Source-linked AI summary
LinDA: linear models for differential abundance analysis of microbiome compositional data
Huijuan Zhou, Kejun He, Jun Chen, Xianyang Zhang
TL;DR
Microbiome sequencing provides relative abundances, making differential abundance analysis vulnerable to compositional effects and false discoveries. The paper proposes LinDA, which fits linear models to CLR-transformed data and corrects compositional bias, with extensions for correlated data. LinDA generally achieved a favorable FDR–power trade-off and was competitive with ANCOM-BC while offering greater computational scalability.
Problem
Microbiome data reveal relative abundances rather than total microbial loads, making compositional effects and false-discovery control central challenges for differential abundance analysis.
Method
LinDA fits linear regression models on centered log-ratio-transformed data, corrects the resulting compositional bias, and extends to mixed-effect models for correlated microbiome data.
Results
LinDA had the best FDR and power trade-off overall and was competitive with ANCOM-BC in most settings.
Takeaways & Limitations
LinDA provides a scalable approach for differential abundance analysis, with practical applicability to correlated microbiome datasets.
Takeaways & Limitations
LinDA showed some FDR inflation when the number of taxa was small or under a very strong compositional effect.
Abstract
from arXiv · showhide
Differential abundance analysis is at the core of statistical analysis of microbiome data. The compositional nature of microbiome sequencing data makes false positive control challenging. Here, we show that the compositional effects can be addressed by a simple, yet highly flexible and scalable, approach. The proposed method, LinDA, only requires fitting linear regression models on the centered log-ratio transformed data, and correcting the bias due to compositional effects. We show that LinDA enjoys asymptotic FDR control and can be extended to mixed-effect models for correlated microbiome data. Using simulations and real examples, we demonstrate the effectiveness of LinDA.
1 Background
Microbiome sequencing data provide relative rather than absolute abundances, creating compositional effects that complicate differential abundance analysis and false-discovery control. LinDA addresses this challenge with bias-corrected linear modeling and is designed for scalable, flexible analysis.
- Motivation: Sequencing experiments capture relative abundance, while total read count does not reliably reflect total microbial load.Absolute-abundance measurement techniques exist but have severe limitations that prevent wide adoption.
- Motivation: Changes in some taxa automatically alter the relative abundances of others, producing compositional effects.Ignoring this dependence with standard tests or regression can lead to a large number of false discoveries.
- Assumptions: Differential abundance methods depend on assumptions such as sparse signals, although dense signals with many small effects are also supported by some studies.The validity of a method and the definition of true or false positives depend on the assumptions accepted.
- Related methods: Existing approaches address compositionality through robust normalization, reference taxa, or log-ratio methods such as CLR.These strategies include TMM, RLE, CSS, GMPR, ALDEx2, and ANCOM-based methods.
- Methodological gap: Prior evaluations found ubiquitous FDR inflation and no method satisfactory in every aspect, motivating a method that is efficient, robust, powerful, and flexible.The desired method should allow covariate adjustment and application to correlated microbiome data.
2 Results
Simulations found that LinDA generally offered strong FDR control and power across signal structures, covariates, confounders, library sizes, and correlated samples. Real-data analyses showed discoveries broadly consistent with competing robust methods, while LinDA-LMM recovered additional taxa in correlated data.
- Simulation performance: LinDA and ANCOM-BC generally provided the best FDR and power trade-off across simulation settings.LinDA controlled FDR near target levels and often maintained high or highest power, while competitors showed setting-dependent inflation or low power.
- Simulation performance: Dense signals exposed substantial FDR inflation in ANCOM-BC and several competing methods, whereas LinDA remained near the target level with high power.This pattern was reported when 20% of taxa carried signal.
- Robustness: LinDA achieved better FDR control and power than ALDEx2, while adaptive zero handling controlled false positives when library sizes differed tenfold.The adaptive approach retained power when library sizes were similar.
- Correlated data: For correlated samples, LinDA-LMM controlled FDR at the target level and was more powerful than LinDA-OLS.Treating replicate samples as independent caused significant FDR inflation in LinDA-OLS.
- Computational performance: LinDA was 100–1000 times faster than ANCOM-BC, supporting its practical scalability.The paper summarizes LinDA and ANCOM-BC as having the most robust overall performance among evaluated methods, while noting ANCOM-BC is computationally intensive.
- Real-data applications: At 10% FDR in the CDI dataset, LinDA discovered eight associated taxa compared with six for MaAsLin2 and three for ANCOM-BC, ALDEx2, and Wilcoxon.LinDA’s discoveries included additional taxa from Lachnospiraceae and Erysipelotrichaceae.
- Real-data applications: Across IBD and RA datasets, LinDA detected numbers of taxa similar to ANCOM-BC and generally more than other methods, with substantial overlap between LinDA and ANCOM-BC discoveries.The real-data results were consistent with the simulation studies.
