使用最大概似估計法探討有母數擴充風險模型;Maximum likelihood estimation for parametric extended hazard model

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/68567

Title:	使用最大概似估計法探討有母數擴充風險模型;Maximum likelihood estimation for parametric extended hazard model
Authors:	陳怡瑄;Chen,I-Hsuan
Contributors:	統計研究所
Keywords:	存活資訊;擴充風險模型;概似比檢定;Survival;Extended hazard model;Likelihood ratio test
Date:	2015-07-21
Issue Date:	2015-09-23 12:37:54 (UTC+8)
Publisher:	國立中央大學
Abstract:	半母數存活模型在聯合模型中扮演著很重要的角色，有關聯合模型的文獻中，探討存活的部分大多假設為半母數模型，已經有許多估計參數的方法被提出，但是推導標準差時通常是透過拔靴法(bootstrap method) 而得到的，使用上相當費時。為補足文獻上的這項缺失，因此本篇將探討有母數存活模型，並透過費雪資訊(Fisher informatione) 有效率的得到標準差。在參數估計上，使用參數模型也比半母數模型更有效率，而且參數模型被廣泛應用在工業以及醫學上。而在參數模型的部分設定為存活分析中常用的Weibull、Log-logistic、 Gamma 以及Log-normal 四個分配。本篇使用最大概似估計法得到參數估計並計算各分配下擴充風險模型的 AIC 值與概似比統計量(likelihood ratio statistic)。由於擴充風險模型為Cox 模型與AFT 模型之廣義模型，本篇將擴充風險模型視為完整模型，將Cox 與AFT 模型視為簡約模型，因此概似比檢定可以幫助我們透過巢狀結構去做模型選擇，選擇AFT 模型或是Cox 模型。;So far, in joint model approaches, semi-parametric survival model has been played an important role for modelling event time data. Although many approaches have been proposed, the estimation encounters difficulties in deriving standard error estimates through bootstrap method, which is extremely time consuming. Therefore, to complement the literature, we employ parametric survival model for the joint model with standard error estimates obtained from Fisher information. The estimation of parametric joint model is dramatically faster than that of semiparametric one and thus is feasible for practical application. We assume four common parametric distributions in survival analysis, Weibull, Loglogistic, Log-normal, and Gamma distribution. We use the maximum likelihood approach to estimate parameter and to calculate AIC value, and likelihood ratio statistic to do model selection. Since the extended hazard model is the generalized model for Cox model and AFT model, we regard the extended hazard model as the full model. Also, we consider Cox model and AFT model as reduced model. Therefore, LRT can be conducted to do model selection through nested structure.
Appears in Collections:	[Graduate Institute of Statistics] Electronic Thesis & Dissertation

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