Two-Sample Empirical Likelihood Ratio Tests for Paired Data Applied to a Treatment Study of Attention-Deficit/Hyperactivity Disorder and Severe Mood Dysregulation

• Activity Number: 662
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Wan-Min Tsai*+ and Albert Vexler and Gregory Gurevich
• Companies: University at Buffalo and New York State University at Buffalo and Shamoon College of Engineering
• Keywords: empirical likelihood ; paired data ; two-sample problem ; nonparametric test ; Parametric likelihood

Abstract

In biology and epidemiology, we often study paired data from an experiment using a group with different treatments on homogeneous subjects or units in order to investigate if there is any treatment difference in a group, indicating different kinds of treatment effects. This motivates us to test if there is any treatment effect in a new and old therapy group in addition to testing any therapy group difference. Parametric likelihood ratios can efficiently be applied to these problems in practice provided that corresponding parametrical assumptions are correct. In many cases, we cannot assume parametric form of distributions. Recently, a density-based empirical likelihood methodology has been created to provide efficient tools to construct nonparametric tests that approximate Neyman-Pearson test statistics. We adapt and extend this method to deal with various testing scenarios involved in the two-sample testing problems based on paired data. We apply to a real data example that examines the efficacy of a group-based therapy program for children with Attention-Deficit/Hyperactivity Disorder and severe Mood Dysregulation, demonstrating the practical applicability of the proposed tests.