Power and sample-size estimation for microbiome studies using pairwise distances and PERMANOVA

Abstract

Motivation: The variation in community composition between microbiome samples, termed beta diversity, can be measured by pairwise distance based on either presence-absence or quantitative species abundance data. PERMANOVA, a permutation-based extension of multivariate analysis of variance to a matrix of pairwise distances, partitions within-group and between-group distances to permit assessment of the effect of an exposure or intervention (grouping factor) upon the sampled microbiome. Within-group distance and exposure/intervention effect size must be accurately modeled to estimate statistical power for a microbiome study that will be analyzed with pairwise distances and PERMANOVA. Results: We present a framework for PERMANOVA power estimation tailored to marker-gene microbiome studies that will be analyzed by pairwise distances, which includes: (i) a novel method for distance matrix simulation that permits modeling of within-group pairwise distances according to pre-specified population parameters; (ii) a method to incorporate effects of different sizes within the simulated distance matrix; (iii) a simulation-based method for estimating PERMANOVA power from simulated distance matrices; and (iv) an R statistical software package that implements the above. Matrices of pairwise distances can be efficiently simulated to satisfy the triangle inequality and incorporate group-level effects, which are quantified by the adjusted coefficient of determination, omega-squared (x2). From simulated distance matrices, available PERMANOVA power or necessary sample size can be estimated for a planned microbiome study.