Survival analysis is a frequently used method with important applications in evaluating lifetime outcomes in clinical trials. This type of Bayesian survival analysis is possible thanks to the recent development of flexible tools for fitting Bayesian models (such as JAGS and Stan ) and efficient techniques for estimating marginal likelihoods (such as bridge-sampling ). In this paper, we leverage the advantages of the longstanding Bayesian estimation, hypothesis testing, and model-averaging approaches and apply them to parametric survival analysis. There has been a steady increase in the popularity and interest in Bayesian statistics in the past years. It uses data more efficiently, is capable of considerably shortening the length of clinical trials, and provides a richer set of inferences. The outlined Bayesian framework provides several benefits when applied to parametric survival analyses. We have made the analytic approach readily available to other researchers in the RoBSA R package. We found no noticeable differences for survival predictions. In fixed-n designs, the Bayesian framework showed slightly higher power, slightly elevated error rates, and lower bias and RMSE when estimating treatment effects in small samples. Under model misspecification, the Bayesian framework resulted in higher false-negative rate compared to the frequentist counterparts, which resulted in a higher proportion of undecided trials. In a simulation study with sequential designs, the Bayesian framework on average reached a decision in almost half the time required by the frequentist counterparts, while maintaining the same power, and an appropriate false-positive rate. Furthermore, the Bayesian sequential analysis would have terminated the trial 10.3 months earlier than the standard frequentist analysis. In the retrospective re-analysis of the example data set, the Bayesian framework provided evidence for the absence of a positive treatment effect of adding Cetuximab to FOLFOX6 regimen on disease-free survival in patients with resected stage III colon cancer. We assess the performance of Bayesian parametric survival analysis and maximum likelihood survival models with AIC/BIC model selection in fixed-n and sequential designs with a simulation study. We illustrate the application of the outlined Bayesian approaches on an example data set, retrospective re-analyzing a colon cancer trial. We contrast the Bayesian framework to the currently dominant frequentist approach and highlight advantages, such as seamless incorporation of historical data, continuous monitoring of evidence, and incorporating uncertainty about the true data generating process. We provide an overview of Bayesian estimation, hypothesis testing, and model-averaging and illustrate how they benefit parametric survival analysis.
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