# Simulation-based assessment of a Bayesian M-spline survival model with flexible baseline hazard and time-dependent effects

## TL;DR

This paper evaluates a Bayesian survival model using simulations to assess its performance in medical trials, focusing on flexible hazard modeling and treatment effects.

## Contribution

The study introduces a simulation-based evaluation of a Bayesian M-spline survival model for medical applications, highlighting its performance and usability in HTA.

## Key findings

- The Bayesian model shows good fit and convergence for complex baseline hazards and time-dependent effects.
- A weighted random walk prior on M-spline coefficients provides smooth hazard estimates without overfitting.
- Non-proportional hazards models in survextrap sometimes show greater bias compared to frequentist tools.

## Abstract

There is increasing interest in flexible Bayesian models for the analysis of time-to-event data, especially with their use in medical applications such as Health Technology Assessment (HTA). While these Bayesian approaches offer advantages of incorporating prior knowledge and transparently expressing model uncertainty to aid decision-making, they remain underused in practice. A flexible Bayesian model has recently been proposed for use in HTA settings which uses M-splines to model the hazard function, and is implemented in the survextrap R package.

We conducted a simulation study to assess the statistical performance of the Bayesian survival model implemented in survextrap. We simulate survival outcomes based on control arm data from two oncology clinical trials, and generate treatment arm survival based on different realistic treatment effect scenarios. Statistical performance in modelling a single treatment arm or the difference between treatment arms is compared across a range of flexible models, varying the M-spline specification, smoothing procedure, priors, treatment effect modelling choices and other computational settings.

We demonstrate good model fit and convergence of complex baseline hazard functions and time-dependent covariate effects across realistic clinical trial scenarios. We show that a sufficiently flexible M-spline, implemented using a weighted random walk prior on the spline coefficients, can provide a smooth fit to the hazard without risk of overfitting, and gives unbiased estimates of restricted mean survival over the trial follow-up with good coverage of the credible intervals. Bayesian model fitting with an efficient Laplace approximation provides unbiased estimation but overestimates posterior variance. In some treatment effect scenarios, the survextrap non-proportional hazards models displayed greater bias than standard frequentist survival modelling tools such as flexsurv and rstpm2.

This work helps inform key considerations to guide model selection and estimation performance when fitting flexible Bayesian models to trial data. These findings help identify appropriate default model settings in the software that should perform well in a broad range of settings, as well as more specific considerations to guide model selection for advanced users. This work further ensures users have greater confidence in the validity of these survival models and their implementation.

The online version contains supplementary material available at 10.1186/s12874-026-02783-7.