A Note on MAR, Identifying Restrictions, Model Comparison, and Sensitivity Analysis in Pattern Mixture Models with and without Covariates for Incomplete Data

Authors

  • Chenguang Wang,

    Corresponding author
    1. Division of Biostatistics, Center for Devices and Radiological Health, FDA, Silver Spring, Maryland 20993, U.S.A.
      email: chenguang.wang@fda.hhs.gov
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  • Michael J. Daniels

    Corresponding author
    1. Department of Statistics, University of Florida, Gainesville, Florida 32611, U.S.A.
      email: mdaniels@stat.ufl.edu
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Errata

This article is corrected by:

  1. Errata: Correction to “A Note on MAR, Identifying Restrictions, Model Comparison, and Sensitivity Analysis in Pattern Mixture Models with and without Covariates for Incomplete Data,” by Chenguang Wang and Michael J. Daniels; 67, 810–818, September 2011 Volume 68, Issue 3, 994, Article first published online: 26 September 2012

email:chenguang.wang@fda.hhs.gov

email:mdaniels@stat.ufl.edu

Abstract

Summary Pattern mixture modeling is a popular approach for handling incomplete longitudinal data. Such models are not identifiable by construction. Identifying restrictions is one approach to mixture model identification (Little, 1995, Journal of the American Statistical Association90, 1112–1121; Little and Wang, 1996, Biometrics52, 98–111; Thijs et al., 2002, Biostatistics3, 245–265; Kenward, Molenberghs, and Thijs, 2003, Biometrika90, 53–71; Daniels and Hogan, 2008, in Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis) and is a natural starting point for missing not at random sensitivity analysis (Thijs et al., 2002, Biostatistics3, 245–265; Daniels and Hogan, 2008, in Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis). However, when the pattern specific models are multivariate normal, identifying restrictions corresponding to missing at random (MAR) may not exist. Furthermore, identification strategies can be problematic in models with covariates (e.g., baseline covariates with time-invariant coefficients). In this article, we explore conditions necessary for identifying restrictions that result in MAR to exist under a multivariate normality assumption and strategies for identifying sensitivity parameters for sensitivity analysis or for a fully Bayesian analysis with informative priors. In addition, we propose alternative modeling and sensitivity analysis strategies under a less restrictive assumption for the distribution of the observed response data. We adopt the deviance information criterion for model comparison and perform a simulation study to evaluate the performances of the different modeling approaches. We also apply the methods to a longitudinal clinical trial. Problems caused by baseline covariates with time-invariant coefficients are investigated and an alternative identifying restriction based on residuals is proposed as a solution.

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