A Latent Autoregressive Model for Longitudinal Binary Data Subject to Informative Missingness

Authors

  • Paul S. Albert,

    Corresponding author
    1. Biometric Research Branch, National Cancer Institute, National Institutes of Health, Bethesda, Maryland 20892, U.S.A.
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  • Dean A. Follmann,

    1. Office of Biostatistics Research, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, U.S.A.
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  • Shaohua A. Wang,

    1. Division of Computational Biosciences, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, U.S.A.
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  • Edward B. Suh

    1. Division of Computational Biosciences, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, U.S.A.
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*email:albertp@ctep.nci.nih.gov

Abstract

Summary. Longitudinal clinical trials often collect long sequences of binary data. Our application is a recent clinical trial in opiate addicts that examined the effect of a new treatment on repeated binary urine tests to assess opiate use over an extended follow-up. The dataset had two sources of missingness: dropout and intermittent missing observations. The primary endpoint of the study was comparing the marginal probability of a positive urine test over follow-up across treatment arms. We present a latent autoregressive model for longitudinal binary data subject to informative missingness. In this model, a Gaussian autoregressive process is shared between the binary response and missing-data processes, thereby inducing informative missingness. Our approach extends the work of others who have developed models that link the various processes through a shared random effect but do not allow for autocorrelation. We discuss parameter estimation using Monte Carlo EM and demonstrate through simulations that incorporating within-subject autocorrelation through a latent autoregressive process can be very important when longitudinal binary data is subject to informative missingness. We illustrate our new methodology using the opiate clinical trial data.

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