Statistical inference for right-censored data with nonignorable missing censoring indicators  

作　　者：SUN ZhiHua XIE TianFa LIANG Hua 

机构地区：[1]School of Mathematical Sciences, University of Chinese Academy of Sciences [2]College of Applied Sciences, Beijing University of Technology [3]Department of Biostatistics and Computational Biology, University of Rochester,Rochester, NY 14642, USA

出　　处：《Science China Mathematics》2013年第6期1263-1278,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 10901162 and 10926073);China Postdoctoral Science Foundation and Foundation of the Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences;supported by National Natural Science Foundation of China (Grant Nos. 10971007 and 11101015);the fund from the government of Beijing (Grant No. 2011D005015000007);supported by National Science Foundation of US (Grant Nos. DMS0806097 and DMS1007167)

摘　　要：We consider the statistical inference for right-censored data when censoring indicators are missing but nonignorable, and propose an adjusted imputation product-limit estimator. The proposed estimator is shown to be consistent and converges to a Gaussian process. Furthermore, we develop an empirical processbased testing method to check the MAR (missing at random) mechanism, and establish asymptotic properties for the proposed test statistic. To determine the critical value of the test, a consistent model-based bootstrap method is suggested. We conduct simulation studies to evaluate the numerical performance of the proposed method and compare it with existing methods. We also analyze a real data set from a breast cancer study for an illustration.We consider the statistical inference for right-censored data when censoring indicators are missing but nonignorable, and propose an adjusted imputation product-limit estimator. The proposed estimator is shown to be consistent and converges to a Gaussian process. Furthermore, we develop an empirical process- based testing method to check the MAR （missing at random） mechanism, and establish asymptotic properties for the proposed test statistic. To determine the critical value of the test, a consistent model-based bootstrap method is suggested. We conduct simulation studies to evaluate the numerical performance of the proposed method and compare it with existing methods. We also analyze a real data set from a breast cancer study for an illustration.

关 键 词：MAR mechanism testing nonignorable missing censoring indicators survival function QUASI-LIKELIHOOD 

分 类 号：O212.1[理学—概率论与数理统计] Q958.15[理学—数学]