Empirical Likelihood Approaches to Two-Group Comparisons of Upper Quantiles Applied to Biomedical Data

In many biomedical studies, a difference in upper quantiles is of specific interest since the upper quantile represents the upper range of biomarkers and/or is used as the cutoff value for a disease classification. In this article, we investigate two-group comparisons of an upper quantile based on the empirical likelihood methodology. Two approaches, the classical empirical likelihood and "plug-in" empirical likelihood, are used to construct the test statistics and their properties are theoretically investigated. Although the plug-in method is developed by the framework of the empirical likelihood, the test statistic is not based on maximization of the empirical likelihood and is simplified by using an indicator function in its construction, making it a unique test to investigate. Extensive simulation results demonstrate that the "plug-in" empirical likelihood approach performs better to compare upper quantiles across various underlying distributions and sample sizes. For the actual application, we employ the developed methods to test the differences in upper quantiles in two different studies: oral colonization of pneumonia pathogens for intensive care unit patients treated by two different oral treatments, and biomarker expressions of normal and abnormal bronchial epithelial cells.