One goal in survival analysis of right-censored data is to estimate the marginal survival function in the presence of dependent censoring. When many auxiliary covariates are sufficient to explain the dependent censoring, estimation based on either a semiparametric model or a nonparametric model of the conditional survival function can be problematic due to the high dimensionality of the auxiliary information. In this paper, we use two working models to condense these high-dimensional covariates in dimension reduction; then an estimate of the marginal survival function can be derived nonparametrically in a low-dimensional space. We show that such an estimator has the following double robust property: when either working model is correct, the estimator is consistent and asymptotically Gaussian; when both working models are correct, the asymptotic variance attains the efficiency bound.