# [R] (slightly off topic, but...) More of a stat design question...

From: David L. Van Brunt, Ph.D. <dlvanbrunt_at_gmail.com>
Date: Wed 22 Jun 2005 - 11:24:28 EST

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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