  In health-related experiments, treatment effects can be identified using
paired data that consist of pre- and post-treatment measurements. In this
framework, sequential testing strategies are widely accepted statistical tools
in practice. Since performances of parametric sequential testing procedures
vitally depend on the validity of the parametric assumptions regarding
underlying data distributions, we focus on distribution-free mechanisms for
sequentially evaluating treatment effects. In fixed sample size designs, the
density-based empirical likelihood (DBEL) methods provide powerful
nonparametric approximations to optimal Neyman-Pearson type statistics. In this
article, we extend the DBEL methodology to develop a novel sequential DBEL
testing procedure for detecting treatment effects based on paired data. The
asymptotic consistency of the proposed test is shown. An extensive Monte Carlo
study confirms that the proposed test outperforms the conventional sequential
Wilcoxon signed-rank test across a variety of alternatives. The excellent
applicability of the proposed method is exemplified using the
ventilator-associated pneumonia study that evaluates the effect of
Chlorhexidine Gluconate treatment in reducing oral colonization by pathogens in
ventilated patients.
