TSD 21 – Flexible Methods for Survival Analysis – November 2020
Appendices to Technical Support Document
A.1 Stata code to generate simulation study data; A.2 Stata code used to undertake analyses; A.3 Stata code to calculate marginal expected survival and hazard
A4. Simulation study results
Survival analysis modelling approaches are often required to capture the survival functions seen in clinical trial data and to further extrapolate to estimate lifetime benefits in economic evaluations. Often complex hazard function shapes can arise both within and beyond the trial period, meaning that increasingly sophisticated survival models are required and are being applied in NICE Technology Appraisals (TAs), going beyond standard parametric survival models.
The objective of this Technical Support Document (TSD) is to describe a variety of survival modelling approaches that have been, and can be, used, when hazard functions are complex. Flexible parametric survival methods incorporating splines or fractional polynomials, models that enforce cure proportions, and more general mixture models have been applied in NICE TAs in the presence of complexity of observed hazard functions. Further approaches that have been used in practice take a conditional approach to dealing with the issue of complex hazard functions, namely piecewise modelling approaches and landmarking on a point of treatment response.
We present the motivation behind each approach, their details with respect to formulae and assumptions, and their limitations, all from the perspective of applying them to observed trial data. We further provide specific recommendations for consideration for each of the considered complex approaches; both in their fitting to observed data and the consideration of how to evaluate extrapolated survival functions.
We apply each of the survival modelling approaches to complex simulated survival data; simulating from scenarios with turning points in the true hazard functions driven by competing risks of both disease-specific and other-cause mortality. We evaluate each of the described approaches in capturing the true survival functions both within the range of follow-up and extrapolated to a lifetime horizon. We discuss when, and why, both the simple and complex approaches fail, and further when the incorporation of external data may improve long-term extrapolation. We also provide illustrative examples of some of the issues highlighted in the simulation study and discuss implications for practice.