08
Latimer NR (2011, last updated 2013). NICE DSU Technical Support Document 14: Undertaking survival analysis for economic evaluations alongside clinical trials, extrapolation with patient-level data. Sheffield: NICE DSU. sheffield.ac.uk/nice-dsu
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