With such a wide range of backgrounds here, I thought I'd toss this out here 
to get ideas.

I've lucked into some clinical trial data where schizophrenic patients were 
randomly assigned to start on one of three drugs, then were followed 
"naturalistically" over a year (or more, depending on when they enrolled). 
They were assessed with a standard battery of instruments at baseline, and 
at regular intervals. Apart from the initial random assignment, treatment 
decisions were left up to patients and their doctors. Thus, one of the main 
outcomes of the trial is the "all-cause time to discontinuation" which is 
believed to be the patient-centric tipping point where the risks and costs 
of using the drug outweight the benefit, so the patient either switches or 
just stops. The outcome variable, therefore, is a censored time variable. I 
have the number of days, and a flag to identify if that number is actual 
discontinuation or just the end of observation.

Now, the a priori analysis is done and gone (Cox regression of which drug 
had longest time to d/c), and a more clinical question has come up: using 
these data, can we build a model to predict, for each patient, the drug 
which is likely to be best for that individual. Sounds like a bayesian 
opportunity to me, a separate model for each drug based on an analysis of 
the patients randomized to each drug, then apply each model to a holdout 
sample, and see if patients matched to therapy did better than patients who 
were not.

If I were just predicting a single continuous measure, or a dichotomous 
outcome, I'd have no problem. The question is, given that the outcome is a 
censored time variable, which approaches would get me closest to the 
"posterior probability of success" or "expected number of days, give or take 
Y" in the clinical sense, not the frequentist sense ("if you repeated this 
study K times,...")?

Just interested in hearing some thoughts on this.

---------------------------------------
David L. Van Brunt, Ph.D.
mailto:dlvanbrunt@gmail.com

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