Using Auxiliary Data for Binomial Parameter Estimation with Nonignorable Nonresponse

Abstract

Nonignorable nonresponse is a nonresponse mechanism that depends on the values of the variable having nonresponse. When an observed data of a binomial distribution suffer missing values from a nonignorable nonresponse mechanism, the binomial distribution parameters become unidentifiable without any other auxiliary information or assumption. To address the problems of non identifiability, existing methods mostly based on the log-linear regression model. In this article, we focus on the model when the nonresponse is nonignorable and we consider to use the auxiliary data to improve identifiability; furthermore, we derive the maximum likelihood estimator (MLE) for the binomial proportion and its associated variance. We present results for an analysis of real-life data from the SARS study in China. Finally, the simulation study shows that the proposed method gives promising results.

Keywords:

• Identifiability
• Information matrix
• Nonignorable nonresponse
• Odds ratio
• Variance estimator

2000 Mathematics Subject Classification:

• 62F30

Acknowledgments

The authors would like to thank the Co-Editor, an Associate Editor, and anonymous referees for their valuable suggestions which greatly improved the presentation of this article. This research was supported by the National Natural Science Foundation of China (NSFC 10801019) and the Fundamental Research Funds for the Central Universities (BUPT 2012RC0708). Xiao-Hua (Andrew) Zhou, Ph.D., is presently a Core Investigator and Biostatistics Unit Director at the Northwest HSR&D Center of Excellence, Department of Veterans Affairs Medical Center, Seattle, WA. The views expressed in this article are those of the authors and do not necessarily represent the views of the Department of Veterans Affairs.