SurvExtrap has at least two areas of application, which are demonstrated through two examples.
Example 1: Obtaining Consistency With An External Data Source
There is increasing demand for ways to incorporate into technology assessments information from data registries which boast much larger sample sizes and longer follow-up than clinical trials. However, access to patient level survival data may not be available. Conference abstracts are a common example where patient survival may be minimally reported, e.g. only be reported at 5 and 10 year milestones, without reporting any further information on survival rates at other times.7 Using SurvExtrap this information can easily be turned into a range of potential survival extrapolations, or it can be combined with a point estimate taken from an alternative data source, e.g. combining a clinical trial and a historical cohort.
In the technology appraisal TA519 of pembrolizumab for previously treated advanced or metastatic urothelial cancer, one key discussion point was the survival of the comparator population who received best-supportive care (BSC).8 The company’s extrapolations of the BSC data from their KEYNOTE 045 trial produced estimates that disagreed with the 5 year survival rates reported by Cancer Research UK (CRUK). Figure 1 demonstrates a visual representation of the problem, showing the inconsistency of the extrapolations and the CRUK data. This problem persisted even after the company applied an adjustment for the treatment switching that had occurred in the control arm. Whilst this could be explained by differences in baseline characteristics, there was still a desire to use a model that was consistent with the CRUK report, however it was not possible to get a reasonable extrapolation.
Using SurvExtrap and interpolating the median survival time as estimated by the Kaplan-Meier curve of the recreated unadjusted data for the BSC arm from KEYNOTE 045 (7.7 months) and the 5-year CRUK estimate (10%) provides a simple way of obtaining a model that is consistent with the data and with the external source. On this occasion a Gompertz model provided the best visual fit to the data (Fig. 2). The Gompertz model obtained using SurvExtrap appears an equivalent fit to the models fitted to the data. Any difference in the life-years estimated for the observed period would be negligible, and the reliability of the life-years estimated for the extrapolated period has improved considerably.
Example 2: Exploring Uncertainty
Consider the case where the uncertainty associated with the long-term efficacy of a therapy is high, with a wide disparity of estimates made by clinical experts about the survival of patients beyond the observed period. New and emerging cell gene therapies are relevant example of this. Typically, the uncertainty could be explored by exploring the uncertainty around the parameters of a particular model, or by varying the choice of survival model. However, in such a case, these may be unsatisfactory and fail to fully explore the uncertainty expressed by clinical experts.
Such an approach assumes that the unobserved survival outcomes can be predicted by those that have been observed, yet there might be a clear distinction between the mortality rates of these two groups that cannot be accurately estimated from the data.
Using hypothetical data, we show a range of parametric extrapolations (dashed – black) fitted to observed data show by the pink Kaplan Meier curve (Fig. 3). Beyond the observed period, there are three differing opinions on the long-term survival of the patient population. The Weibull model may be selected as it best suits the neutral opinion, but the possibility of the other opinions being right should also be considered. In this case, the Gompertz model fitted to the observed data could be a considered satisfactory to explore a pessimistic scenario, and the two log-models acceptable for an optimistic scenario. The problem with both of these assumptions is that neither are consistent with the opinions provided by the clinical experts. The curves for both scenarios overestimate survival relative to the opinions, the worst violation being the long-term prediction of the log models exceeding the expert’s predictions.
Using the SurvExtrap, and specifying interpolation of the points S(1.46) = 0.691 and either S(4.73) = 0.101 for the pessimistic scenario or S(12.7) = 0.108 for the optimistic scenario produced estimates of Weibull curve parameters that allowed modelling of the curves seen in Fig. 4. A comparison of the two shows that the models coming from SurvExtrap are much closer fits to the predictions made, whilst are also consistent to the observed data. No great care was taken when selecting these points, and the user could prioritise better fits to earlier or later points, depending on their preference and convergence of the solving algorithm.