Roy Tamura writes:
I am trying to implement a recommendation you made a few years ago. In my clinical trial of drug versus placebo, patients were stratified into two cohorts and randomized within strata. Time to event is the endpoint with the proportional hazards regression with strata and treatment as independent factors.
There is evidence of a strata x trt interaction. You have recommended a Bayesian analysis and comparing this to the traditional within strata analysis. I am not a practicing Bayesian so I am asking how to define the priors on the parameters. I presume there are 3 parameters, strata, trt and strata x trt. For the priors for trt and strata x trt, should they be centered at zero? (null) or somewhere else? What would you recommend?
My reply: Without knowing more about the context, I’m not sure, but my inclination would be to have all priors centered at zero and, as you say, to parameterize in terms of main effects and interactions. I guess what we really need here is an analysis for a particular example, a template that you and others could use.
This is a weakness of our Bayesian Data Analysis book: We don’t have a lot of examples with informative priors.
Thanks for posting Andrew. Since I first contacted you, a manuscript has been submitted to a journal so we are waiting to see what happens with the review. I will add a bit more clinical context in case anyone is interested. The population is women with breast cancer who will be treated with herceptin. In this population, oncologists also combine herceptin with anthracyclines (chemotherapy agents) in some patients. Both herceptin and anthracyclines have a serious adverse event – they are cardiotoxic in about 20% of the women. The trial was placebo control, randomized, and stratified by anthryacylcine use (yes or no). The drug tested is a well known beta-blocker. It was known that the combination of herceptin and anthracyclines would have higher toxicity than just herceptin and this was observed. The endpoint is cardiotoxicity.
We struggled with how to present the results and eventually decided, 1) present first the analysis as defined in the protocol pooling over the strata (no significant drug effect), 2) present the analysis for interaction (p-value about 0.07) and 3) present the within strata analyses which show non-significant drug effect for the herceptin only strata (virtually overlapping KM curves) but significant drug effect for the herceptin + anthracycline strata.
It would be interesting to compare the frequentist versus a Bayesian analysis of the trial.