Extrapolation of survival curves in health: a methodological approach for direct fitting to aggregated data

Abstract

Introduction: Economic evaluation models often adopt long time horizons, making it necessary to extrapolate data from clinical research for economic evaluation models. The common methodological proposals available are strongly based on individual patient data (IPD), a scenario not always feasible for the daily routine of the Health Technology Assessment (HTA). Thus, the objective of this study was to propose a method for extrapolation with survival curves with direct fitting to aggregated data. Methods: The case study consisted of the application of parametric models of survival analysis with the main recommended distributions: exponential, Weibull, log-normal, log-logistics, generalized gamma and Gompertz. The models were adjusted to data from a randomized clinical trial testing therapies (anastrozole and fulvestrant) in the context of metastatic breast cancer with 10 years of follow-up on progression-free survival (PFS) and overall survival (OS). After making the adjustments to the individualized data, obtained by contacting the authors, we sought to validate the application of the adjustment to the aggregated data using nonlinear regressions and optimization algorithms. Both methods were compared in terms of visual inspection and quality of fit (Akaike Information Criteria – AIC and Bayesian Information Criteria – BIC). Results: In the two treatment arms, the Weibull and generalized gamma distributions were the ones that best fitted the OS data, both in the individualized and in the aggregated approach, according to statistical and visual inspection criteria. For PFS, log-logistic and log-normal curves were used for anastrozole. In the case of fulvestrant, the best choices would be the log-normal and generalized gamma curves for the individualized data and Gompertz and generalized gamma curves for the aggregated data. In terms of visual inspection, the difference was barely perceptible between the use of the individualized and aggregated models. Conclusion: Direct fitting data with survival curves to aggregated data is feasible. Despite differences in the choice of some curves, visual inspection suggests that it is unlikely that these differences have an impact on decision making. The algorithm presented here may be useful in situations where access to IPD is not possible.