MOTIVATION: Microbiome datasets provide rich information about microbial communities. However, vast library size variations across samples present great challenges for proper statistical comparisons. To deal with these challenges, rarefaction is often used in practice as a normalization technique, although there has been debate whether rarefaction should ever be used. Conventional wisdom and previous work suggested that rarefaction should never be used in practice, arguing that rarefying microbiome data is statistically inadmissible. These discussions, however, have been confined to particular parametric models and simulation studies. RESULTS: We develop a semiparametric graphical model framework for grouped microbiome data and analyze in the context of differential abundance testing the statistical trade-offs of the rarefaction procedure, accounting for latent variations and measurement errors. Under the framework, it can be shown rarefaction guarantees that subsequent permutation tests properly control the Type I error. In addition, the loss in sensitivity from rarefaction is solely due to increased measurement error; if the underlying variation in microbial composition is large among samples, rarefaction might not hurt subsequent statistical inference much. We develop the rarefaction efficiency index (REI) as an indicator for efficiency loss and illustrate it with a dataset on the effect of storage conditions for microbiome data. Simulation studies based on real data demonstrate that the impact of rarefaction on sensitivity is negligible when overdispersion is prominent, while low REI corresponds to scenarios in which rarefying might substantially lower the statistical power. Whether to rarefy or not ultimately depends on assumptions of the data generating process and characteristics of the data. AVAILABILITY AND IMPLEMENTATION: Source codes are publicly available at https://github.com/jcyhong/rarefaction. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Ordered testing procedures are multiple testing procedures that exploit a pre-specified ordering of the null hypotheses, from most to least promising. We analyze and compare the power of several recent proposals using the asymptotic framework of Li & Barber (2015). While accumulation tests including ForwardStop can be quite powerful when the ordering is very informative, they are asymptotically powerless when the ordering is weaker. By contrast, Selective SeqStep, proposed by Barber & Candes (2015), is much less sensitive to the quality of the ordering. We compare the power of these procedures in different regimes, concluding that Selective SeqStep dominates accumulation tests if either the ordering is weak or non-null hypotheses are sparse or weak. Motivated by our asymptotic analysis, we derive an improved version of Selective SeqStep which we call Adaptive SeqStep, analogous to Storey’s improvement on the Benjamini-Hochberg procedure. We compare these methods using the GEO-Query data set analyzed by (Li & Barber, 2015) and find Adaptive SeqStep has favorable performance for both good and bad prior orderings.