OBJECTIVES: Copula functions are often used to analyze the patient-level dependence of overall survival (OS) outcomes on progression-free survival (PFS). We conservatively account for survival heterogeneity within this framework by representing the marginal OS and PFS distributions using parametric mixture cure models (MCMs) with a shared cure fraction parameter. We apply this bivariate MCM approach to observations for patients receiving nivolumab in the phase 3 ATTRACTION-3 study and demonstrate its utility in predicting long-term quality-adjusted life years (QALYs).

METHODS: Five suitable copula functions (Clayton, Gumbel-Hougaard, Frank, Plackett, and Joe) were applied to jointly model OS and PFS data with 36 months of minimum follow-up. In the copula functions, the structures of the marginal survival functions for each endpoint were chosen as the best-fitting univariate MCMs obtained from separate modelling of endpoints. The shared cure fraction and all other parameters of the bivariate copula MCMs were estimated concomitantly by maximum likelihood, and models were evaluated by statistical goodness-of-fit criteria. QALYs over a 20-year horizon were estimated from partitioned survival models based on the preferred bivariate MCM, univariate MCMs, and standard parametric models (SPMs), using local discounting schemes and tariffs from nine selected countries including the USA, UK, France, Australia, and Canada.

RESULTS: The estimated cure fraction was 5.2% [95% CI: 2.7-9.8%] according to the best-fitting copula (Gumbel-Hougaard) and up to 6.3% among the next most reasonable copulas (Plackett, Frank). The ranges of QALY estimates across all countries, obtained from the statistically best-fitting models, were: 1.00-1.46 from bivariate MCMs, 1.17-1.81 from univariate MCMs, and 0.90-1.38 from SPMs.

CONCLUSIONS: Incorporating a shared cure fraction parameter into copula models provides an elegant method for simultaneous extrapolations of OS and PFS outcomes. Long-term QALY projections generated by bivariate MCMs were more conservative than the univariate MCMs, but more optimistic than the SPMs, for previously treated aESCC patients receiving nivolumab.