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Non‐ignorable missing covariates in generalized linear models
Author(s) -
Lipsitz Stuart R.,
Ibrahim Joseph G.,
Chen MingHui,
Peterson Harriet
Publication year - 1999
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/(sici)1097-0258(19990915/30)18:17/18<2435::aid-sim267>3.0.co;2-b
Subject(s) - covariate , categorical variable , missing data , statistics , mathematics , logistic regression , econometrics
We propose a likelihood method for estimating parameters in generalized linear models with missing covariates and a non‐ignorable missing data mechanism. In this paper, we focus on one missing covariate. We use a logistic model for the probability that the covariate is missing, and allow this probability to depend on the incomplete covariate. We allow the covariates, including the incomplete covariate, to be either categorical or continuous. We propose an EM algorithm in this case. For a missing categorical covariate, we derive a closed form expression for the E‐ and M‐steps of the EM algorithm for obtaining the maximum likelihood estimates (MLEs). For a missing continuous covariate, we use a Monte Carlo version of the EM algorithm to obtain the MLEs via the Gibbs sampler. The methodology is illustrated using an example from a breast cancer clinical trial in which time to disease progression is the outcome, and the incomplete covariate is a quality of life physical well‐being score taken after the start of therapy. This score may be missing because the patients are sicker, so this covariate could be non‐ignorably missing. Copyright © 1999 John Wiley & Sons, Ltd.