A Sequential Density-Based Empirical Likelihood Ratio Test for Treatment Effects

TL;DR

This paper introduces a new distribution-free sequential testing method based on density-based empirical likelihood for detecting treatment effects in paired health data, demonstrating superior performance over traditional tests.

Contribution

The paper develops a novel sequential density-based empirical likelihood ratio test for treatment effects, extending nonparametric methods to sequential analysis with proven consistency.

Findings

Outperforms the sequential Wilcoxon signed-rank test in simulations.

Proven asymptotic consistency of the proposed test.

Successfully applied to a clinical pneumonia study.

Abstract

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.