Statistical Modelling 20 (3) (2020), 310–338

A Bayesian transition model for missing longitudinal binary outcomes and an application to a smoking cessation study

Li Li,
Department of Mathematics and Statistics,
University of New Mexico,
Albuquerque, NM,
USA
e-mail: llis@unm.edu

Ji-Hyun Lee,
Division of Quantitative Sciences,
University of Florida Health Cancer Center; Department of Biostatistics,
University of Florida,
Gainesville, FL,
USA


Steven K Sutton,
Department of Biostatistics and Bioinformatics,
Moffitt Cancer Center,
Tampa, FL,
USA


Vani N Simmons,
Department of Health Outcomes and Behaviour,
Moffitt Cancer Center,
Tampa, FL,
USA


Abstract:

Smoking cessation intervention studies often produce data on smoking status at discrete follow-up assessments, often with missing data in different amounts at each assessment. Smoking status in these studies is a dynamic process with individuals transitioning from smoking to abstinent, as well as abstinent to smoking, at different times during the intervention. Directly assessing transitions provides an opportunity to answer important questions like ‘Does the proposed intervention help smokers remain abstinent or quit smoking more effectively than other interventions?’ In this article, we model changes in smoking status and examine how interventions and other covariates affect the transitions. We propose a Bayesian approach for fitting the transition model to the observed data and impute missing outcomes based on a logistic model, which accounts for both missing at random (MAR) and missing not at random (MNAR) mechanisms. The proposed Bayesian approach treats missing data as additional unknown quantities and samples them from their posterior distributions. The performance of the proposed method is investigated through simulation studies and illustrated by data from a randomized controlled trial of smoking cessation interventions. Finally, posterior predictive checking and log pseudo marginal likelihood (LPML) are used to assess model assumptions and perform model comparisons, respectively.

Keywords:

transition model; Bayesian method; generalized linear mixed model; missing values; smoking cessation.

Downloads:

Example data and code in zipped archive.
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