Borrowing from historical control data in a Bayesian time-to-event model with flexible baseline hazard function

Currently, there is a focus on statistical methods that can use historical trial information to help accelerate the discovery, development, and delivery of medicines. Bayesian methods enable "dynamic" borrowing, allowing the similarity between current and historical data to help determine the extent of information incorporated. In the time-to-event setting, Bayesian borrowing methods typically impose a constraint on the shape of the baseline hazard, simplifying the modelling and improving the computational speed of estimation. However, we show that this approximation comes at a cost when trying to borrow historical information. We propose a Bayesian borrowing semiparametric model for one historical dataset, which allows the baseline hazard to take any form through an ensemble average. We introduce priors to smooth the shape of the posterior baseline hazard, improving both model estimation and borrowing characteristics. By accurately modelling the baseline hazard rather than approximating its form, power is improved and bias of the estimated treatment effect reduced when the borrowing assumption of parameter exchangeability holds. In the presence of prior-data conflict, the type I error inflation is reduced. We explore a variety of prior borrowing structures within our proposed model and evaluate their performance against established approaches. We show the benefit of a lump-and-smear borrowing prior in our joint model for improving type I error in the presence of prior-data conflict and increased power. A principled approach is proposed for the choice of hyperparameters to control the dynamic borrowing, based on the tolerated difference between the historical and log-baseline hazards. We have developed accompanying software available in R enabling easy implementation of our approach in clinical trial analysis.