Modeling nonignorable missing data for clustered longitudinal discrete outcomes: A Bayesian approach.

Abstract

This thesis develops Bayesian methods for analyzing clustered longitudinal data of discrete outcomes with nonignorable (NI) missing values. The research was motivated by an applied project that evaluates the effect of an intervention program to reduce the number of hospitalizations and to improve the quality of life (QOL) for asthma patients. Transition Markov models with random effects for Poisson and ordinal outcomes are used to model change in patients status over time. Current methods of fitting such models require complete data or restricted assumptions on the missing data. We propose Bayesian pattern-mixture models that have the flexibility to incorporate models for missing data in both outcome and time varying covariates. The underlying assumptions related to NI missing data are represented using easy to understand parameters, which are used to perform sensitivity analysis. Simulations results demonstrate that the proposed method is more efficient under certain conditions than standard methods, which perform poorly under nonignorable missing data mechanisms. The proposed method was applied to analyze the data from the asthma project. The results of the analyses show no evidence of an intervention effect on the number of hospitalizations during the first 12 month follow-up period. During the second follow up the rate of hospitalization for patients in the intervention group was reduced by 77% (95%<italic>CI</italic> = (26%, 93%)) when compared to patients in the control group. Sensitivity analysis showed that these findings hold under several NI missing data mechanisms. With respect to the QOL, the intervention effect was more likely to occur during the first follow-up period. There was some evidence that for parents with high QOL at baseline, the odds of having high QOL at the first follow-up were 1.65 (90%<italic>CI</italic> = (1.04, 2.60)) times higher for parents in the treatment group as compared to parents in the control group. There was no such evidence in the second follow-up period. These findings were unchanged even when different assumptions about the dropouts at the second follow-up were used. The proposed methodology can be implemented to other situations involving longitudinal data with discrete outcomes from studies with complex design.