In a frequentist parametric survival model, median survival is simply calculated as exp(XB), with XP being the linear predictor (sum of the coefficients of all variables).

However, Bayesian statistics do not give point estimates of XP, but its continuous probability function. So for XP, I would not have a number but a continuous function. My basic question would be the following:

After a Bayesian model I get the 95% credible interval of the linear predictor.

If XPinf and XPsup are the lower and upper limits of that interval, then are exp (XPinf) and exp(XPsup) the limits of the 95% credible interval of the median survival?

Is the same true for the prediction of % of patients alive at fixed time?

I’ve been working on these ideas to build an online Bayesian calculator and I wanted to know if this is right for the bands of the survival curve, as shown below.