  We overview Bayesian estimation, hypothesis testing, and model-averaging and
illustrate how they benefit parametric survival analysis. 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 illustrate the application of the Bayesian approaches on
an example data set from a colon cancer trial. We compare the Bayesian
parametric survival analysis and frequentist models with AIC/BIC model
selection in fixed-n and sequential designs with a simulation study. In the
example data set, the Bayesian framework provided evidence for the absence of a
positive treatment effect on disease-free survival in patients with resected
colon cancer. Furthermore, the Bayesian sequential analysis would have
terminated the trial 10.3 months earlier than the standard frequentist
analysis. 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. 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
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. We have made the analytic approach readily available in RoBSA
R package. The outlined Bayesian framework provides several benefits when
applied to parametric survival analyses. It uses data more efficiently, is
capable of greatly shortening the length of clinical trials, and provides a
richer set of inferences.
