llperm: a permutation of regressor residuals test for microbiome data.

Background: Differential abundance testing is an important aspect of microbiome data analysis, where each taxa is fitted with a statistical test or a regression model. However, many models do not provide a good fit to real microbiome data. This has been shown to result in high false positive rates. Permutation tests are a good alternative, but a regression approach is desired for small data sets with many covariates, where stratification is not an option.

Results: We implement an R package 'llperm' where the The Permutation of Regressor Residuals (PRR) test can be applied to any likelihood based model, not only generalized linear models. This enables distributions with zero-inflation and overdispersion, making the test suitable for count regression models popular in microbiome data analysis. Simulations based on a real data set show that the PRR-test approach is able to maintain the correct nominal false positive rate expected from the null hypothesis, while having equal or greater power to detect the true positives as models based on likelihood at a given false positive rate.

Conclusions: Standard count regression models can have a shockingly high false positive rate in microbiome data sets. As they may lead to false conclusions, the guaranteed nominal false positive rate gained from the PRR-test can be viewed as a major benefit.