Survival analysis TSD
A series of TSDs have been produced in the area of survival analysis.
TSD 14
TSD 14 one page summary (PDF, 102KB)
Related publications
N Latimer (2013) Survival analysis for economic evaluations alongside clinical trials – extrapolation with patient-level data. Inconsistencies, limitations, and a practical guide. Medical Decision Making, 33 (6), pp. 743-754. DOI: https://doi.org/10.1177/0272989x12472398
A Bagust, S Beale (2013) Survival analysis and extrapolation modeling of time-to-event clinical trail data for economic evaluation: an alternative approach. Medical Decision Making, 34(3), pp.343–351. DOI: https://doi.org/10.1177/0272989X13497998
N Latimer (2013) Response to “Survival analysis and extrapolation modeling of time-to-event clinical trial data for economic evaluation: an alternative approach” by Bagust and Beal. Medical Decision Making, 34(3), pp. 279–282. DOI: https://doi.org/10.1177/0272989X13511302
TSD 16
Adjusting survival time estimates in the presence of treatment switching (PDF, 450KB)
TSD 21
Flexible methods for survival analysis (PDF, 5.7MB) – November 2020 - updated version uploaded March 2022
Appendices to technical support document
- A1. Stata code to generate simulation study data
- A2. Stata code used to undertake analyses
- A3. Stata code to calculate marginal expected survival and hazard
- A4. Simulation study results
Zip file for A1, A2, A3 (ZIP, 84KB)
A4. Simulation study results (PDF, 16.5MB)
About
- TSD 14
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A review of methods for undertaking survival analysis for use in an economic evaluation when patient-level data are available and evidence synthesis is not necessary, with recommendations on systematic processes.
- TSD 16
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Treatment switching occurs when patients in the control group of a clinical trial are allowed to switch onto the experimental treatment at some point during follow-up. Switching is common in clinical trials of cancer treatments and can also occur in trials of treatments for other diseases.
When switching occurs, an “intention to treat” (ITT) analysis – whereby the data are analysed according to the arms to which patients were randomised – of the overall survival (OS) advantage associated with the new treatment will be biased: If control group patients switch treatments and benefit from the new treatment the OS advantage of the new treatment will be underestimated.
For interventions that impact upon survival, health technology assessment (HTA) bodies such as the National Institute for Health and Care Excellence (NICE) require that economic evaluations consider a lifetime horizon. This is problematic in the presence of treatment switching, because standard ITT analyses are likely to be inappropriate.
Various statistical methods are available to adjust survival estimates in the presence of treatment switching, but each makes important assumptions and is subject to limitations. “Simple” adjustment methods such as censoring switchers at the point of switch, or excluding them entirely from the analysis, are highly prone to selection bias because switching is likely to be associated with prognosis.
More complex adjustment methods, which are theoretically unbiased given certain assumptions are satisfied, are also available. Rank Preserving Structural Failure Time Models (RPSFTM) and the Iterative Parameter Estimation (IPE) algorithm represent randomisation-based methods for estimating counterfactual survival times (i.e. survival times that would have been observed in the absence of switching). The Inverse Probability of Censoring Weights (IPCW) method represents an observational-based approach, whereby data for switchers are censored at the point of switch and remaining observations are weighted with the aim of removing any censoring-related selection bias.
This Technical Support Document (TSD) introduces the RPSFTM, IPE, IPCW and other adjustment methods that may be used in the presence of treatment switching. The key assumptions and limitations associated with each method are described, and the use of these in past NICE technology appraisals and their performance in simulation studies is reviewed. Based upon this, advice is offered in the form of an analysis framework, to help analysts determine adjustment methods that are likely to be appropriate on a case-by-case basis.
- TSD 21
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Survival analysis modelling approaches are often required to capture the survival functions seen in clinical trial data. These approaches are also used to extrapolate to estimate lifetime benefits in economic evaluations. Often complex hazard function shapes can arise both within and beyond the trial period. This means 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 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, from the perspective of applying it to observed trial data. We evaluate details with respect to formulae and assumptions, and highlight their limitations. 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.