Estimation of the Time-Dependent Accelerated Failure Time Model in the Presence of Confounding Factors

Cox & Oakes (1984, p. 66) introduced the ‘strong version’ of the accelerated failure time model with time-dependent exposures. We provide conditions under which this model could be used to estimate, from observational data, the causal effect of a time-varying exposure or treatment on time to an event of interest in the presence of time-dependent confounding variables. We propose a class of semiparametric tests and estimators for the model parameters. This class contains an estimator that is semiparametric efficient in the sense of Begun et al. (1983).