Asymptotic properties of the GMLE with case 2 interval-censored data

Yu, Qiqing; Schίck, Anton; Li, Linxiong; Wong, George Y.

doi:10.1016/s0167-7152(97)00120-x

Cited by 39 publications

(30 citation statements)

References 5 publications

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“…The uniform strong consistency of the GMLE has been established by , van de Geer (1993, Example 3.3a), Wang and Gardiner (1996) and Yu et al (1998a) for continuous Fo using various assumptions and techniques. In the case 2 model, the uniform strong consistency of the GMLE has been established by , van de Geer (1993, Example 3.3b), and Yu et al (1998b) for continuous FQ.…”

Section: Note That (L R) Is a Function Of The Random Vector (U V Imentioning

confidence: 81%

“…The average age of the participants was 46.7 years (range 22-74). The average age at menarche was 12.4 years (range [8][9][10][11][12][13][14][15][16][17][18]. Forty (70%) of the women were pre-menopausal, and 38 (67%) of the women have been pregnant at least once.…”

Section: Dose-ranging Analysismentioning

confidence: 99%

“…On consistency of the self-consistent estimator of survival functions with interval censored data. Scandinavian Journal of Statistics.(In press).[c] Yu, Q., Schick, A., Li, L. and Wong, G. Y. C. (1998). Asymptotic properties of the GMLE in the case 1 interval-censorship model with discrete inspection times.…”

mentioning

confidence: 99%

“…Sankhya, A. 60, 184-197.[e] Yu, Q., Schick, A., Li, L. and Wong, G. Y. C. (1998). Asymptotic properties of the GMLE of a survival function with case 2 interval-censored data.…”

mentioning

confidence: 99%

“…For case 2 model the GMLE is a.n. with rate n 1 / 2 if the censoring vector takes on finitely many values (Yu et al, 1998c), and conjecture that under certain smoothness conditions the GMLE has a pointwise convergence rate of (nhm) 1//3 . For more recent development on the latter conjecture, we refer to Groeneboom (1996) and Van De Geer (1996) .…”

mentioning

confidence: 99%

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Statistical Methods for Analyzing Time-Dependent Events in Breast Cancer Chemoprevention Studies.

Wong¹

1997

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Public reDorting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data'needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget,, Washington, DC 20503 AGENCY USE ONLY (Leave blank) 2. REPORT DATEOctober 1999 REPORT TYPE AND DATES COVERED Final (30 Sep 94 -29 Sep 99) TITLE AND SUBTITLE Statistical Methods for Analyzing Time-Dependent Events in Breast Cancer Chemoprevention Studies AUTHOR(S)George Wong, Ph.D. FUNDING NUMBERS DAMD17-94-J-4332 PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)Strane Cancer Prevention Center New York, New York 10021 e-mail: gwong@strang. org PERFORMING ORGANIZATION REPORT NUMBER SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES)U 12a. DISTRIBUTION / AVAILABILITY STATEMENTApproved for public release distribution unlimited 12b. DISTRIBUTION CODE■IO «peTP«/~r /.*-: __-... . , The overall aim of our research proposal is the statistical non- ABSTRACT (Maximum 200 Words) iparametric inferences of the redistribution-to-the-center estimator (RTCE) and the generalized maximum likelihood estimator (GMLE) for the survival function of a time-to-event variable that is subject to interval censoring. The RTCE, which is proposed by us, has a closed-form expression and is equal to GMLE under a homogeneous condition. The GMLE is the standard estimator in survival analysis. However, it cannot be expressed in a closedform expression, and asymptotic distribution theory for it has been limited. Prom the study of the asymptotic properties of RTCE, we have gained important insight into proofs of asymptotic properties of GMLE. Specifically, we have established consistency, asymptotic normality and efficiency of GMLE under different conditions. Also, we have derived an asymptotic nonparametric two-sample distance test for comparing two populations. Under finite distributional assumptions on the survival and censoring distributions, we have established consistency, asymptotic normality for both the regression coefficients and the survival function of the Cox regression model. We point out major computational limitations associated with the Newton-Raphson algorithm for computing the asymptotic estimates of the .Cox regression parameters, and suggest a simpler two-step estimation alternative SUBJECT TERMSBreast Cancer, Interval-Censored Data, Consistency, Asymptotic Normality, Cox Regression Where copyrighted material is quoted, permission has been obtained to use such material.Where material from documents designated for limited distribution is quoted, permission has been obtained to use the material.Citations o...

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Section: Note That (L R) Is a Function Of The Random Vector (U V Imentioning

confidence: 81%

Section: Dose-ranging Analysismentioning

confidence: 99%

mentioning

confidence: 99%

“…Sankhya, A. 60, 184-197.[e] Yu, Q., Schick, A., Li, L. and Wong, G. Y. C. (1998). Asymptotic properties of the GMLE of a survival function with case 2 interval-censored data.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Statistical Methods for Analyzing Time-Dependent Events in Breast Cancer Chemoprevention Studies.

Wong¹

1997

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Estimation of a Joint Distribution Function with Multivariate Interval-Censored Data when the Nonparametric MLE is not Unique

Wong

2000

Biom. J.

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An Independence Test for Doubly Censored Failure Time Data

Sun¹,

Lim

Zhao

2004

Biometrical J

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SummaryThe analysis of doubly censored failure time data has recently attracted a great deal of attention and for this, a number of methods have been proposed (De Gruttola and Lagakos, 1989;Kim et al., 1993;Pan, 2001;Sun, 2004). To simplify the analysis, most of these methods make an independence assumption: the distribution of the survival time of interest is independent of the occurrence of the initial event that defines the survival time. Although it is well-known that the assumption may not be true, there does not seem to be any existing research discussing the checking of the assumption. In this article, a Wald test is developed for testing this assumption and the method is applied to an AIDS cohort study.

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Asymptotic properties of the GMLE with case 2 interval-censored data

Cited by 39 publications

References 5 publications

Statistical Methods for Analyzing Time-Dependent Events in Breast Cancer Chemoprevention Studies.

Statistical Methods for Analyzing Time-Dependent Events in Breast Cancer Chemoprevention Studies.

Estimation of a Joint Distribution Function with Multivariate Interval-Censored Data when the Nonparametric MLE is not Unique

An Independence Test for Doubly Censored Failure Time Data

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