Bayesian two-sample survival probability curves with comparative summary measures and sensitivity analyses

Two-sample survival probability curves (TSSPCs) provide a concise way to visualize treatment differences in randomized controlled trials (RCTs). In this paper, we propose various area under the curve (AUC) metrics for TSSPCs as numerical measures for treatment effects. First, in the same spirit as the restricted mean survival time, we propose the restricted AUC (R-AUC) for the TSSPC. This metric can be estimated regardless of incomplete curve estimates caused by censoring and has a clear probabilistic interpretation. Additionally, we introduce sensitivity analysis measures, the worst- and best-case AUC (W-AUC and B-AUC), to represent extreme scenarios of the treatment effect beyond a specified restriction time point. We further propose to estimate the TSSPC and AUC measures using Bayesian models, and compare them against their counterparts derived from the Kaplan-Meier (KM) and Cox proportional hazards (PH) model frameworks. Using simulations and real oncology RCT data, we demonstrate that all methods perform well when the PH assumption holds. However, when the PH assumption is violated, the proposed Bayesian estimators outperform the Cox model in our simulations and data examples. Across all studied scenarios, the proposed person-period Bayesian approach offers flexibility comparable to the KM approach, while producing smoother curve estimates.