Multilevel models with binary responses: An application to group-randomized intervention trials with small number of clusters

There are several statistical methods commonly used for modeling correlated binary outcome data from cluster randomized trials. One such method is the multilevel (random effects) logistic regression model based on likelihood based estimation method. However, the use of likelihood based estimation approaches for fitting the multilevel logistic model is known to produce downwardly biased estimates for variance components particularly when the number of clusters is small.; The Bayesian methods based on the Gibbs sampling implementation of the Monte Carlo Markov Chain (MCMC) and the bootstrap procedure are suggested as alternatives to the likelihood based methods. The methods seem to provide unbiased estimation and correct confidence intervals. In practice however, little is known on how the likelihood-based estimation method compares with these simulation based estimation methods for fitting random effects logistic models, especially under the situation of small number of clusters.; In this thesis, we compare the performance of the three alternative approaches (likelihood-based, Bayesian MCMC and bootstrap) to estimate parameters of the multilevel logistic model by means of Monte Carlo simulation study and actual data set. Even though the bootstrap and Bayesian estimation procedures are computationally complex, our results suggest that these procedures produce type I error rates that are more closer to the nominal level than those obtained from the approximate likelihood based methods.; In addition, we examined the robustness of parameter estimates to the violation of the normality assumption for the random effects needed for likelihood estimation of the multilevel logistic model. We also examined the robustness of parameter estimates to different assumptions for the variance structure of the observations. Our results from simulation studies show that, when small clusters are employed, estimates of parameters for the multilevel logistic model are not entirely robust to misspecification of the distribution of the random effects. In addition, the results indicate that inference for cluster level covariates such as the intervention effect can be very sensitive to the assumed variance structure.