A Bayesian Shrinkage Model for Incomplete Longitudinal Binary Data With Application to the Breast Cancer Prevention Trial

• Published in: Journal of the American Statistical Association Vol. 105; no. 492; pp. 1333 - 1346
• Main Authors: Wang, C., Daniels, M. J., Scharfstein, D. O., Land, S.
• Format: Journal Article
• Language: English
• Published: Alexandria, VA American Statistical Association 01.12.2010; Taylor & Francis Ltd
• Subjects: Applications; Applications and Case Studies; Bayesian analysis; Bayesian method; Binary data; Biometrics; Breast cancer; Cancer; Clinical trials; Disease prevention; Distribution; Distribution theory; Exact sciences and technology; Experimentation; General topics; Inference; Linear inference, regression; Longitudinal studies; Mathematics; Medicine; Methodology; Missing data; Modeling; Parametric models; Placebos; Probability and statistics; Probability theory and stochastic processes; Sample size; Sciences and techniques of general use; Statistical inference; Statistics; Bayes estimation; Ridge regression; Breast disease; Prior distribution; Shrinkage estimator; Binary data; Statistical estimation; Breast cancer; Parametric model; Statistical simulation; Functional; Parametric method; Statistical method; Prevention; Statistical regression; Missing data; Informative drop-out; Distribution function; Observation data; Prior elicitation; Exponential model; Incomplete information; Intermittent missingness
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/jasa.2010.ap09321

We consider inference in randomized longitudinal studies with missing data that is generated by skipped clinic visits and loss to followup. In this setting, it is well known that full data estimands are not identified unless unverified assumptions are imposed. We assume a nonfuture dependence model for the drop-out mechanism and partial ignorability for the intermittent missingness. We posit an exponential tilt model that links nonidentifiable distributions and distributions identified under partial ignorability. This exponential tilt model is indexed by nonidentified parameters, which are assumed to have an informative prior distribution, elicited from subject-matter experts. Under this model, full data estimands are shown to be expressed as functionals of the distribution of the observed data. To avoid the curse of dimensionality, we model the distribution of the observed data using a Bayesian shrinkage model. In a simulation study, we compare our approach to a fully parametric and a fully saturated model for the distribution of the observed data. Our methodology is motivated by, and applied to, data from the Breast Cancer Prevention Trial.