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Bayesian Sensitivity Analysis for Non-ignorable Missing Data in Longitudinal Studies

Author

Listed:
  • Tian Li

    (Simon Fraser University)

  • Julian M. Somers

    (Simon Fraser University)

  • Xiaoqiong J. Hu

    (Simon Fraser University)

  • Lawrence C. McCandless

    (Simon Fraser University
    Simon Fraser University)

Abstract

The use of Bayesian statistical methods to handle missing data in biomedical studies has become popular in recent years. In this paper, we propose a novel Bayesian sensitivity analysis (BSA) technique that accounts for the influences of missing outcome data on the estimation of treatment effects in longitudinal studies with non-ignorable missing data. The approach uses a pattern-mixture model for the complete data, which is indexed by non-identifiable sensitivity parameters that accounts for the effect of missingness on the observations. We implement the method using the probabilistic programming language Stan, and apply it to data from the Vancouver At Home Study, which is a randomized control trial that provided housing to homeless people with mental illness. We compare the results of BSA to those from an existing Bayesian longitudinal model that ignores the missing data mechanism in the outcome. Furthermore, we demonstrate in a simulation study that when we use a diffuse conservative prior that describes a range of assumptions about the non-ignorable missingness, then BSA credible intervals have greater length and higher coverage rate of the target parameters than existing methods.

Suggested Citation

  • Tian Li & Julian M. Somers & Xiaoqiong J. Hu & Lawrence C. McCandless, 2019. "Bayesian Sensitivity Analysis for Non-ignorable Missing Data in Longitudinal Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(1), pages 184-205, April.
    • Handle: RePEc:spr:stabio:v:11:y:2019:i:1:d:10.1007_s12561-019-09234-6
    DOI: 10.1007/s12561-019-09234-6
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    References listed on IDEAS

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    1. van Buuren, Stef & Groothuis-Oudshoorn, Karin, 2011. "mice: Multivariate Imputation by Chained Equations in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 45(i03).
    2. Uttaro, Thomas & Lehman, Anthony, 1999. "Graded response modeling of the Quality of Life Interview," Evaluation and Program Planning, Elsevier, vol. 22(1), pages 41-52.
    3. Siddique, Juned & Belin, Thomas R., 2008. "Using an Approximate Bayesian Bootstrap to multiply impute nonignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 405-415, December.
    4. Chenguang Wang & Michael J. Daniels, 2011. "A Note on MAR, Identifying Restrictions, Model Comparison, and Sensitivity Analysis in Pattern Mixture Models with and without Covariates for Incomplete Data," Biometrics, The International Biometric Society, vol. 67(3), pages 810-818, September.
    5. Kaciroti, Niko A. & Raghunathan, Trivellore E. & Schork, M. Anthony & Clark, Noreen M. & Gong, Molly, 2006. "A Bayesian Approach for Clustered Longitudinal Ordinal Outcome With Nonignorable Missing Data: Evaluation of an Asthma Education Program," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 435-446, June.
    6. Niko A. Kaciroti & Trivellore E. Raghunathan & M. Anthony Schork & Noreen M. Clark, 2008. "A Bayesian model for longitudinal count data with non‐ignorable dropout," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(5), pages 521-534, December.
    7. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
    8. Nandram B. & Choi J.W., 2002. "Hierarchical Bayesian Nonresponse Models for Binary Data From Small Areas With Uncertainty About Ignorability," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 381-388, June.
    Full references (including those not matched with items on IDEAS)

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