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Measurement error in the Cox regress...

Zhong, Ming.

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Measurement error in the Cox regression model.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Measurement error in the Cox regression model./
作者:	Zhong, Ming.
面頁冊數:	132 p.
附註:	Directors: Pranab K. Sen; Jianwen Cai.
Contained By:	Dissertation Abstracts International61-04B.
標題:	Biology, Biostatistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9968707
ISBN:	0599735376

Measurement error in the Cox regression model.
Zhong, Ming.

Measurement error in the Cox regression model. - 132 p.

Directors: Pranab K. Sen; Jianwen Cai.

Thesis (Ph.D.)--The University of North Carolina at Chapel Hill, 2000.

Through theoretical evaluations and simulations, we conclude that the proposed plug-in semiparametric method is an appropriate method in general settings to estimate the regression parameters in the Cox model with measurement error.

ISBN: 0599735376Subjects--Topical Terms:

1018416
Biology, Biostatistics.

Measurement error in the Cox regression model.
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245 1 0 $a Measurement error in the Cox regression model.
300 $a 132 p.
500 $a Directors: Pranab K. Sen; Jianwen Cai.
500 $a Source: Dissertation Abstracts International, Volume: 61-04, Section: B, page: 2025.
502 $a Thesis (Ph.D.)--The University of North Carolina at Chapel Hill, 2000.
520 $a Through theoretical evaluations and simulations, we conclude that the proposed plug-in semiparametric method is an appropriate method in general settings to estimate the regression parameters in the Cox model with measurement error.
520 $a Standard regression methods are developed assuming accurate measurement of the covariates. When variables are measured with error, appropriate adjustment should be made. The aim of this dissertation is to study an estimating procedure for the Cox's regression model with presence of non-differential measurement error in the covariates.
520 $a Existing methods in this area include (1) the calibration method which replaces the unobserved covariate by its expectation conditioned on the observed covariate; (2) the induced hazard method which estimates the risk of those with unobserved data by averaging those with matching covariate in the validation sample; (3) the step function approximation method which converts the semiparametric problem into a parametric problem through parameterizing the nonparametric baseline hazard function λ(<italic> t</italic>) by a step function; and (4) the point-mass assumption method which assumes point-mass function of λ(<italic>t</italic>) at the observed failure times and treats the semiparametric model as a parametric model.
520 $a In this dissertation, we propose and study the following Cox-type plug-in semiparametric method. It consists of two steps: the polynomial approximation and the Cox-type semiparametric estimation. At the first step, the nonparametric λ(<italic> t</italic>) is approximated by an exponential of a polynomial function and the EM algorithm is used to obtain the approximate estimators. At the second step, the underlying parameters in the conditional arguments are replaced by the approximation estimators and the Cox semiparametric procedure is proceeded treating the approximation estimators as fixed. The reason of including the first step is that the convergence and consistence properties of the EM algorithm are unknown for semiparametric models.
520 $a When the underlying log λ(<italic>t</italic>) is a polynomial function, the proposed estimators are <math> <f> <rad><rcd>n</rcd></rad></f> </math>-consistent, asymptotically normal, and efficient. If the approximation function over-fits the underlying function, <math> <f> <rad><rcd>n</rcd></rad></f> </math>-consistency retains for the proposed method, although the efficiency is reduced due to over-parameterization. When the approximation function under-fits the underlying function, bias will be introduced. Because of the semiparametric estimation step, however, the bias is less than that of using the parametric approximation only. Since according to the Weierstrass Approximation Theorem, any continuous function of log λ(<italic>t</italic>) can be approximated arbitrarily well by a polynomial function, consistency of the proposed method holds for general models. The rate of convergence, however, may be less than <math> <f> <rad><rcd>n</rcd></rad></f> </math> depending on the nature of the underlying function. This is a trade-off of gaining robustness in model assumption. These results can be generalized to non-polynomial models used the approximation step.
590 $a School code: 0153.
650 4 $a Biology, Biostatistics. $3 1018416
650 4 $a Health Sciences, Public Health. $3 1017659
650 4 $a Statistics. $3 517247
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710 2 0 $a The University of North Carolina at Chapel Hill. $3 1017449
773 0 $t Dissertation Abstracts International $g 61-04B.
790 $a 0153
790 1 0 $a Cai, Jianwen, $e advisor
790 1 0 $a Sen, Pranab K., $e advisor
791 $a Ph.D.
792 $a 2000
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9968707