- Correlated data: Using both left and right throat samples, LinDA-LMM identified 21 differential taxa, including five missed by separate analyses and seven more than MaAsLin2.The joint analysis covered most taxa identified from either throat side alone.
3 Discussion
LinDA addresses compositional microbiome data with an efficient CLR-based regression framework that corrects compositional bias and extends to correlated datasets. Simulations indicate strong overall performance, while limitations include assumptions about signal sparsity, feature size, model form, finite-sample control, and sequencing variability.
- Method and scope: LinDA uses CLR regression with bias correction, scales to hundreds of thousands of taxa, and extends naturally to linear mixed-effects models for correlated microbiome data.The framework supports differential abundance analysis for clustered, paired, and repeated-measures datasets.
- Comparative performance: Wilcoxon and MaAsLin2 performed similarly, but both began to break down under stronger compositional effects, whereas ANCOM-BC remained robust but inflated type I error at small sample sizes.MaAsLin2’s similarity to Wilcoxon is attributed to its log-linear modeling structure without confounders.
- Comparative performance: LinDA was competitive with ANCOM-BC in most settings and offered better FDR control when sample sizes were small or covariates were continuous.The authors report that LinDA had the best overall FDR–power trade-off, despite some inflation under small feature sizes and very strong compositional effects.
- Library-size confounding: Library-size confounding caused severe type I error inflation across existing methods, while LinDA’s heuristic imputation substantially reduced this inflation after CLR transformation.Rarefaction can control uneven library sizes but discards reads and information, whereas LinDA uses imputed values proportional to library sizes.
- Limitations: LinDA assumes a mode at zero for regression coefficients and can fail when signals are extremely dense, although it remained robust around 20% signal density.The authors also assume a log-linear relationship for absolute abundance, which may not capture more complex host–microbiome interactions.
- Limitations: LinDA’s finite-sample FDR control is not guaranteed, and the authors do not recommend applying it to datasets with small feature sizes such as m < 50.Its relative-abundance framework also does not model read-count sampling variability, potentially reducing power for less abundant taxa.
4 Conclusions
LinDA addresses differential abundance analysis for microbiome compositional data by estimating and correcting bias in CLR-based linear models. It extends to correlated microbiome data and other high-dimensional compositional datasets.
- LinDA is proposed for differential abundance analysis of microbiome compositional data.
- LinDA identifies bias in traditional linear regression models based on CLR-transformed abundance data and proposes estimating and correcting that bias.
- LinDA can be extended to linear mixed-effects models for analyzing correlated microbiome data.
- As a general methodology, LinDA can be applied to differential abundance analysis of other high-dimensional compositional data.
5 Methods
LinDA models CLR-transformed microbiome data with linear regression, then corrects the compositional bias in OLS estimates. Its testing pipeline combines bias correction, p-values, and BH FDR control, with extensions to correlated data and large-scale analyses.
- Model and bias correction: The method adopts CLR transformation and develops a bias-correction procedure to address compositional effects in differential abundance analysis.Absolute abundance and observed read counts are distinguished, with multinomial modeling used for stratified count data.
- Model and bias correction: OLS estimation on CLR-transformed data is biased by the average coefficient term ¯α.Under sparse differential taxa, the mode of the estimated centered coefficients is expected to approximate −¯α, enabling estimation of the bias.
- Testing pipeline: LinDA runs OLS on CLR observations, computes bias-corrected estimates, calculates p-values, and applies the BH procedure.The three-step algorithm uses CLR-based OLS, correction ˆαi = ˜αi + ˜α, and BH-based FDR control.
- Correlated data: The method extends the linear regression framework to mixed-effect models for correlated microbiome data.The extension is intended for replicates, spatial sampling, family-based studies, and longitudinal microbiome studies.
- Theoretical guarantees: The theoretical framework establishes asymptotic FDR control under stated regularity conditions as the numbers of taxa and samples increase.The conditions support consistency of variance estimators and mode estimation, while allowing the number of taxa to be exponentially larger than the sample size.
- Theoretical conditions: For weak signals, the mode of √nαi + √ρεis slightly deviates from zero, whereas for strong signals it is exactly zero.The simulation example uses sparse signals with π0 = 0.8 and signal values 2 and 5.
Declarations
The paper provides software and reproducibility resources, identifies the source datasets, reports funding, and declares no competing interests.
- Software and data: LinDA is implemented as the linda function in the CRAN R package MicrobiomeStat.The package and code are also available through GitHub.
- Software and data: The presented results’ code and data are available through Zenodo and GitHub under the MIT License.The repositories include materials for generating the reported results.
- Funding and disclosures: The authors declare no competing interests and acknowledge support from the National Institutes of Health and National Science Foundation.The work also acknowledges support from the Mayo Clinic Center for Individualized Medicine.
- Author contributions: The authors describe contributions spanning conception, method development, theoretical analysis, evaluation, software, and writing.Different author groups are assigned responsibility for these activities.
Figures and Tables
The figures and tables report simulation-based false discovery and true positive rates, distributional examples, dataset characteristics, and computational measurements.
