存活分析所使用的模型中最常使用的是乘法效應模型，例如，Cox 比
例風險模型、加速失敗AFT 模型，然而，在實際情況中，有一些生物
醫學研究的資料其共變數以加法效應描述較合適，故採用加法模型，例
如Aalen 加法模型。然而，現今醫學研究所蒐集的資料越來越複雜，在
眾多共變數中常有部分適合以乘法效應描述，而其餘部分適合以加法
效應描述，針對如此複雜的資料結構，更廣義的加乘法模型有其必要，
故本研究提出一個加乘法模型來分析資料，並以Weibull、loglogistic、lognormal 分配做為基底風險。另外，對於長期追蹤的共變數以混合效應模型來描述，參數估計以聯合概似函數透過EM 方法求得。乘法模型與加法模型均為加乘法模型之特殊案例，故可利用概似比檢定來做模型選擇。以模擬研究來評估本論文所提出之估計方法並以台灣愛滋病世代研究資料來驗證本論文新方法之實用性。

The most commonly used model for survival analysis is the multiplicative effect model, such as Cox proportional hazard model, accelerated failure time model. However, the covariates of some biomedical data are more appropriately described by additive effects, such as the Aalen additive model.In complicated data sets some of the covariates maybe suitable for multiplicative effects,
and others maybe suitable for additive effects. In this case, a more generalized additive-multiplicative model maybe appropriate for this kind of data. In this study, we propose an additive-multiplicative model to analyze data, and with the baseline hazards function based on Weibull, loglogitic and lognormal distribution.
In addition, the longitudinal covariates are described by the mix-effects model, and the parameters are estimated through the joint likelihood function using EM algorithm. The multiplicative model and additive model are the special case of the additive-multiplicative model, we may use the likelihood ratio test to do the model selection. The simulation study is used to evaluate the proposed
approach, which is applied to the data of Taiwanese HIV/AIDS cohort study to verify its usefulness.

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