When treatment is found to be effective in a clinical study, attention often focuses on assessing the relationship of treatment duration to response. It is common in such studies that treatment duration is left to the discretion of the investigators and that some patients prematurely terminate treatment; that is, the intended treatment duration may be censored. In such observational studies, we do not know the intended treatment duration for patients who are censored and, even if we did, it may be unreasonable to assume subjects are prognostically similar. We propose an estimator for mean response as a function of treatment duration that appropriately adjusts for early treatment termination and confounding that commonly occur in observational studies. Our method uses counter-factual random variables and introduces assumptions that allow us to consistently estimate mean response. We evaluate our estimator through simulation studies and apply the method to the ESPRIT infusion trial from the Duke University Medical Center.
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