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

Iain R. Timmins, Fatemeh Torabi Orcid Logo, Christopher H. Jackson, Paul C. Lambert, Michael J. Sweeting

BMC Medical Research Methodology, Volume: 26, Issue: 1

Swansea University Author: Fatemeh Torabi Orcid Logo

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DOI (Published version): 10.1186/s12874-026-02783-7

Abstract

Background: 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 transparent...

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Published in: BMC Medical Research Methodology
ISSN: 1471-2288
Published: Springer Science and Business Media LLC 2026
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URI: https://cronfa.swan.ac.uk/Record/cronfa71648
Abstract: Background: 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. Methods: 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. Results: 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. Conclusions: 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.
Keywords: Bayesian; Survival analysis; Clinical trials; HTA; MCMC; Parametric models; Spline estimator; Hazard function; Statistical software
College: Faculty of Medicine, Health and Life Sciences
Funders: C.H.J. is funded by the Medical Research Council, programme number MC_UU_00040/4. F.T. is funded by the UKRI-MRC - programme number MR/T033371/1. P.C.L. is funded by The Swedish Cancer Society (211890) and the Swedish Research Council (2021 − 01875).
Issue: 1

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