WITHDRAWN: A Dimension-Reduction Approach for Conditional Kaplan-Meier Estimators

• Activity Number: 650
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Valentin Patilea and Weiyu Li
• Companies: ENSAI - Campus de Ker-Lann and CREST-Ensai
• Keywords: Bootstrap ; Cure models ; Kernel Smoothing ; Semipaprametric regression ; Single-index ; U-statistics

Abstract

In many situations, the quantities of interest in survival analysis are smooth, closed-form expression functionals of the law of the observations. This is, for instance, the case for the conditional law of a lifetime of interest under random right censoring and for the conditional probability of being cured in mixture cure survival models. In such cases, one can easily derive nonparametric estimators for the quantities of interest by plugging-into the functional the nonparametric estimators of the law of the observations. However, in the presence of multivariate covariates, the nonparametric estimation suffers from the curse of dimensionality. Here, a new dimension reduction approach for conditional models in survival analysis is proposed. First, we consider a single-index hypothesis on the conditional law of the observations and propose a root-n-asymptotically normal semiparametric estimator. Next, we apply the smooth functionals to the estimator of the conditional law of the observations. This results in semiparametric estimators of the quantites of interest that avoid the curse of dimensionality. Confidence regions for the index and the functional of interest are easily derived.