A Bayesian Approach for Clustered Longitudinal Ordinal Outcome With Nonignorable Missing Data

Abstract

Asthma, a chronic inflammatory disease of the airways, affects an estimated 6.3 million children under age 18 in the United States. A key to successful asthma management, and hence improved quality of life (QOL), calls for an active partnership between asthma patients and their health care providers. To foster this partnership, an intervention program was designed and evaluated using a randomized longitudinal study. The study focused on several outcomes where typically missing data remained a pervasive problem. We suspected that the underlying missing-data mechanism may not be ignorable. Thus here we present a method for analyzing clustered longitudinal data with missing values resulting from a nonignorable missing-data mechanism. The transition Markov model with random effects was used to investigate changes in ordinal outcomes over time. A Bayesian pattern-mixture model with the flexibility to incorporate models for missing data in both outcome and time-varying covariates was used to model the nonignorable missing-data mechanism. The pattern-mixture model uses easy-to-understand parameters—namely, ratios of the cumulative odds across patterns with the complete-data pattern—as the reference pattern. Sensitivity analysis was performed using different prior distributions for the parameters. A fully Bayesian approach was derived by integrating over a class of prior distributions. The data from the Asthma Intervention Study were analyzed to explore the effect of the intervention program on improving QOL.