Extrapolation of Survival Curves from Cancer Trials Using External Information

Abstract

Background: Estimates of life expectancy are a key input to cost-effectiveness analysis (CEA) models for cancer treatments. Due to the limited follow-up in Randomized Controlled Trials (RCTs), parametric models are frequently used to extrapolate survival outcomes beyond the RCT period. However, different parametric models that fit the RCT data equally well may generate highly divergent predictions of treatment-related gain in life expectancy. Here, we investigate the use of information external to the RCT data to inform model choice and estimation of life expectancy. Methods: We used Bayesian multi-parameter evidence synthesis to combine the RCT data with external information on general population survival, conditional survival from cancer registry databases, and expert opinion. We illustrate with a 5-year follow-up RCT of cetuximab plus radiotherapy v. radiotherapy alone for head and neck cancer. Results: Standard survival time distributions were insufficiently flexible to simultaneously fit both the RCT data and external data on general population survival. Using spline models, we were able to estimate a model that was consistent with the trial data and all external data. A model integrating all sources achieved an adequate fit and predicted a 4.7-month (95% CrL: 0.4; 9.1) gain in life expectancy due to cetuximab. Conclusions: Long-term extrapolation using parametric models based on RCT data alone is highly unreliable and these models are unlikely to be consistent with external data. External data can be integrated with RCT data using spline models to enable long-term extrapolation. Conditional survival data could be used for many cancers and general population survival may have a role in other conditions. The use of external data should be guided by knowledge of natural history and treatment mechanisms.

Can’t see the wood for the trees: Using common likelihoods to share information regarding selection of functional form in survival analysis

“…Whilst external information such as administration data, registries, or expert opinion has been used for validation of extrapolation, recent approaches have proposed its use to inform extrapolation [4,5]. Guyot et al [4] proposed using external information, such as registries, to inform model extrapolation through the use of polynomial functions and population matching techniques. This raises questions about the availability and choice of such data, obtaining access, heterogeneity compared to the study population, missing data, and analysis complexity.…”

“…Recommendations for identification of the most appropriate parametric survival function have been published [1][2][3]. These recommendations focus on identifying a -preferred‖ parametric survival function from a set of candidates for an individual study and reference the use of external information on expected survival to validate and inform model selection [4,5].…”

Using Evidence from Randomised Controlled Trials in Economic Models: What Information is Relevant and is There a Minimum Amount of Sample Data Required to Make Decisions?

“…There is an extensive literature on modelling time-to-event data, including standard parametric models that are members of the generalised F distribution [22], flexible parametric models [23], piecewise models, and mixture models which include the standard cure rate model as a special case [24], and a growing body of work in the health economic literature on fitting parametric survival functions to time-to-event data [25][26][27][28][29], combining evidence on time-to-event outcomes across multiple clinical trials [30][31][32], and on incorporating external information in addition to sample data [33,34]. A limitation with standard parametric models is that they only capture certain shapes for the hazard function; for example, the hazard function of a generalised F distribution can be only decreasing, decreasing but not necessarily monotone and arc shaped, while the hazard function of the generalised gamma subfamily can be only monotonically increasing and decreasing, bathtub and arc-shaped.…”

“…It is not sufficient to attempt to fit complex parametric survival models such as a four-parameter generalised F distribution unless there is reasonable clinical justification for it, and attempting to do so based on the sample data alone with limited follow-up and events may simply result in a model with parameters that fail to converge whether or not it is the true model. When complex parametric survival models such as spline models, fractional polynomials and cure rate models are considered, there may not be sufficient sample data alone with which to estimate parameters, although this would not negate their relevance and it is important to incorporate any relevant external evidence about parameters including registry data [34] beliefs [35,36]. Finally, there are several ways in which uncertainty about a model might be assessed: 1) A single encompassing model can be constructed based on the set of possible alternative models.…”

Methodology and results of real-world cost-effectiveness of carfilzomib in combination with lenalidomide and dexamethasone in relapsed multiple myeloma using registry data

“…relative treatment effects) and RW data [i.e. baseline risks such as progression-free survival (PFS) and overall survival (OS) in patients receiving the comparator treatment] may provide more relevant and less uncertain estimates than those based on RCTs only, as long as the evidence available from observational databases is robust and representative of the RW patient population [8,9,19,20]. Therefore, this modelling approach is deemed to be appropriate to support well-informed decision-making in the RW, as it may minimise the risk of inefficient allocation of resources, including the chances of neglecting the access to more efficacious therapies erroneously considered not cost-effective, as well as the likelihood of inaccurate budget impact predictions [8,9,19,20].…”