Despite appealing characteristics for the clinical trials setting, Bayesian inference methods remain scarcely used, especially in randomized controlled clinical trials (RCT). This is particularly true when dealing with a survival endpoint, likely due to the additional complexities to model specifications. We propose to use Bayesian inference to estimate the treatment effect in this setting, using a proportional hazards (PH) model for right-censored data. Implementation of such an estimation process is illustrated on two working examples from cancer RCTs, the ALLOZITHRO and the CLL7-SA trials, both originally analyzed using a frequentist approach. In these two different settings, we show that Bayesian sequential analyses can provide early insight on treatment effect in RCTs. Relying on posterior distributions and predictive posterior probabilities, we find that Bayesian sequential analyses of the ALLOZITHRO trial, which was terminated early due to an unanticipated deleterious effect of the intervention on survival, allow quantifying early that the treatment effect was opposite to what was expected. Then, incorporating historical data in the sequential analyses of the CLL7-SA trial would have allowed the treatment effect to be closer to the protocol hypothesis. These post-hoc results give grounds to advocate for a wider use of Bayesian approaches in RCTs, including those with right-censored endpoints, as informative decision tools.