加乘法風險模型結合長期追蹤資料之聯合模型;Joint Modeling of Additive-Multiplicative Hazard Model and Longitudinal Data

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题名:	加乘法風險模型結合長期追蹤資料之聯合模型;Joint Modeling of Additive-Multiplicative Hazard Model and Longitudinal Data
作者:	徐永東;Hsu,Yong-Dong
贡献者:	統計研究所
关键词:	比例風險模型;計數方法;聯合模型;加乘法模型
日期:	2016-07-21
上传时间:	2016-10-13 14:06:49 (UTC+8)
出版者:	國立中央大學
摘要:	許多存活分析研究中，常可發現Cox 比例風險模型被廣泛討論以及應用。然而，當Cox 模型處理多個共變量時，所有共變量均需滿足比例風險此條件，一旦有共變量違背，Cox 模型即無法使用。為了解決以上問題，本篇建議一個較廣義之Cox-Aalen 加乘法模型，將無法滿足Cox 比例風險假設的共變量放置於加法部分，使得模型得以使用。本篇將以Cox-Aalen 模型搭配現有之統計方法―計數方法，協助模擬之研究與愛滋病資料之分析。然而計數方法類似部分概似法，需有完整共變量歷史之要求並且無法容忍測量之誤差。而對應於部分概似法之聯合模型法不會有以上困難，因此，本篇於統計方法將以聯合模型法予以建模，進一步以EM -演算法做估計。;In many survival studies, we know that the Cox PH model is a popular model, which is widely discussed and applied in lots of situations. However, there is a problem if we use the Cox model with more covariates, It assumes that all covariates in the model should satisfy the proportional hazard assumption. Once one covariate fails to the assumption, the model can not be used. So in this paper, we suggest a way to solve this problem. We suggest using the Cox-Aalen model, and we put those covariates, failing to that assumption, into the additive part in the Cox-Aalen model, which provides a valid way to proceed in the research. In this paper, we will use a counting process method to help us do the simulation study and data analysis. However, the method is like the partial likelihood method, which needs complete covariate history and can not accommodate the measurement error. So, we will also construct the joint model, which is iii one of the best models to analyze the survival data combining with longitudinal data. Further, we do the parameter estimation with EM-algorithm.
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