D-MANOVA: fast distance-based multivariate analysis of variance for large-scale microbiome association studies

PERMANOVA (permutational multivariate analysis of variance based on distances) has been widely used for testing the association between the microbiome and a covariate of interest. Statistical significance is established by permutation, which is computationally intensive for large sample sizes. As large-scale microbiome studies, such as American Gut Project (AGP), become increasingly popular, a computationally efficient version of PERMANOVA is much needed. To achieve this end, we derive the asymptotic distribution of the PERMANOVA pseudo-F statistic and provide analytical P-value calculation based on chi-square approximation. We show that the asymptotic P-value is close to the PERMANOVA P-value even under a moderate sample size. Moreover, it is more accurate and an order-of-magnitude faster than the permutation-free method MDMR. We demonstrated the use of our procedure D-MANOVA on the AGP dataset.