Semiparametric estimation of structural failure time model in continuous-time processes

Structural failure time models are causal models for estimating the effect of time-varying treatments on a survival outcome. G-estimation and artificial censoring have been proposed to estimate the model parameters in the presence of time-dependent confounding and administrative censoring. However, most of existing methods require preprocessing data into regularly spaced data such as monthly data, and the computation and inference are challenging due to the non-smoothness of artificial censoring. We propose a class of continuous-time structural failure time models and semiparametric estimators, which do not restrict to regularly spaced data. We show that our estimators are doubly robust, in the sense that the estimators are consistent if either the model for the treatment process is correctly specified or the failure time model is correctly specified, but not necessarily both. Moreover, we propose using inverse probability of censoring weighting to deal with dependent censoring. In contrast to artificial censoring, our weighting strategy does not introduce non-smoothness in estimation and ensures that the resampling methods can be used to make inference.