Higher Order Influence Functions for Inference in Monotone Missing Data Models

• Activity Number: 207
• Type: Contributed
• Date/Time: Monday, August 7, 2006 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Eric Tchetgen*+ and Lingling Li and James Robins and Aad van der Vaart
• Companies: Harvard School of Public Health and Harvard School of Public Health and Harvard School of Public Health and Vrije Universiteit Amsterdam
• Keywords: monotone missing ; higher order u-statistic ; CAR ; doubly-robust ; nonparametric

Abstract

Suppose we collect n iid high dimensional random vectors of time varying covariates {L(t),t=1,...,T} where t indexes time and T denotes the end of the study. Suppose that the main interest is in the mean of Y, a component of L(T), but some patients are missing Y due to dropping out of the study prior to completion. Under the assumption of Coarsening at Random (CAR), recent advances in semiparametric theory for monotone missing data models have led to doubly-robust (DR) estimators that are n1/2 consistent if either (i) a working model for the missingness mechanism , or (ii) a working model for the full data distribution are correctly specified. We introduce novel estimators for the mean of Y that remain consistent under weaker assumptions than (i) and (ii); however we must sacrifice n1/2 consistency for slower convergence rates comparable to those encountered in nonparametric inference.