The human microbiome plays an important role in human disease and health. Identification of factors that affect the microbiome composition can provide insights into disease mechanism as well as suggest ways to modulate the microbiome composition for therapeutical purposes. Distance-based statistical tests have been applied to test the association of microbiome composition with environmental or biological covariates. The unweighted and weighted UniFrac distances are the most widely used distance measures. However, these two measures assign too much weight either to rare lineages or to most abundant lineages, which can lead to loss of power when the important composition change occurs in moderately abundant lineages.