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.
