Two-sample density-based empirical likelihood ratio tests based on paired data, with application to a treatment study of attention-deficit/hyperactivity disorder and severe mood dysregulation

It is a common practice to conduct medical trials to compare a new therapy with a standard-of-care based on paired data consisted of pre- and post-treatment measurements. In such cases, a great interest often lies in identifying treatment effects within each therapy group and detecting a between-group difference. In this article, we propose exact nonparametric tests for composite hypotheses related to treatment effects to provide efficient tools that compare study groups utilizing paired data. When correctly specified, parametric likelihood ratios can be applied, in an optimal manner, to detect a difference in distributions of two samples based on paired data. The recent statistical literature introduces density-based empirical likelihood methods to derive efficient nonparametric tests that approximate most powerful Neyman-Pearson decision rules. We adapt and extend these methods to deal with various testing scenarios involved in the two-sample comparisons based on paired data. We show that the proposed procedures outperform classical approaches. An extensive Monte Carlo study confirms that the proposed approach is powerful and can be easily applied to a variety of testing problems in practice. The proposed technique is applied for comparing two therapy strategies to treat children's attention deficit/hyperactivity disorder and severe mood dysregulation.