- Simulation results: Empirical false discovery rates and true positive rates are averaged over 100 simulation runs.False discovery rate panels include 95% confidence intervals, with a dashed line marking the target FDR level of 0.05.
- Distributional illustration: The distribution figure compares a standard normal density with densities from a sparse signal mixture involving √nαi + εis.The mixture assigns probability 0.8 to √nαi = 0 and probability 0.2 to √nαi = 2.
- Computational and dataset details: The computational experiment reports a 67.7 GB setting and bases the result on one simulation run.The elapsed time is obtained from an R command, while dataset tables list taxa counts and sample sizes for filtered datasets.
Supplementary material
The supplementary materials provide additional normalization, zero-handling, simulation-setting, effect-size, volcano-plot, and proof-related results.
- Theoretical supplements: Supplementary lemmas provide intermediate results for proving Theorem 1, whose proof also uses results from cited prior work.The supplementary notes contain the technical proof details.
- Supplementary comparisons: Supplementary figures compare LinDA with alternative zero-handling and normalization approaches across selected simulation settings.They include comparisons with CLR-OLS and MaAsLin2 and examine ANCOM-BC zero treatment.
- Simulation settings: Additional supplementary figures present results for multiple simulation settings and the full results of all methods.Settings include S0C1, S0C2, S1C0, S2C0, S4C0, S5C0, S6C0, S7C0, S8.1C0, and S8.2C0.
- Real-data and effect-size analyses: Supplementary figures include effect-size and volcano plots for the CDI, IBD, RA, and SMOKE datasets.A supplementary figure also depicts results under setting S6C0, while another examines stronger compositional effects under S0C0.
S1 Normalization approaches
Table S1 lists robust normalization methods; the passage also clarifies that square-bracket numbers refer to references.
- Table S1 is titled “Some robust normalization methods.”
- Square-bracket numbers represent reference numbers in the document.
S2 Technical details
The technical details establish supporting lemmas under stated conditions and use convergence, concentration, and continuity arguments to prove the main theorem.
- Lemmas S1–S4 provide intermediate results used before proving Theorem 1.
- Lemma S1 establishes consistency of determinant-based quantities through oP(1) determinant differences.
- The proofs invoke sub-Gaussian assumptions, exponential-tail bounds, and the union bound to control estimated variances.
- Lemma S3 uses uniform continuity and boundedness of fn(x; a) to control approximation differences.
- Lemma S4 proves sup0<t<t0 |m^-1Sm,n(t) − S∞,n(t)| = oP(1).
- Theorem 1 follows after establishing t* < t0 for sufficiently large n and applying Lemma 8.3 of Cao et al., 2021.
S1 Additional main comparisons of numerical studies
The supplementary numerical studies compare LinDA with alternative zero-handling and normalization approaches across multiple simulation settings.
- Figures S1 and S2 compare LinDA with different zero-handling approaches under settings S6C0 and S0C0.
- Figure S3 compares LinDA, CLR-OLS, and MaAsLin2 with different normalization approaches under setting S0C0.
- Figure S11 compares disabling versus enabling zero treatment for ANCOM-BC under setting S6C0.
- Figure S15 examines setting S0C0 with stronger compositional effects.
S2 Additional results of real data applications
Supplementary figures report effect-size and volcano plots for four real-data applications: CDI, IBD, RA, and SMOKE.
- Figures S16–S19 show effect-size plots and volcano plots for the CDI, IBD, RA, and SMOKE datasets.
S3 Full comparisons of numerical studies
The numerical studies compare LinDA with multiple differential-abundance methods across varied distributions, covariates, library sizes, sample sizes, and compositional-effect strengths. Evaluations report empirical false discovery rates and true-positive rates, with additional analyses of zero handling, coefficient debiasing, and real-data detection differences.
- Method variants: Zero-handling performance is evaluated for LinDA, while other analyses compare LinDA with multiple normalization and transformation variants of MaAsLin2.The variants include TSS, TMM, CSS, and CLR approaches.
- Simulation design: 100 simulation runs are used for many comparisons of empirical false discovery rate and true-positive rates, with a target FDR level of 0.05.Some comparisons use 1000 simulation runs.
- Simulation settings: The simulations vary binary or continuous covariates, confounders, library-size differences, sample size, feature number, and strong compositional effects.Supplementary comparisons include a 10-fold library-size difference, smaller m or n, and strong compositional effects.
- Real-data analyses: Effect-size plots and volcano plots distinguish bias-corrected from original regression coefficients and identify taxa detected uniquely or jointly across methods.The real-data comparisons include CDI, IBD, RA, and SMOKE datasets.
- Method comparisons: LinDA is compared with ANCOM-BC, ALDEx2, metagenomeSeq2, MaAsLin2, Wilcoxon, DESeq2, edgeR, and metagenomeSeq across the numerical studies.The full comparisons cover multiple simulation settings, including log-normal, zero-inflated, correlated, gamma, and negative-binomial abundance distributions.