Improving Small-Sample Inference in Group Randomized Trials and Other Sources of Correlated Binary Outcomes.

Abstract

Group Randomized Trials (GRTs), along with many other types of studies, commonly can be composed of a small to moderate number of independent clusters of correlated data. In this dissertation, we focus on statistical inference in these settings. Particularly, we concentrate on test size and estimation variability when a marginal model is employed. Our first focus is in a general GRT setting in which a logistic regression only implements an indicator of treatment assignment. A Wald test, using a model-based standard error, for a marginal treatment effect can tend to have a realized test size smaller than its nominal value. We therefore propose a pseudo-Wald statistic that consistently produces test sizes at their nominal value, therefore increasing or maintaining power. Our second focus is on the estimation performance of QIF as compared to GEE when the number of clusters is not large, with a focus on GRT settings. GEE is commonly used for the analysis of correlated data, while QIF is a newer method with the theoretical advantage of being equally or more efficient. Therefore, it would be reasonable to believe that QIF should maintain or increase power in GRTs, which typically have low power. We show, however, that QIF may not have this advantage in GRT settings, and estimates from QIF can have greater variability than estimates from GEE due to the empirical impact of imbalance in cluster sizes and covariates, therefore concluding GEE is a more appropriate method in these settings. We finally focus on improving the small-sample estimation performance of QIF. Specifically, we propose multiple alternative weighting matrices to use in QIF that combat its small-sample deficiencies. These weighting matrices are expected to perform better in small-sample settings, such as for GRTs, but maintain QIF's large-sample advantages. We compare the performances of the proposed QIF modifications via simulations, which show they can improve small-sample estimation. We also demonstrate that two of the proposed QIF versions work best.Ph.D.BiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89710/1/pwestgat_1.pd