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Multinomial, Dirichlet-multinomial, and gamma-Poisson parameters were fit using actual OTU tables from many global environments.
Fold change represents the fold change of the true positive OTUs from one condition e. The height of each bar represents the median value from three simulations. Vertical lines extend to the upper quartile of the simulation results. Blue lines in, e. Differential abundance detection false discovery rate with varied library sizes that are approximately even on average between groups.
For simplicity, only those methods where the FDR exceeds or is close to 0. Full methods are in Additional file 7 : Figure S6. Labels are the same as in Fig. We recognize that the multinomial and the Dirichlet-multinomial DM distributions are not necessarily appropriate for the microbial taxon counts because under such probability distributions, every pair of taxa are negatively correlated, whereas as discussed in Mosimann [ 39 ] and Mandal et al.
However, because multinomial and DM distributions have been used by several authors [ 50 , 67 , 68 ], we include those distributions in our simulation study for purely comparative purposes.
Additionally, we simulate data using the gamma-Poisson [ 7 ] Figs. As expected, sensitivity increased with library size, but much more so for higher sample sizes, for all methods. Again as expected, for the nonparametric methods and small sample sizes, sensitivity was lower compared to parametric methods. For the parametric methods, in particular fitZIG and edgeR, the underlying data distribution changed results dramatically Fig.
Also, the 0. One of the objectives of a microbiome study is to compare the abundance of taxa in the ecosystem of two or more groups using the observed taxa abundance in specimens drawn from the ecosystem. As noted in Mandal et al. Thus, drawing inferences regarding the mean taxon abundance between ecosystems using the specimen level data is a challenging problem.
We performed a simulation study to evaluate the performance of various methods in terms of the false discovery rate and power when testing hypotheses regarding mean taxon abundance between ecosystems using the specimen level data. Proportion normalization is known to have high FDR when faced with compositional data [ 6 ]. Because most researchers want to infer ecosystem taxon relative abundances from sampling, this indicates a large previously unsolved problem in differential abundance testing [ 6 ].
Differential abundance detection performance when sample relative abundances do not reflect ecosystem relative abundances. For simplicity, only a multinomial model of OTUs was used, but is the same model as that in Figs.
Most methods, except fitZIG, correctly predict no or very few false positives and are more conservative with decreasing sample size. However, for uneven library sizes and with 20— samples per group Fig.
This was especially so for the no normalization and proportion normalization approaches. The lack of increased type I error with rarefied data could simply be due to the loss of power resulting from rarefied data [ 18 ].
Additionally, manually adding a pseudocount e. Instead, one may consider standard zero imputation methods [ 69 ]. This suggests that in the case of very small systematic biases, rank-based non-parametric tests except fitZIG could actually underperform parametric tests, as they do not take into account effect sizes.
However, more investigation is necessary. False discovery rate increases when methods are challenged with very uneven library sizes. Real data from one body site was randomly divided into two groups, creating a situation in which there should be no true positives. Voom was excluded because it was found to have a higher type I error rate than fitZIG. While the no normalization or proportion approaches control the FDR in cases where the average library size is approximately the same between the two groups Figs.
Therefore, we reiterate that neither the no normalization nor the sample proportion approach should be used for most statistical analyses. To demonstrate this, we suggest the theoretical example of a data matrix with half the samples derived from diseased patients and half from healthy patients.
The same warning applies for proportions, especially for rare OTUs that could be deemed differentially abundant because the rare OTUs may not be detected zero values in low library size samples, but are non-zero in high library size samples. Ranges of dataset sizes were analyzed for environments that likely contain differentially abundant OTUs, as evidenced by the previously published PCoA plots and significance tests Fig. Six human skin and eight soil samples from Caporaso et al.
Although we do not necessarily know which OTUs are true positives in these actual data, it is of interest to investigate how the most promising techniques compare to each other.
Additionally, in Fig. While the disagreement in significantly differentially abundant OTU predictions decreases with increased library size, there is concern that simulations, no matter how carefully constructed, cannot mimic the complexity of real microbiome data. On real datasets, methods disagree especially for few samples per group.
Darker colors indicate a larger proportion of OTUs discovered by a technique or combination of techniques. We confirm that recently developed more complex techniques for normalization and differential abundance testing hold potential. Of methods for normalizing microbial data for ordination analysis, we found that DESeq normalization [ 30 , 42 ], which was developed for RNA-Seq data and makes use of a log-like transformation, does not work well with ecologically useful metrics, except weighted UniFrac [ 58 ].
DESeq normalization requires more development for general use on microbiome data. With techniques other than rarefying, library size is a frequent confounding factor that obscures biologically meaningful results.
