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We consider studies for evaluating the short-term effect of a treatment of interest on a time-to-event outcome. The studies we consider are only partially controlled in the following sense: (1) Subjects' exposure to the treatment of interest can vary over time, but this exposure is not directly controlled by the study; (2) subjects' follow-up time is not directly controlled by the study; and (3) the study directly controls another factor that can affect subjects' exposure to the treatment of interest as well as subjects' follow-up time. When factors 1 and 2 are both present in the study, evaluating the treatment of interest using standard methods, including instrumental variables, does not generally estimate treatment effects. We develop the methodology for estimating the effect of treatment 1 in this setting of partially controlled studies under explicit assumptions using the framework for principal stratification for causal inference. We illustrate our methods by a study to evaluate the efficacy of the Baltimore Needle Exchange Program to reduce the risk of human immunodeficiency virus (HIV) transmission, using data on distance of the program's sites from the subjects.
Frangakis et al. (Mon,) studied this question.