Modelling the Survival Outcomes of Immuno-Oncology Drugs in Economic Evaluations: A Systematic Approach to Data Analysis and Extrapolation

Abstract

Background New immuno-oncology (I-O) therapies that harness the immune system to fight cancer call for a reexamination of the traditional parametric techniques used to model survival from clinical trial data. More flexible approaches are needed to capture the characteristic I-O pattern of delayed treatment effects and, for a subset of patients, the plateau of long-term survival. Objectives Using a systematic approach to data management and analysis, the study assessed the applicability of traditional and flexible approaches and, as a test case of flexible methods, investigated the suitability of restricted cubic splines (RCS) to model progression-free survival (PFS) in I-O therapy. Methods The goodness of fit of each survival function was tested on data from the CheckMate 067 trial of monotherapy versus combination therapy (nivolumab/ipilimumab) in metastatic melanoma using visual inspection and statistical tests. Extrapolations were validated using long-term data for ipilimumab. Results Modelled PFS estimates using traditional methods did not provide a good fit to the Kaplan-Meier (K-M) curve. RCS estimates fit the K-M curves well, particularly for the plateau phase. RCS with six knots provided the best overall fit, but RCS with one knot performed best at the plateau phase and was preferred on the grounds of parsimony. Conclusions RCS models represent a valuable addition to the range of flexible approaches available to model survival when assessing the effectiveness and cost-effectiveness of I-O therapy. A systematic approach to data analysis is recommended to compare the suitability of different approaches for different diseases and treatment regimens. Key Points for Decision MakersThe use of traditional parametric survival functions can underestimate survival with immuno-oncology (I-O) therapies, primarily when a plateau of long term survival is observed, and therefore give a misleading estimate of life expectancy.Flexible models including restricted cubic splines (RCS) can provide a good fit to trial data and valid extrapolations of clinical trial endpoints, as demonstrated by the case study of progression free survival in I-O treatment of melanoma.Methods including the RCS-based approaches can be considered an option for survival analysis by health technology assessment bodies when considering effectiveness and cost-effectiveness.

Cohort versus patient level simulation for the economic evaluation of single versus combination immuno-oncology therapies in metastatic melanoma

“…RCS models are polynomial functions fitted to segmented portions of the data at points known as knots, which define the degree of smoothness of the data fit 35 . Survival analysis applied to CheckMate 067 data found that RCS models performed better than conventional functions in terms of goodness-of-fit and coherence, with longer term data, as supported by research conducted by Gibson et al 14…”

“…This paper extends a program of research being undertaken on innovative approaches to economic modeling and more accurate survival extrapolation 14 in I-O to represent clinical trial and long-term observational data in a more meaningful way. It builds on a previous comparison 15 of the 3-state PSM and extensions thereof vs a Markov modeling approach (a commonly used structure in health care evaluations) to represent I-O therapies ( Figure 2).…”

“…However, these approaches have shortcomings when the number of categories needed to define homogeneous groups is large. In addition, partitioning data as done with the PSM is reliant on observed clinical data, while cohort models generally organize the model structure to predict the reported results (over the time horizon of the clinical trial, with methods of extrapolation used to model longer term outcomes) 14 . To provide an adequate representation of the range of patient profiles, it has been argued that the number of groups would need to be vast, requiring the analyst to focus on a feasible few.…”

“…The model builds on an earlier analysis of standard (including Weibull, loglogistic, lognormal) and flexible functions with restricted cubic splines (RCS) with 0, 1, and 2 knots to identify the most appropriate way of modeling the unique K-M curves from the CheckMate 067 trial 14 . Parametric survival models allow predictions at any time point for any set of covariates and more flexible representations of the hazard function such as RCS can be applied, with the ability to capture the plateau observed in K-M curves (unlike traditional parametric methods assessed including Weibull).…”

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.…”