Estimation of Treatment Dose-effect by Adjusting for Dependent Censoring Using High-dimensional Auxiliary Information

In right-censored data, one goal is to to obtain an estimator of treatment dose-effect, which is represented by some parameter in a marginal model of lifetime given treatment dose variable. When dependent censoring is explained by both the dose variable and many other auxiliary covariates (high-dimensional auxiliary information), an intuitive approach to estimate the dose effect is to first estimate the conditional distribution of lifetime given the whole covariates using a semiparametric model then average out the auxiliary information. However, this intuitive approach is problematic in practice since the semiparametric model can be easily misspecified. In this article, a novel way is proposed to enable us to condense the high-dimensional auxiliary information through the utilization of two working models for the distribution of lifetime given all the covariates and the distribution of censoring time given all the covariates. The estimator of the treatment dose-effect is then obtained by maximizing a pseudo-likelihood function over a sieve space. Such an estimator is shown to be consistent and asymptotically normal when either of the two working models is correct; additionally, its asymptotic variance is the same as the generalized Cramér-Rao bound when both working models are correct.