title: Bayesian Sensitivity Analysis of Statistical Models with Missing Data.
abstract: Methods for handling missing data depend strongly on the mechanism that generated the missing values, such as missing completely at random (MCAR) or missing at random (MAR), as well as other distributional and modeling assumptions at various stages. It is well known that the resulting estimates and tests may be sensitive to these assumptions as well as to outlying observations. In this paper, we introduce various perturbations to modeling assumptions and individual observations, and then develop a formal sensitivity analysis to assess these perturbations in the Bayesian analysis of statistical models with missing data. We develop a geometric framework, called the Bayesian perturbation manifold, to characterize the intrinsic structure of these perturbations. We propose several intrinsic influence measures to perform sensitivity analysis and quantify the effect of various perturbations to statistical models. We use the proposed sensitivity analysis procedure to systematically investigate the tenability of the non-ignorable missing at random (NMAR) assumption. Simulation studies are conducted to evaluate our methods, and a dataset is analyzed to illustrate the use of our diagnostic measures.
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, 3109 McGavran-Greenberg Hall, Campus Box 7420, Chapel Hill, North Carolina 27516, U.S.A. hzhu@bios.unc.edu.
authors.forename: Hongtu
authors.initials: H
authors.lastname: Zhu
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, 3109 McGavran-Greenberg Hall, Campus Box 7420, Chapel Hill, North Carolina 27516, U.S.A. ibrahim@bios.unc.edu.
authors.forename: Joseph G
authors.initials: JG
authors.lastname: Ibrahim
authors.affiliation: Department of Statistics, Yunnan University, Kunming 650091, P. R. China nstang@ynu.edu.cn.
authors.forename: Niansheng
authors.initials: N
authors.lastname: Tang
keywords: Influence measure; Missing data mechanism; Perturbation manifold; Sensitivity analysis
references.citation: Biometrics. 2003 Jun;59(2):410-9
references.pmid: 12926726
references.citation: Biometrics. 2001 Mar;57(1):7-14
references.pmid: 11252620
references.citation: AIDS Care. 1998 Apr;10(2):213-20
references.pmid: 9625904
references.citation: Test (Madr). 2009 May 1;18(1):1-43
references.pmid: 21218187
references.citation: Biometrics. 2009 Dec;65(4):1164-74
references.pmid: 19210738
references.citation: Stat Med. 1998 Mar 15-Apr 15;17(5-7):767-79
references.pmid: 9549822
references.citation: Biometrika. 2011 Jun;98(2):307-323
references.pmid: 24453379