Supplementary Material - Current Polution Reports

This website contains supplementary material to the paper:

Integrative Analytical Approaches in Exposomics: An overview of available frameworks and existing methodological challenges

Summary:

 

Methodology

Research questions

  • RQ1: What is the current spectrum of integrative analytical approaches in exposomics, and how can they be classified into a unified taxonomy?

  • RQ2: What are the recurring methodological limitations across these integrative frameworks?

  • RQ3: What emerging tools and strategies are being developed to overcome these persistent challenges?

Literature search

This section overviews the methodology applied to search and select the literature for the "Unresolved Challenges" section of this review. To ensure a balance between quantitative impact and qualitative relevance, we employed a multi-stage search strategy across two primary scientific databases: PubMed and Web of Science (WoS).

 

We defined the following objectives for our literature search:

  • Identifying innovative integrative frameworks or tools used in this context published predominantly within the past 5 years.
  • Capturing high-impact methodological developments specifically addressing the six core challenges identified in the taxonomy: (1) explainability, (2) longitudinal modeling, (3) missing data, (4) outcome imbalance, (5) causal/mediation analysis, and (6) technical noise.

To perform the searches, terms were grouped into two fundamental categories to ensure the intersection of integration technology and specific methodological hurdles:

  • Category (A) - Core Integration Keywords: "multi-om*", "multimodal data", "multi-view".
  • Category (B) - Methodological Challenge Keywords: "temporal", "longitudinal", "imbalanced", "resampling", "imputation", "missing", "xAI", "explainable", "interpretable", "Trustworthy AI", "batch".

The final queries associated with these databases were constructed using the following logic:

  • $Q_{PubMed}$​: ("multi-om*"[ti] OR "multimodal data"[ti] OR "multi-view"[ti]) AND ("temporal"[ti] OR "longitudinal"[ti] OR "imbalanced"[ti] OR "resampling"[ti] OR "imputation"[ti] OR "missing"[ti] OR "xAI"[ti] OR "explainable"[ti] OR "interpretable"[ti] OR "batch"[ti])
  • $Q_{WoS}$​: TS=("multi-om*" OR "multimodal data" OR "multi-view") AND TS=("temporal" OR "longitudinal" OR "imbalanced" OR "resampling" OR "imputation" OR "missing" OR "xAI" OR "explainable" OR "interpretable" OR "Trustworthy AI" OR "batch")

The final selection of articles was not determined by a single metric but quantitative impact (number of citations, metrics like CNCI), temporal relevance and novelty as well as

Search limitations

  • Time Period: The search focused predominantly on state-of-the-art developments published within the past 5 years (2020–2026) to capture the latest advancements in deep learning and foundation models.

  • Language: The search was restricted to English-language publications.

  • Document Types: Inclusion was limited to peer-reviewed research articles or pre-prints indexed in databases and comprehensive books.

Inclusion and exclusion criteria

Inclusion Criteria:

  • Primary studies, systematic reviews, or surveys investigating the integration of the external exposome with internal multi-omic responses.

  • Studies addressing at least one of the six core methodological challenges identified: explainability, longitudinal modeling, missing data, outcome imbalance, causal analysis, or technical noise.

 

Exclusion Criteria:

  • Papers that describe general integration requirements without providing evaluation methods, metrics, or specific tools.

Evaluation and selection

  • Screening: A title and abstract-based filtering to remove duplicates and records clearly unrelated to exposomics or integration technology.
  • Eligibility: A full-text assessment to ensure studies met the criteria defined for final inclusion into the review.
  • Priotitization: Final selection was guided by a multi-metric approach, such as journal impact factor, normalized citation scores (percentile, CNCI...) and  temporal novelty.

Results

Tools and models for multi-omic data integration

1. True Multi-Omics Integration Models

These are the core mathematical frameworks that accept multiple datasets simultaneously as distinct "blocks" and fuse them into a shared space.

