Correcting for non-compliance in randomized trials using rank preserving structural failure time models

We propose correcting for non-compliance in randomized trials by estimating the parameters of a class of semi-parametric failure time models, the rank preserving structural failure time models, using a class of rank estimators. These models are the structural or strong version of the “accelerated failure time model with time-dependent covariates” of Cox and Oakes (1984). In this paper we develop a large sample theory for these estimators, derive the optimal estimator within this class, and briefly consider the construction of “partially adaptive” estimators whose efficiency may approach that of the optimal estimator. We show that in the absence of censoring the optimal estimator attains the semiparametric efficiency bound for the model.