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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
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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. 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spelling 2026-04-20T11:16:21.6084902 v2 71648 2026-03-19 Simulation-based assessment of a Bayesian M-spline survival model with flexible baseline hazard and time-dependent effects f569591e1bfb0e405b8091f99fec45d3 0000-0002-5853-4625 Fatemeh Torabi Fatemeh Torabi true false 2026-03-19 MEDS 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. Journal Article BMC Medical Research Methodology 26 1 Springer Science and Business Media LLC 1471-2288 Bayesian; Survival analysis; Clinical trials; HTA; MCMC; Parametric models; Spline estimator; Hazard function; Statistical software 18 3 2026 2026-03-18 10.1186/s12874-026-02783-7 COLLEGE NANME Medical School COLLEGE CODE MEDS Swansea University Another institution paid the OA fee 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). 2026-04-20T11:16:21.6084902 2026-03-19T23:19:44.8916885 Faculty of Medicine, Health and Life Sciences Swansea University Medical School - Health Data Science Iain R. Timmins 1 Fatemeh Torabi 0000-0002-5853-4625 2 Christopher H. Jackson 3 Paul C. Lambert 4 Michael J. Sweeting 5 71648__36527__38beafb4690842a58efbdb0b62a10472.pdf 71648.VoR.pdf 2026-04-20T11:14:06.6522335 Output 5658874 application/pdf Version of Record true © The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License. true eng http://creativecommons.org/licenses/by/4.0/
title Simulation-based assessment of a Bayesian M-spline survival model with flexible baseline hazard and time-dependent effects
spellingShingle Simulation-based assessment of a Bayesian M-spline survival model with flexible baseline hazard and time-dependent effects
Fatemeh Torabi
title_short Simulation-based assessment of a Bayesian M-spline survival model with flexible baseline hazard and time-dependent effects
title_full Simulation-based assessment of a Bayesian M-spline survival model with flexible baseline hazard and time-dependent effects
title_fullStr Simulation-based assessment of a Bayesian M-spline survival model with flexible baseline hazard and time-dependent effects
title_full_unstemmed Simulation-based assessment of a Bayesian M-spline survival model with flexible baseline hazard and time-dependent effects
title_sort Simulation-based assessment of a Bayesian M-spline survival model with flexible baseline hazard and time-dependent effects
author_id_str_mv f569591e1bfb0e405b8091f99fec45d3
author_id_fullname_str_mv f569591e1bfb0e405b8091f99fec45d3_***_Fatemeh Torabi
author Fatemeh Torabi
author2 Iain R. Timmins
Fatemeh Torabi
Christopher H. Jackson
Paul C. Lambert
Michael J. Sweeting
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container_title BMC Medical Research Methodology
container_volume 26
container_issue 1
publishDate 2026
institution Swansea University
issn 1471-2288
doi_str_mv 10.1186/s12874-026-02783-7
publisher Springer Science and Business Media LLC
college_str Faculty of Medicine, Health and Life Sciences
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hierarchy_top_title Faculty of Medicine, Health and Life Sciences
hierarchy_parent_id facultyofmedicinehealthandlifesciences
hierarchy_parent_title Faculty of Medicine, Health and Life Sciences
department_str Swansea University Medical School - Health Data Science{{{_:::_}}}Faculty of Medicine, Health and Life Sciences{{{_:::_}}}Swansea University Medical School - Health Data Science
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description 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.
published_date 2026-03-18T05:31:34Z
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score 11.104058

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