Informed Bayesian survival analysis

TL;DR

This paper demonstrates how Bayesian methods improve parametric survival analysis by enabling earlier decision-making, better data utilization, and richer inferences compared to traditional frequentist approaches, with practical implementation in R.

Contribution

It introduces a Bayesian framework for survival analysis, compares it to frequentist methods through simulations and real data, and provides an accessible R package for implementation.

Findings

Bayesian analysis can terminate trials 10.3 months earlier on average.

Bayesian methods reach decisions faster, nearly half the time of frequentist approaches.

Under model misspecification, Bayesian methods have higher false-negative rates but more undecided trials.

Abstract

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.