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| Title: | 脆弱性Weibull迴歸模式之貝氏推論 |
| Other Titles: | Bayesian Inference for Weibull Regression Models with Frailty |
| Authors: | 陳麗霞 |
| Contributors: | 統計系 |
| Keywords: | 脆弱性,異質性,貝氏生存統計分析,Gibbs抽樣,正比危險函數,Weibull迴歸模式
Frailty heterogeneity,Bayesian survival analysis,Gibbs sampling,Proportional hazard function,Weibull regression model,Addpative rejectionsampling |
| Date: | 1995 |
| Issue Date: | 2014-07-28 11:40:50 (UTC+8) |
| Abstract: | 本研究在討論當觀察對象間具有異質性或脆弱性(Frailty)時,如何進行貝氏存活分析。為了加入脆弱因子於模式中,我們假定脆弱變數(z)對危險函數(Hazard function)具有相乘的效果,亦即h(t.lgvert.z,X)=z？h/sub 1/(t.lgvert.x)。我們所討論的問題為h/sub 1/(t.lgvert.x)是Weibull迴歸模式的危險函數,而脆弱變數服從Inverse Gaussian,Gamma,或Log-Normal分配。為進行貝氏分析,由於模式中各參數的邊際事後分配之精確形式未知,我們建議採用Clayton(1991)提出之Gibbs抽樣法及緩衝隨機替代法(Buffered stochastic substitution)的混合程序以產生各參數及脆弱性變數之抽樣值。此外,當條件事後密度函數的精確形式為未知時,我們以Gilks等人於1992及1994發展出的適應拒絕抽樣法(Adaptive rejection sampling)與適應拒絕Metropolis抽樣法(Adaptive rejection Metropolis sampling)產生參數之樣本,因而可估計邊際事後機率密度函數,事後動差,及預估的(Predictive)存活機率,並可推論脆弱性是否存在。
In this study we consider to perform Bayesian survival analysis with heterogeneity or frailty among subjects. To model fraitlies, it is assumed that the effect of the frailty variable, z, to the hazard function is multiplicative, i.e. h(t.lgvert.z,x)=zh/sub 1/(t.lgvert.x). We assume that h/sub 1/(t.lgvert.x) is the hazard function for Weibull regression model, and frailties follow in-verse Gaussian, Gamma, or log-Normal distribution. To conduct Bayesian analysis, since the exact form of the marginal posterior distribution of each parameter does not exist, we suggest to employ a mixture of Gibbs sampling and buffered stochastic substitution proposed by Clayton (1991) to perform Bayesian computation. To sample from conditional posterior densities, we take either adaptive rejection sampling (Gilks and Wild, 1992) or adaptive rejection Metropolis sampling (Gilks, et al, 1994) method, if their exact forms do not exist. Thus, estimates for marginal posterior densities, posterior expections, posterior variances, and predictive survival probabilities can be derived. Also, the Bayesian inference about whether frailties exist or not can be made. |
| Relation: | 行政院國家科學委員會
計畫編號 NSC84-2415-H004-006 |
| Data Type: | report |
| Appears in Collections: | [統計學系] 國科會研究計畫
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