近年來存活分析應用於各領域中，所欲探討的事件並不一定會發生，且所觀察到的存活時間並不一定為連續型。當個體不會發生所欲探討的事件時，稱此個體為治癒個體。此外，當每一個個體所提供的存活資料為兩筆以上時，稱此個體內的存活資料為一集群資料，且同一集群內的存活資料具有相依性。但目前尚未有學者對集群離散存活資料於治癒模式下提供參數估計方法，所以本論文針對集群離散存活資料，將應用Yu和Peng (2008)所使用的邊際方法，求Zhao和Zhou (2008)所推導出非等比例治癒模式中參數的估計量。接著以模擬的方式，驗證參數估計量之一致性，且在不同設限比例與不同集群數下，探討參數估計量之表現。最後，以非等比例治癒模型探討植牙資料，利用邊際方法求得參數的估計量，以探討影響植牙發生併發症的因素。

Clustered survival data with a cure fraction arise naturally from biomedicine, econometrics and sociology studies. The mixture cure rate models have been well developed for univariate or multivariate (or clustered) continuous right censored data. When the correlation structure within clusters is not of interest, Yu and Peng (2008) used a marginal regression approach constructed estimating equations for estimating the parameters in mixture cure rate models.
Recently, Zhao and Zhou (2008) proposed discrete-time survival models with long-term survivors (cured individuals) for univariate grouped or discrete-time survival data. However, their methodologies can not be directly applied to clustered discrete-time survival data. Therefore, the marginal regression approach is proposed to construct estimating equations based on a non-proportional cure rate model. The accuracy of the estimators is examined by simulation. In addition, the implementation of the marginal approach to a dental implant study is presented.

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