群集資料下復發間隔時間之邊際存活函數的聯立信賴帶

Abstract

由於擁有長期追蹤資料的大型資料庫日益增加，因此如何從中有效地擷取有用的訊息以及如何處理群集的問題已是現在重要的議題。許多領域中，生物醫學與公共衛生領域方面，對於長期追蹤下的復發事件早已是常見的資料型態。Wang(2013)推廣Wang & Chang(1999)提出的無母數加權風險集合法，以處理群集和個體對復發事件所產生的影響來估計群集復發事件資料下復發間隔時間的邊際存活函數。Chang(2013)推導出對應的漸近常態化與穩健變異數估計。然而，群集復發資料下復發間隔時間的邊際存活函數估計時的整體不確定性卻未曾被討論，因此，我們將藉由無母數加權風險集合法的存活估計曲線與對應的變異數估計，來建構復發間隔時間的邊際存活函數的信賴帶。我們運用重抽法和拔靴法建構兩種信賴帶，並透過模擬比較兩者的估計表現。

As the result of prosperity of large databases with longitudinal data nowadays, acquiring informative data efficiently from them and resolving their clustering phenomenon have been an inevitable topic. Recurrent events are ubiquitous to be observed in longitudinal data in epidemiology and medical areas and many other areas. Non-parametric estimation of the marginal survival function of recurrent gap time for clustered recurrent event data by extending the weighted risk set method (Wang and Chang, 1999) to tackle the latent subject-specific and cluster-specific effects has been discussed by Wang (2013). The corresponding asymptotic normality and robust variance estimate were derived by Chang (2013). However, the global uncertainty of the estimated marginal function of recurrent gap times based on clustered recurrent event data has not yet been investigated. Hence, we construct the confidence bands of the marginal survival function of recurrent gap time by implementing its non-parametric weighted risk-set estimated survival curve and the corresponding variance estimates. We use resampling and bootstrapping methods to develop two types of confidence bands. The performance of the proposed confidence bands are evaluated by simulations.