Weibull Proportional Hazard in pymc I’m looking to create a Bayesian proportional hazard model where the baseline hazard is modeled by a Weibull distribution (or some similar continuous distribution).
I’ve reviewed (and implemented) the cox proportional hazard example here where the baseline hazard is piece wise constant and modeled with a Poisson’s distribution: https://docs.pymc.io/en/v3/pymc-examples/examples/survival_analysis/survival_analysis.html
I’ve reviewed (and implemented) the accelerated failure Weibull models at
https://docs.pymc.io/en/v3/pymc-examples/examples/survival_analysis/bayes_param_survival_pymc3.html
It’s not obvious to me how to put them together. I started down the path of thinking of logs of hazard ratios, but couldn’t quite land how to model this and bring in my measured and censored survival times.
Any advice?

EdM's answer on 4/8 is the right one.  For Weibull survival models AFT and PH are the same.  Where I was confusing myself was thinking that a Weibull model was the same as a CoxPH model where the piecewise constant hazard of the CoxPH model is replaced by a smooth parametric Weibull fit of the same data.  Those are different things.
