In a recent clinical trial of patients with coronary heart disease who were scheduled to undergo percutaneous coronary intervention (PCI), patients randomized to receive Integrilin therapy had significantly better outcomes than patients randomized to placebo. The protocol recommended that Integrilin be given as a continuous infusion for 18--24 hours. There was debate among the clinicians on the optimal infusion duration in this 18--24-hour range, and we were asked to study this question statistically. Two issues complicated this analysis: (i) The choice of treatment duration was left to the discretion of the physician and (ii) treatment duration would have to be terminated (censored) if the patient experienced serious complications during the infusion period. To formalize the question, "What is the optimal infusion duration?" in terms of a statistical model, we developed a framework where the problem was cast using ideas developed for adaptive treatment strategies in causal inference. The problem is defined through parameters of the distribution of (unobserved) counterfactual random variables. We then show how, under some reasonable assumptions, these parameters could be estimated.
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