title: Fully Bayesian inference under ignorable missingness in the presence of auxiliary covariates.
abstract: In order to make a missing at random (MAR) or ignorability assumption realistic, auxiliary covariates are often required. However, the auxiliary covariates are not desired in the model for inference. Typical multiple imputation approaches do not assume that the imputation model marginalizes to the inference model. This has been termed "uncongenial" [Meng (1994, Statistical Science 9, 538-558)]. In order to make the two models congenial (or compatible), we would rather not assume a parametric model for the marginal distribution of the auxiliary covariates, but we typically do not have enough data to estimate the joint distribution well non-parametrically. In addition, when the imputation model uses a non-linear link function (e.g., the logistic link for a binary response), the marginalization over the auxiliary covariates to derive the inference model typically results in a difficult to interpret form for the effect of covariates. In this article, we propose a fully Bayesian approach to ensure that the models are compatible for incomplete longitudinal data by embedding an interpretable inference model within an imputation model and that also addresses the two complications described above. We evaluate the approach via simulations and implement it on a recent clinical trial.
authors.affiliation: Division of Statistics and Scientific Computation and Section of Integrative Biology, University of Texas at Austin, Austin, Texas 78712, U.S.A.
authors.forename: M J
authors.initials: MJ
authors.lastname: Daniels
authors.forename: C
authors.initials: C
authors.lastname: Wang
authors.forename: B H
authors.initials: BH
authors.lastname: Marcus
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D001499:Bayes Theorem; D001521:Behavior Therapy; D002248:Carbon Monoxide / Q000032:analysis; D003198:Computer Simulation; D003367:Cotinine / Q000032:analysis; D003627:Data Interpretation, Statistical; D015444:Exercise; D005260:Female; D006801:Humans; D008137:Longitudinal Studies / Q000379:methods*; D008875:Middle Aged; D015233:Models, Statistical; D016540:Smoking Cessation / Q000379:methods / Q000523:psychology; D055815:Young Adult
chemical_list: D002248:Carbon Monoxide; D003367:Cotinine
keywords: Auxiliary variable MAR; Congenial imputation; Marginalized models; Multiple imputation