“Statistical Inference for Data-Adaptive Doubly Robust Estimators With Survival Outcomes”, 2017-09-01 ():
The consistency of doubly robust estimators relies on consistent estimation of at least one of two nuisance regression parameters. In moderate to large dimensions, the use of flexible data-adaptive regression estimators may aid in achieving this consistency. However, n^1⁄2-consistency of doubly robust estimators is not guaranteed if one of the nuisance estimators is inconsistent.
In this paper we present a doubly robust estimator for survival analysis with the novel property that it converges to a Gaussian variable at n^1⁄2-rate for a large class of data-adaptive estimators of the nuisance parameters, under the only assumption that at least one of them is consistently estimated at a n^1⁄4-rate. This result is achieved through adaptation of recent ideas in semiparametric inference, which amount to: (1) Gaussianizing (ie. making asymptotically linear) a drift term that arises in the asymptotic analysis of the doubly robust estimator, and (2) using cross-fitting to avoid entropy conditions on the nuisance estimators.
We present the formula of the asymptotic variance of the estimator, which allows computation of doubly robust confidence intervals and p-values. We illustrate the finite-sample properties of the estimator in simulation studies, and demonstrate its use in a phase III clinical trial for estimating the effect of a novel therapy for the treatment of HER2 positive breast cancer.