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Abstract Details

Activity Number: 576
Type: Contributed
Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #304403
Title: A Necessary and Sufficient Condition for Justifying Nonparametric Likelihood with Censored Data
Author(s): Qiqing Yu*+ and Yuting Hsu and Kai Yu
Companies: Binghamton University and Penn State University and University of Mississippi
Address: Mathematics Dept, Binghamton, NY, 13902, United States
Keywords: Right-censoring ; doubly-censoring ; interval-censorship model
Abstract:

The non-parametric likelihood L(F) for censored data, including univariate or multivariate right-censored, doubly-censored, interval-censored, or masked competing risks data, is proposed by Peto (1973). It does not involve censoring distributions. In the literature, several sufficient conditions are proposed to justify L(F) so that the NPMLE can be consistent. Typically, one assumes that the censoring vector and survival time are independent. We raise 4 questions in this regard. (1) What is the necessary and sufficient N&S condition~? (2) Can we characterize it in a way that is easy to check in applications~? (3) Is it realistic ? (4) Is the NPMLE consistent then ? We give positive answers to the first 3 questions and we have preliminary results on question 4. In particular, we present a N&S condition that is relatively easy to check in practical applications. We present two applications to cancer research data that satisfy the N&S condition but has dependent censoring.


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