申訴理賠時間與醫療成本的二元分配函數

Abstract

目前有關二元分配函數分析的研究, 都集中於處理雙存活時間的資料結構, 以及探討其相關的 統計推論。有別於目前大部分的研究主題, 在這篇論文中, 我們關心存活時間(申訴理賠時間) 和指標變數(申訴產生的醫療理賠) 的二元分配函數。根據實際觀測的右設限資料, 我們利用機 率倒數加權法(Inverse Probability Weighting Method) 和替換法(Imputation Method) 提出了更具延伸性的估計式。同時, 我們也運用機率倒數加權法, 針對有終點事件(Terminal Events) 發生的情況, 提出相關的二元分配函數的估計式。進一步, 我們更建立上述估計式的 大樣本性質, 利用估計式的高斯過程逼近, 配合著變異矩陣的估計式, 建構其相對應的信賴區 間。我們執行了一系列的模擬檢證這些估計式以及信賴區間在有限樣本下之特性, 此外, 應用 所提出的估計法在SEER-Medicare 資料庫有關結腸癌的資料上。

Although numerous attempts have been made on bivariate failure times, however, there is little attention on the study of relation between failure time(claiming time) and mark variable(medicare reimbursement). Meanwhile, from the viewpoints of brokers and the management in insurance company, it is more attractive and engrossing to capture the dynamic pattern so that our research interest would focus on the joint distribution of claiming time and the corresponding medicare reimbursement. Based on survival censored data, we propose two estimation procedures: the inverse probability weighting (IPW) method and the imputation method. Furthermore, it is meaningful to accommodate terminal events occurring prior to the realization of failure time and the IPW method could lead to the resolution of this obstacle. Moreover, the limiting Gaussian processes of estimated distributions and the estimators of variance-covariance functions are developed and enable us to construct approximated regions. To investigate the finite sample properties of proposed estimators and the performance of inference procedures, a class of simulations would be conducted. An application to the colorectal cancer data retrieved from the Surveillance, Epidemiology, and End Results (SEER) Medicare database is also presented. In the end, we provide a brief discussion and further research topics of interest.