Bivariate Copula Models With Event‐Free Cure Effect for Survival Extrapolations and Individual‐Level Correlation Analysis

OBJECTIVES: Overall survival (OS) extrapolations from mixture cure models (MCMs) are often sensitive to the cure fraction, which is challenging to estimate when data are immature. Furthermore, in some cancer populations, it may be unreasonable to assume curative effects among patients who are not event-free. We addressed these problems using bivariate copula MCMs to jointly model OS and progression- (PFS) or recurrence-free survival (RFS), with a single event-free cure fraction parameter. METHODS: We proposed a practical framework for parametric survival copula model selection and interpretation, which involves estimating five representative candidate copula functions and examining OS distributions conditioned on intermediate event times. Bivariate MCMs with event-free cure fraction, based on previously selected marginal distributions, were estimated for two studies of nivolumab with contrasting survival patterns, namely, in previously treated advanced esophageal squamous cell carcinoma (OS-PFS correlation) and resected melanoma (OS-RFS correlation). RESULTS: OS extrapolations from bivariate MCMs with an effective PFS (or RFS) cure fraction were more conservative than from univariate MCMs. Although patient-level OS-PFS/RFS correlation coefficients were sensitive to the copula, model averaging and inspecting estimated conditional OS distributions enabled clinically meaningful inference on the prognostic impact of intermediate events. CONCLUSIONS: Bivariate MCMs with event-free cured subpopulation incorporated curative effects into OS extrapolations more cautiously than conventional MCMs, based on a more rapidly maturing composite endpoint. The model is especially useful when OS data are immature and if post-event cure is clinically implausible. Employing alternative copulas that cover archetypal association patterns mitigated model selection bias in patient-level correlation analysis.