Hi, I have a cohort of patients with a rare type of tumor. These patients have received two different therapies, A and B, and there are currently no clinical trials comparing them. After reading Datamethods I am convinced that the Bayesian analysis is the best approach. Therefore, I chose a bayesian AFT lognormal survival model (multivariable). However, I have some doubts about how I should proceed, and I wanted to ask you about the best strategy.
 There is no historical information for prior distributions, but clinicians have differing views on the differential effect. Therefore, I thought to analyze the data according to the proposal by Spiegelhalter et al for interim analysis (with noninformative, skeptical or enthusiastic priors). Since my data are observational I wanted to ask if extrapolation is wise.
https://www.jstor.org/stable/4144380?seq=1#page_scan_tab_contents
The idea could be to report the probability that A is equivalent or not to B (e.g., estimate 0 +/ 0.1), according to the a posteriori distribution.

I am not sure about applying the informative prior only to the main variable, or I should also do it with the rest of covariates, or even on the rest of the parameters of AFT models. For example, with Weibull models I would have two parameters (shape/scale), with the lognormal, only one.

Finally, I have read (Fayers & Parmar) that the variance of normal priors can be surprisingly 4/ number of events. However, my feeling is that this variance is a very small number that dwarfs the likelihood and makes the prior effect predominate by far. What do you think?
Thanks.