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arxiv: 2605.22181 · v1 · pith:AUWSGSEAnew · submitted 2026-05-21 · 📊 stat.OT

A critical comparison of handling zeros in high-dimensional compositional count data

Wenqi Tang , Kamila Fa\v{c}evicov\'a , Klaus Nordhausen , Sara Taskinen This is my paper

Pith reviewed 2026-05-22 02:03 UTC · model grok-4.3

classification 📊 stat.OT
keywords compositional data analysiszero imputationcount datazero inflationlog-ratio transformationsmicrobiome sequencingdiscrete datahigh-dimensional data
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The pith

Existing imputation strategies for zeros in compositional count data must be adapted to discrete and zero-inflated structures.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This review surveys methods for dealing with zeros in high-dimensional compositional count data produced by high-throughput sequencing. It explains that log-ratio transformations rest on continuity assumptions that sequencing count data violate, resulting in numerical instabilities and biased inferences. The paper then compares how standard imputation approaches perform once applied to discrete, lattice-valued counts and shows that performance changes under these conditions. A sympathetic reader cares because these data dominate microbiome studies, where mishandled zeros can alter conclusions about community composition and differential abundance.

Core claim

The review establishes that violations of continuity assumptions in the log-ratio framework induce numerical instabilities and biased statistical inferences when applied to sequencing-derived compositional count data. Systematic comparison of imputation strategies reveals that their behavior shifts when the discrete, lattice-valued nature of the counts is respected, and it identifies open challenges that motivate future zero-handling frameworks capable of jointly accommodating compositional constraints, zero inflation, and the lattice nature of count data.

What carries the argument

Log-ratio transformations whose continuity assumptions conflict with discrete zero-inflated count observations, together with the adaptation of imputation procedures to the integer lattice structure of the data.

If this is right

  • Imputation accuracy and stability decline when the discrete lattice nature of counts is ignored.
  • Log-ratio calculations on sequencing count data produce numerical instabilities and distorted inferences without adaptation.
  • Statistical conclusions about compositional structure become biased under unadjusted zero-handling methods.
  • Future zero-handling methods must simultaneously respect sum constraints, zero inflation, and integer-valued observations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Analyses of microbiome count tables that rely on off-the-shelf CoDA pipelines may systematically understate or overstate taxon associations until zero methods are updated for discreteness.
  • The same continuity mismatch could affect abundance modeling in single-cell or ecological count data, suggesting broader testing of lattice-aware imputations.
  • Software implementations could be extended to enforce integer constraints during imputation while preserving the compositional sum-to-one property.

Load-bearing premise

Violations of continuity assumptions in the log-ratio framework induce numerical instabilities and biased statistical inferences when applied to sequencing-derived compositional count data.

What would settle it

A controlled simulation on zero-inflated compositional counts that applies both standard and discretely adapted imputation, then compares resulting bias in log-ratio estimates or downstream inference accuracy, would settle whether adaptation is required.

Figures

Figures reproduced from arXiv: 2605.22181 by Kamila Fa\v{c}evicov\'a, Klaus Nordhausen, Sara Taskinen, Wenqi Tang.

Figure 1
Figure 1. Figure 1: Diagram outlining the structure of Sec. 3. This review covers the classification of zeros, the methods for [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Integer lattice N 2 (left) and the continuous 3-part simplex S 3 (right). Left panel: Shows all 11 × 11 = 121 possible integer pairs (x, y) where x, y ∈ {0, . . . , 10}. Right panel: Displays N = 1000 simulated compositions generated from a symmetric Dirichlet distribution Dir(1, 1, 1), projected onto the 2-simplex. Count data from HTS technology are realized on a discrete lattice, whereas classical CoDA a… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of compositional geometry across sequencing depths. We simulate a sample size of 500 three-part [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Effect of global scaling and ceiling quantization on Dirichlet–multinomial count data. Simulations are [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) shows the log–log mean–variance relationship across species, illustrating the over-dispersion typical of [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of imputation methods in terms of CED (top) and ADCS (bottom) metrics under varying [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of imputation methods in terms of CED and ADCS metrics under varying dimensionality and [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of CED and ADCS metrics (Raw and Ceil) across varying dimensions [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Trends of computational runtime under different settings. The upper panel shows the change of mean runtime [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Local inspection of imputation behavior under [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of imputation methods in terms of CED and ADCS metrics under varying dimensionality and [PITH_FULL_IMAGE:figures/full_fig_p029_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of CED and ADCS metrics (Raw and Ceil) across different dimensions m under a fixed missingness probability of p = 0.2 under simulation dataset. 29 [PITH_FULL_IMAGE:figures/full_fig_p029_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Simulation-based comparison of imputation methods in terms of CED (top) and ADCS (bottom) metrics [PITH_FULL_IMAGE:figures/full_fig_p030_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: (a) corresponds to m = 100, p = 0.20 with abnormal variable MG820, and (b) corresponds to m = 500, p = 0.30 with abnormal variable MG650. Each panel summarizes the distribution of imputed values across methods together with true–imputed comparisons for representative variables. 32 [PITH_FULL_IMAGE:figures/full_fig_p032_14.png] view at source ↗
read the original abstract

