  The intermittent intake of treatment is commonly seen in patients with
chronic disease. For example, patients with atrial fibrillation may need to
discontinue the oral anticoagulants when they experience a certain surgery and
re-initiate the treatment after the surgery. As another example, patients may
skip a few days before they refill a treatment as planned. This treatment
dispensation information (i.e., the time at which a patient initiates and
refills a treatment) is recorded in the electronic healthcare records or claims
database, and each patient has a different treatment dispensation. Current
methods to estimate the effects of such treatments censor the patients who
re-initiate the treatment, which results in information loss or biased
estimation. In this work, we present methods to estimate the effect of
treatments on failure time outcomes by taking all the treatment dispensation
information. The developed methods are based on the continuous-time structural
failure time model, where the dependent censoring is tackled by inverse
probability of censoring weighting. The estimators are doubly robust and
locally efficient.
