Estimation and goodness-of-fit for the Cox model with various types of censored data

    Authors

    J. J. Ren;B. He

    Comments

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    Abbreviated Journal Title

    J. Stat. Plan. Infer.

    Keywords

    Bivariate right censored data; Bivariate data under univariate right; censoring; Bootstrap; Doubly censored data; Empirical likelihood; Goodness-of-fit; Partly interval-censored data; PROPORTIONAL HAZARDS MODEL; FAILURE TIME DATA; EMPIRICAL LIKELIHOOD; SURVIVAL FUNCTION; SELF-CONSISTENT; NONPARAMETRIC-ESTIMATION; ASYMPTOTIC; PROPERTIES; REGRESSION-ANALYSIS; WEAK-CONVERGENCE; TESTS; Statistics & Probability

    Abstract

    The currently existing estimation methods and goodness-of-fit tests for the Cox model mainly deal with right censored data, but they do not have direct extension to other complicated types of censored data, such as doubly censored data, interval censored data, partly interval-censored data, bivariate right censored data, etc. In this article, we apply the empirical likelihood approach to the Cox model with complete sample, derive the semiparametric maximum likelihood estimators (SPMLE) for the Cox regression parameter and the baseline distribution function, and establish the asymptotic consistency of the SPMLE. Via the functional plug-in method, these results are extended in a unified approach to doubly censored data, partly interval-censored data, and bivariate data under univariate or bivariate right censoring. For these types of censored data mentioned, the estimation procedures developed here naturally lead to Kolmogorov-Smirnov goodness-of-fit tests for the Cox model. Some simulation results are presented. (C) 2010 Elsevier B.V. All rights reserved.

    Journal Title

    Journal of Statistical Planning and Inference

    Volume

    141

    Issue/Number

    2

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    961

    Last Page

    971

    WOS Identifier

    WOS:000284386500034

    ISSN

    0378-3758

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