The approaches of no normalization and sample proportion are prone to generation of artifactual clusters based on sequencing depth in beta diversity analysis.
Therefore, researchers should proceed with caution and check for these effects in ordination results if the count data was not rarefied. For differential abundance testing, we used both simulations and real data. Overall, we found that simulation results are very dependent upon simulation design and distribution, highlighting the need for gold standard datasets. We confirm that techniques based on GLMs with the negative binomial or log-ratios are promising.
This agrees with prior investigation finding RNA-Seq approaches unsuitable for microbiome data [ 60 ]. If the average library size for each group is approximately equal, then rarefying itself does not increase the false discovery rate.
Prior to analysis, researchers should assess the difference in average library size between groups. If large variability in library sizes across samples is observed, then rarefying is useful as a method of normalization. ANCOM [ 7 ] maintains a low FDR for all sample sizes and is the only method that is suitable for making inferences regarding the taxon abundance as well as the relative abundance in the ecosystem using the abundance data from specimens.
ANCOM with more sensitive statistical tests needs to be investigated. ANCOM differential abundance testing is included in scikit-bio scikit-bio. Samples were generated in sets of 40, as in McMurdie and Holmes [ 18 ].
We also tested smaller and larger sample sizes but saw little difference in downstream results. Additional sets of 40 samples were simulated for varying library sizes , , , and 10, sequences per sample. These simulated samples, done in triplicate for each combination of parameters, were then used to assess normalization methods by the proportion of samples correctly classified into the two clusters by the partitioning around medioids PAM algorithm [ 73 , 74 ].
We amended the rarefying method to the hypergeometric model [ 75 ], which is much more common in microbiome studies [ 23 , 24 ]. Negative values in the DESeq normalized values [ 30 ] were set to zero as in McMurdie and Holmes [ 18 ], and a pseudocount of one was added to the count tables [ 18 ].
We instead quantified cluster accuracy among samples that were clustered following normalization to exclude this rarefying penalty Fig. Conversely, it has since been confirmed that low-depth samples contain a higher proportion of contaminants rRNA not from the intended sample [ 55 , 56 ]. Because the higher depth samples that rarefying keeps may be higher quality and therefore give rarefying an unfair advantage, Additional file 1 : Figure S1 compares clustering accuracy for all the techniques based on the same set of samples remaining in the rarefied dataset.
Thus, we control for library size differences before assessing the effects on the studied biological effect. The basic data generation model remained the same, but the creation of true positive OTUs was either made symmetrical through duplication or moved to a different step, so that the OTU environmental abundances matched their relative abundances. A simple overview of the two methods used for simulating differential abundance is presented in Additional file 4 : Figure S4a.
Thus, although in terms of abundances, their set-up allows for some true positives and true negatives, in terms of relative abundances, by their sampling scheme, some taxa are true positives. Thus, true negatives are possible true positives in terms of relative abundances. However, in general, as noted in Additional file 5 : Statistical Supplement C, equality of taxa abundance between two environments does not translate to equality of the relative abundance of taxa between two environments.
In terms of statistical tests, depending upon what parameter is being tested, this can result in inflated false discovery rates. To illustrate this phenomenon, we conducted a simulation study mimicking Additional file 4 : Figure S4b, with results in Fig. Samples were generated from such environments according to a multinomial distribution and these specimen level data were used to compare the taxa abundance in the two environments.
Besides the above procedural changes to the McMurdie and Holmes [ 18 ] simulation, we also modified the rarefying technique from sampling with replacement multinomial to sampling without replacement hypergeometric—as in the previous normalization simulations [ 75 ].
The testing technique was modified from a two-sided Welch t test to the nonparametric Mann-Whitney test, which is widely used and more appropriate because the OTU distributions in microbiome data usually deviate from normality. This new simulation code, for which all intermediate files and dependencies are easily available, can be found in the supplemental R files Additional file 9 and Dirichlet-multinomial parameters were calculated through the method of moments estimators.
As a check, we ensured that the Dirichlet-multinomial results converged to the multinomial results with large gamma. This simulation was exactly the same as the above multinomial simulation, except that the gamma-Poisson distribution was used instead of the multinomial distribution to model the nine environments found in the Global Patterns [ 72 ] dataset.
The means and the variances of the OTUs across samples for each of the environments were used to estimate the lambdas of the gamma-Poisson distribution. As a check, we ensured that the gamma-Poisson results converged to the multinomial results with large shape parameter. We then randomly divided the samples into two groups, each having 3, 20, and samples, and applied the differential abundance methods.
Thus for each taxon, ANCOM obtains a count random variable W that represents the number of nulls among the m-1 tests that are rejected. To deal with zero counts, we use an arbitrary pseudo count value of 0.
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