# How to do a Bayesian survival analysis and determine which variables are useful?

I can measure two variables on each patient in a survival study (I have the measurements and the survival times; some patients outlive the study and are therefore censored). I know that it is possible to use either of these variables to assign patients to groups with different survival curves (using a simple threshold on the variables). What I want to know is whether using both variables allows me to assign patients better than just one of the variables — i.e., whether the survival characteristics are more different when both variables are included; whether a given variable provides information that the other one doesn't.

I would prefer to do this in a Bayesian manner using JAGS (BUGS); I tend to find these models easier to understand.

Without further details about your model, priors and etcetera, the best thing I can do is to point out a reference for Bayesian variable selection

Faraggi and Simon (1998). Bayesian Variable Selection Method for Censored Survival Data. Biometrics Vol. 54, No. 4, pp. 1475-1485.

Of course, the typical way for conducting Bayesian model selection is the use of Bayes factors (http://www.stat.cmu.edu/~kass/papers/bayesfactors.pdf). You can use the posterior simulations obtained with your favourite software to calculate the Bayes factors using an importance sampling as detailed in

Chopin and Robert (2010). Properties of Nested Sampling. Biometrika 97 (3): 741-755.