江金倉Chiang, Chin-Tsang臺灣大學:數學研究所黃姿蓉Huang, Tzu-JungTzu-JungHuang2010-05-052018-06-282010-05-052018-06-282008U0001-2407200822272400http://ntur.lib.ntu.edu.tw//handle/246246/180587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)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, 我們利用機倒數加權法(Inverse Probability Weighting Method) 和替換法(Imputation Method)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(Terminalvents) 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。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,here is little attention on the study of relation between failure time(claiming time)nd mark variable(medicare reimbursement). Meanwhile, from the viewpoints ofrokers and the management in insurance company, it is more attractive and engrossingo capture the dynamic pattern so that our research interest would focus onhe joint distribution of claiming time and the corresponding medicare reimbursement.ased on survival censored data, we propose two estimation procedures:he inverse probability weighting (IPW) method and the imputation method. Furthermore,t is meaningful to accommodate terminal events occurring prior to theealization of failure time and the IPW method could lead to the resolution ofhis obstacle. Moreover, the limiting Gaussian processes of estimated distributionsnd the estimators of variance-covariance functions are developed and enable us toonstruct approximated regions. To investigate the finite sample properties of proposedstimators and the performance of inference procedures, a class of simulationsould be conducted. An application to the colorectal cancer data retrieved from the Surveillance, Epidemiology, and End Results (SEER) Medicare database is alsoresented. In the end, we provide a brief discussion and further research topics ofnterest.口試委員審定書iable of Contents iiist of Tables iiiist of Figures vcknowledgements vi要viibstract viii Introduction 1 Estimation and Inference Procedures without a Terminal Event 4.1 Review of Huang-Louis Estimator . . . . . . . . . . . . . . . . . . . . 4.2 IPW Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Imputation Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Inferences Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Estimation and Inference Procedures with Terminal Events 13 Numerical Studies 17.1 Simulation Setting of (Xo, Y o) . . . . . . . . . . . . . . . . . . . . . . 17.2 Senario I - Without a terminal event . . . . . . . . . . . . . . . . . . 18.3 Senario II - With terminal events . . . . . . . . . . . . . . . . . . . . 19 Application to Colorectal Cancer Data 32 Discussion 40ibliography 42application/pdf396576 bytesapplication/pdfen-US二元分配函數指標變數醫療成本設限終點事件機率倒數加權法替換法高斯過程bivariate distributionmark variablemedical costcensoringterminal eventsinverse probability weighting (IPW)imputationU-statisticsGaussian processes[SDGs]SDG3thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/180587/1/ntu-97-R95221014-1.pdf