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We estimate the effects of non-randomized time-varying treatments on the discrete-time hazard, using inverse weighting. We consider the special monotone pattern of treatment that develops over time as subjects permanently discontinue an initial treatment, and assume that treatment selection is sequentially ignorable. We use a propensity score in the hazard model to reduce the potential for finite-sample bias due to inverse weighting. When the number of subjects who discontinue treatment at any given time is small, we impose scientific restrictions on the potentially observable discontinuation hazards to improve efficiency. We use predictive inference to account for the correlation of the potential hazards, when comparing outcomes under different durations of initial treatment.
Dawson et al. (Wed,) studied this question.