Clinical trials are typically of (relatively) short duration, but innovative treatments may impact patient survival over multiple years. Health economists and outcomes researchers often are faced with the challenge of extrapolating clinical trial survival curves to estimate long-term survival gains for the typical patient. These estimates may be done parameterically (e.g., exponential, Weibull, Gompertz, log-logistic, gamma, piecewise), using expert elicitation, or other methods. But a key question is how do researchers justify this choice?
A paper by Lattimer (2013) provides options for justifying extrapolation choice. The first option is visual inspection. This approach just visually checking whether the model fits the data well. While this is a useful first step, it clearly is not a statistically-based approach. Statistical tests can help formalize model fit. Akaike information criterion (AIC) and Bayesian information criterion (BIC) are commonly used statistical tests that measure model fit, traded off against model complexity [see this video comparing AIC and BIC]. Log-cumulative hazard plots are useful for determining which parametric models are compatible with the observed hazard ratios as well as validating whether the proportional hazards assumption is valid. To determine the suitability of accelerated failure time models–such as lognormal or log-logistic models–quantile-quantile plots can be used (see Bradburn et al. 2003). External data can also be used to extrapolate survival curves. For instance, real-world data on survival can be used to extrapolate the control arm and then various hazard assumptions can be applied to the control arm extrapolated curve. Registry data–such as SEER data for US cancer survival estimates–is often used. Clinical validity is also an important input. One can ask for clinical experts to weigh in on the best models either informally through interviews or more formally via a Delphi Panel or SHeffield ELicitation Framework (SHELF).
Lattimer recommends using the more standard approaches (e.g., exponential, Gompertz, Weibull, log-logitic, lognormal) first and then only moving to more complex models (e.g., generalized gamma, piecewise, cure models) if the model four approaches described above justify the need for the more complex modelling. Also, researchers should formally document how the combination of visual inspection, statistical tests, external data and clinical input were used to inform the preferred extrapolation specification used in any health economic evaluation.
- Latimer NR. Survival analysis for economic evaluations alongside clinical trials—extrapolation with patient-level data: inconsistencies, limitations, and a practical guide. Medical Decision Making. 2013 Aug;33(6):743-54.
- Bradburn MJ, Clark TG, Love SB, Altman DG. Survival analysis part III: multivariate data analysis—choosing a model and assessing its adequacy and fit. Br J Cancer. 2003;89(4):605–11. 38. Liverpool Reviews and Implementation Group. Pemet
- SHELF: the Sheffield Elicitation Framework (version 3.0). School of Mathematics and Statistics, University of Sheffield, UK [http://tonyohagan.co.uk/shelf]. Accessed 1 Apr 2017.