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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?

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  • $\begingroup$ A Weibull survival model is both AFT and PH. It's just a matter of which emphasis you put on describing the results. $\endgroup$
    – EdM
    Commented Apr 8, 2022 at 21:40
  • $\begingroup$ Ok, I think I'm understanding the referenced link and see how AFT and PH are the same for Weibull models. But now I have to ask the dumber question. The Weibull models I've built don't fit well whereas my CoxPH model fits well and the baseline hazard looks like it could be easily fit with a Weibull curve. Shouldn't that mean that the Weibull should have worked? Or is that something different? Is a CoxPH model where baseline survival is fit with a Weibull curve not the same as a Weibull AFT/PH fit of the same data? $\endgroup$
    – Mike
    Commented Apr 9, 2022 at 16:47

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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.

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