Regression analysis for bivariate gap time with missing first gap time data

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• 作者：Chia-Hui Huang ; Yi-Hau Chen
• 关键词：Bivariate duration time ; Counting process ; Dependent censoring ; Ordered data
• 刊名：Lifetime Data Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：23
• 期：1
• 页码：83-101
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics, general; Statistics for Life Sciences, Medicine, Health Sciences; Quality Control, Reliability, Safety and Risk; Statistics for Business/Economics/Mathematical Finance/Insurance; Operation
• 出版者：Springer US
• ISSN：1572-9249
• 卷排序：23

文摘

We consider ordered bivariate gap time while data on the first gap time are unobservable. This study is motivated by the HIV infection and AIDS study, where the initial HIV contracting time is unavailable, but the diagnosis times for HIV and AIDS are available. We are interested in studying the risk factors for the gap time between initial HIV contraction and HIV diagnosis, and gap time between HIV and AIDS diagnoses. Besides, the association between the two gap times is also of interest. Accordingly, in the data analysis we are faced with two-fold complexity, namely data on the first gap time is completely missing, and the second gap time is subject to induced informative censoring due to dependence between the two gap times. We propose a modeling framework for regression analysis of bivariate gap time under the complexity of the data. The estimating equations for the covariate effects on, as well as the association between, the two gap times are derived through maximum likelihood and suitable counting processes. Large sample properties of the resulting estimators are developed by martingale theory. Simulations are performed to examine the performance of the proposed analysis procedure. An application of data from the HIV and AIDS study mentioned above is reported for illustration.