A Pseudo-Bayesian Shrinkage Approach to Regression with Missing Covariates,∗ and Roderick J. Little2,∗∗1Florida 33612–3085, U.S.A. Department of Epidemiology & Biostatistics, College of Public Health, University of South Florida, Tampa, 2 Michigan 48109–2029, U.S.A. Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor,*email: email@example.com, ∗∗email: firstname.lastname@example.org
Nanhua Zhang 1
Summary.main interest is the effect of complete-case analysis (CC), which discards the incomplete cases, and (ii) ignorable likelihood methods, which base inference on the likelihood based on the observed data, assuming the missing data are missing at random (Rubin, 1976b), and (iii) nonignorable modeling, which posits a joint distribution of the variables and missing data indicators. Another simple practical approach that has not received much theoretical attention is to drop the regressor variables containing missing values from the regression modeling (DV, for drop variables). DV does not lead to bias when either (i) the regression coefficient of zero or (ii) compromises between the CC and DV estimates, exploiting information in the incomplete cases when the data support DV assumptions. We illustrate favorable properties of the method by simulation, and apply the proposed method to a liver cancer study. Extension of the method to more than one missing covariate is also discussed.
Complete-case analysis; Drop variables analysis; Gibbs sampling; Nonignorable modeling; Shrinkage;