The growing use of high-throughput sequencing (HTS) has enabled the large-scale production of compositional count data, driving progress in microbiome research. However, such count data are often high-dimensional, over-dispersed, and heavily zero-inflated, and they conflict with the continuity assumptions underlying log-ratio-based compositional data analysis (CoDA), creating substantial methodological challenges. This review provides an overview of zero-handling strategies in compositional data, covering zero-tolerant transformations, imputation approaches for rounded zeros, and statistical models for essential zeros. We specifically highlight the problems that arise when applying the log-ratio framework to sequencing-derived compositional count data, where violations of continuity can induce numerical instabilities and biased statistical inferences. Motivated by these issues, we systematically examine how existing imputation strategies behave when adapted to discrete, zero-inflated count data, including an evaluation of how the discrete, lattice-valued nature of the data affects imputation performance. Overall, this review consolidates scattered methodological developments, clarifies appropriate use cases, and identifies open challenges that motivate future zero-handling frameworks capable of jointly accommodating compositional constraints, zero inflation, and the lattice nature of count data, while also providing a detailed discussion of the comparison results.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper reviews zero-handling strategies for high-dimensional compositional count data from high-throughput sequencing applications such as microbiome studies. It covers zero-tolerant transformations, imputation methods for rounded zeros, and statistical models for essential zeros. The review emphasizes conflicts between the continuity assumptions of log-ratio CoDA and the discrete, zero-inflated, over-dispersed nature of sequencing count data, which can cause numerical instabilities and biased inferences. It systematically examines the behavior of existing imputation strategies when adapted to such data and evaluates the effects of the lattice-valued discrete structure on imputation performance, ultimately consolidating methods, clarifying use cases, and motivating future frameworks that jointly address compositional constraints, zero inflation, and count-data lattice properties.

Significance. If the evaluation holds, the review provides a timely consolidation of scattered methodological developments in zero handling for compositional count data, which is relevant given the widespread use of HTS in microbiome research. It clarifies appropriate use cases for different strategies and identifies open challenges, potentially guiding practitioners and motivating integrated modeling approaches. The paper's strength lies in its structured overview and explicit discussion of comparison results rather than new derivations or proofs.

major comments (1)
  1. [Abstract and evaluation section] Abstract and the section describing the evaluation of imputation strategies: the claim that existing imputation approaches must be adapted for discrete zero-inflated count data, and that this motivates new joint frameworks, rests on the stated evaluation of how the lattice-valued nature affects performance. If this evaluation consists primarily of literature synthesis without original controlled simulations (e.g., generating multinomial or negative-binomial counts with known zero patterns, applying multiple imputers, and quantifying recovery via Aitchison distance or downstream log-ratio inference error), then the necessity of adaptation is not quantitatively demonstrated and the central motivation for future frameworks is weakened.
minor comments (2)
  1. The abstract could more explicitly state the number of imputation methods compared and the key quantitative findings from the performance evaluation to better orient readers before the detailed discussion.
  2. Notation for compositional constraints and lattice properties could be introduced more consistently in early sections to aid readers unfamiliar with the intersection of CoDA and count-data models.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive and detailed review, which recognizes the value of consolidating zero-handling methods for compositional count data. We address the major comment below and outline revisions to strengthen clarity around the nature of our evaluation.

read point-by-point responses

  1. Referee: [Abstract and evaluation section] Abstract and the section describing the evaluation of imputation strategies: the claim that existing imputation approaches must be adapted for discrete zero-inflated count data, and that this motivates new joint frameworks, rests on the stated evaluation of how the lattice-valued nature affects performance. If this evaluation consists primarily of literature synthesis without original controlled simulations (e.g., generating multinomial or negative-binomial counts with known zero patterns, applying multiple imputers, and quantifying recovery via Aitchison distance or downstream log-ratio inference error), then the necessity of adaptation is not quantitatively demonstrated and the central motivation for future frameworks is weakened.

    Authors: We agree that original controlled simulations would provide stronger quantitative support for the motivation. As this is a review paper, the evaluation section synthesizes and critically discusses results from existing literature studies that have performed such controlled experiments on imputation for zero-inflated count data, including assessments of performance degradation due to the discrete lattice structure (e.g., via recovery metrics and downstream inference errors). These synthesized findings consistently indicate the limitations of unadapted methods. To address the concern and avoid ambiguity, we will revise the abstract and evaluation section to explicitly characterize the evaluation as a structured literature synthesis of prior comparative studies, add specific citations to simulation-based works quantifying the effects, and clarify how this synthesis supports the call for integrated frameworks. This revision will be made without introducing new empirical results. revision: yes

Circularity Check

0 steps flagged

Review paper with no self-referential derivations or fitted predictions

full rationale

This is a review paper whose central contribution is an overview and critique of existing zero-handling strategies drawn from external literature. No new quantities are derived from the paper's own equations, fitted parameters, or self-citations in a load-bearing way; the text instead consolidates scattered methodological developments and identifies open challenges without reducing any claim to a tautological fit or self-citation chain. The evaluation of imputation strategies is presented as a synthesis of prior work rather than a closed-loop prediction, leaving the analysis self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The review rests on standard domain assumptions in compositional data analysis and statistical modeling of zeros; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Log-ratio transformations assume continuous data without zeros.
    Stated in the abstract as conflicting with sequencing-derived count data.

pith-pipeline@v0.9.0 · 5751 in / 1132 out tokens · 56715 ms · 2026-05-22T02:03:53.417383+00:00 · methodology

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