title: Bayesian survival analysis in clinical trials: What methods are used in practice?
abstract: Background Bayesian statistics are an appealing alternative to the traditional frequentist approach to designing, analysing, and reporting of clinical trials, especially in rare diseases. Time-to-event endpoints are widely used in many medical fields. There are additional complexities to designing Bayesian survival trials which arise from the need to specify a model for the survival distribution. The objective of this article was to critically review the use and reporting of Bayesian methods in survival trials. Methods A systematic review of clinical trials using Bayesian survival analyses was performed through PubMed and Web of Science databases. This was complemented by a full text search of the online repositories of pre-selected journals. Cost-effectiveness, dose-finding studies, meta-analyses, and methodological papers using clinical trials were excluded. Results In total, 28 articles met the inclusion criteria, 25 were original reports of clinical trials and 3 were re-analyses of a clinical trial. Most trials were in oncology (n = 25), were randomised controlled (n = 21) phase III trials (n = 13), and half considered a rare disease (n = 13). Bayesian approaches were used for monitoring in 14 trials and for the final analysis only in 14 trials. In the latter case, Bayesian survival analyses were used for the primary analysis in four cases, for the secondary analysis in seven cases, and for the trial re-analysis in three cases. Overall, 12 articles reported fitting Bayesian regression models (semi-parametric, n = 3; parametric, n = 9). Prior distributions were often incompletely reported: 20 articles did not define the prior distribution used for the parameter of interest. Over half of the trials used only non-informative priors for monitoring and the final analysis (n = 12) when it was specified. Indeed, no articles fitting Bayesian regression models placed informative priors on the parameter of interest. The prior for the treatment effect was based on historical data in only four trials. Decision rules were pre-defined in eight cases when trials used Bayesian monitoring, and in only one case when trials adopted a Bayesian approach to the final analysis. Conclusion Few trials implemented a Bayesian survival analysis and few incorporated external data into priors. There is scope to improve the quality of reporting of Bayesian methods in survival trials. Extension of the Consolidated Standards of Reporting Trials statement for reporting Bayesian clinical trials is recommended.
authors.affiliation: 1 Gustave Roussy, Université Paris-Saclay, Service de biostatistique et d'épidémiologie, Villejuif, F-94805, France.|2 Université Paris-Saclay, Univ. Paris-Sud, UVSQ, CESP, INSERM, Villejuif, F-94085, France.
authors.forename: Caroline
authors.initials: C
authors.lastname: Brard
authors.affiliation: 1 Gustave Roussy, Université Paris-Saclay, Service de biostatistique et d'épidémiologie, Villejuif, F-94805, France.|2 Université Paris-Saclay, Univ. Paris-Sud, UVSQ, CESP, INSERM, Villejuif, F-94085, France.
authors.forename: Gwénaël
authors.initials: G
authors.lastname: Le Teuff
authors.affiliation: 1 Gustave Roussy, Université Paris-Saclay, Service de biostatistique et d'épidémiologie, Villejuif, F-94805, France.|2 Université Paris-Saclay, Univ. Paris-Sud, UVSQ, CESP, INSERM, Villejuif, F-94085, France.
authors.forename: Marie-Cécile
authors.initials: MC
authors.lastname: Le Deley
authors.affiliation: 3 Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster, UK.
authors.forename: Lisa V
authors.initials: LV
authors.lastname: Hampson
mesh_terms: D001499:Bayes Theorem; D002986:Clinical Trials as Topic; D017326:Clinical Trials, Phase III as Topic; D006801:Humans; D009369:Neoplasms / Q000628:therapy; D016032:Randomized Controlled Trials as Topic; D013223:Statistics as Topic; D016019:Survival Analysis
keywords: Bayesian; clinical trial; posterior distribution; prior distribution; survival modelling; systematic review; time-to-event