Bayesian Log-Rank Test

Abstract Comparison of two survival curves is a fundamental problem in survival analysis. Although abundant frequentist methods have been developed for comparing survival functions, inference procedures from the Bayesian perspective are rather limited. In this article, we extract the quantity of interest from the classic log-rank test and propose its Bayesian counterpart. Monte Carlo methods, including a Gibbs sampler and a sequential importance sampling procedure, are developed to draw posterior samples of survival functions and a decision rule of hypothesis testing is constructed for making inference. Via simulations and real data analysis, the proposed Bayesian log-rank test is shown to be asymptotically equivalent to the classic one when noninformative prior distributions are used, which provides a Bayesian interpretation of the log-rank test. When using the correct prior information from historical data, the Bayesian log-rank test is shown to outperform the classic one in terms of power. R codes to implement the Bayesian log-rank test are also provided with step-by-step instructions.