OBJECTIVES: The impact of response on survival in oncology varies greatly across cancers, therapies, and patient subgroups, but inference on this relationship is often hindered by sample size. Here, we use historical trial data to inform survival estimates for the responder subpopulation, employing Bayesian copula models to jointly represent time to objective response (TTOR) and overall survival (OS). We demonstrate the method with synthetic datasets emulating observations for immunotherapy plus tyrosine kinase inhibitor (IO+TKI) and “historical” observations for TKI monotherapy in advanced renal cell carcinoma, each with approximately 20 months median follow-up.

METHODS: A Bayesian bivariate TTOR-OS parametric model based on the Clayton copula was fitted to the IO+TKI data. The coupling parameter of the copula, which corresponds to an OS hazard ratio for responders vs non-responders, was informed by a prior maximum-likelihood estimate obtained by fitting a copula model to the TKI dataset. An alternative bivariate model, employing a vague prior for the coupling parameter, was fitted for comparison. Diffuse priors were used for TTOR and OS distributions.

RESULTS: Utilizing historical trial data reduced uncertainty and increased OS estimates, both within and beyond the study follow-up period, for patients who responded to IO+TKI within 6 months (e.g., 3-year responder OS: 79.7% [95% credible interval (CrI): 69.8-87.8%] informed vs 75.7% [95% CrI: 60.1-88.3%] vague). Long-term survival extrapolations for the overall IO+TKI population were almost identical between the two models.

CONCLUSIONS: Leveraging historical trial data for TKI via a responder vs non-responder hazard ratio reduced uncertainty in survival estimates for responders to IO+TKI, and thus the TKI data proved useful despite IO+TKI being known to yield more durable responses than TKI monotherapy. Bayesian copula models provide an elegant approach to incorporate this prior information and jointly model TTOR-OS outcomes, thereby generating informed OS estimates, including extrapolations, for patients who respond within a timeframe of interest.