Partial Least Squares (PLS) & Regression-Based:

  • timeOmics[1]: An integration package (mixOmics framework) that uses block-sPLS to integrate multi-omics data over time.
  • PLASMA[2]: A supervised multi-modal PLS framework designed to extend prediction across modalities.
  • StaPLR[3]: A stacked penalized regression framework that builds an integrative predictive model while handling missingness natively.

 

Matrix Factorization & Latent Clustering:

  • MOFA+[4]: Unsupervised integration that factorizes multiple omics layers into shared latent factors (often used to mathematically isolate batch factors from biological ones).
  • MEFISTO[5]: An extension of MOFA+ specifically designed to integrate continuous spatial and temporal/longitudinal multi-omics data.
  • OmicsNMF[6]: Uses Non-negative Matrix Factorization to jointly project multi-omics data into a lower-dimensional integrated space.
  • LUCID[7]: Explicitly integrates three blocks (Exposure → Omics → Phenotype) into a joint latent clustering framework.

 

Similarity Network & Neighborhood Fusion:

  • miss-SNF (Similarity Network Fusion for missing data)[8]: A true graph-based integration method. It builds patient-similarity networks for each omics layer and uses message-passing to mathematically fuse them into a single, unified graph, uniquely capable of integrating patients who are missing entire omics modalities without requiring raw data imputation.

Deep Learning methods

  • InClust+: 
  • MIMIR[9]: A multi-omics autoencoder that learns a shared representation across modalities (and is explicitly designed to reconstruct missing data layers).
  • MIMA[10]: A multi-omics deep learning framework that uses representation disentanglement to mathematically isolate shared biological signals from lab-specific batch spaces and technical noise during the integration process.
  • DMOIT (Denoised Multi-Omics Integration Approach based on Transformer): Uses a multi-head cross-attention mechanism combined with a denoising function. It explicitly separates true biological cross-talk from technical dropouts and batch noise by forcing the Transformer to reconstruct corrupted signals.
  • MOTGNN (Multi-Omics integration with Tree-generated Graph Neural Network): A state-of-the-art framework that builds patient-similarity graphs for each omics layer using a tree-based generator (XGBoost) before GNN fusion. This creates a true integration structure that naturally resists the biases of skewed, unbalanced outcomes without needing artificial data resampling.

 

2. Interpretable Integration (Ante-hoc xAI)

These tools do perform multi-omics integration, but they are categorized separately because they are explicitly designed to be "glass-box" models. They use biological constraints so the integration isn't a black box.

  • BioLM-NET: A biologically informed multi-omics neural network that uses prior knowledge graphs (like PPI networks) and LLMs to constrain how the data integrates.
  • AE-Trans: An interpretable dual-channel Transformer framework that aligns RNA and DNA methylation data, utilizing counterfactual gradients to explain exactly why features were integrated.
  • EI / GAUDI: Explainable AI algorithms designed to give readable logic (e.g., Bayesian rule sets) to integrated models.

 

3. Tools to Help BEFORE Integration (Data Preparation & Pre-processing)

These tools format, clean, balance, or correct the data matrices so that the integration models (like MOFA+ or DIABLO) do not fail or learn biased noise.

 

Handling Imbalance & Missingness:

  • SMOGN: A pre-processing data-augmentation tool (Synthetic Minority Over-Sampling) to fix skewed target distributions before modeling.
  • LDS / FDS: Label/Feature Distribution Smoothing techniques to artificially balance datasets with long-tail (rare) outcomes.
  • TSK-IR (Takagi-Sugeno-Kang for Imbalanced Regression): A fuzzy logic-based algorithm that adjusts predictive rules so that rare, skewed outcomes are given proper mathematical weight before or during the modeling phase.
  • Linguistic-IR: A linguistic fuzzy rule-based system for imbalanced regression. Similar to TSK-IR, it generates human-readable fuzzy rules to prevent models from being biased toward majority populations when predicting continuous target variables.
  • bwm: Algorithms designed to explicitly impute or handle block-wise missingness in multi-modal matrices prior to analysis.

 

Batch Effect Correction & Harmonization:

  • MultiBaC: A pre-processing tool designed to remove batch effects across different multi-omics datasets before integration.
  • MoDAmix: Uses adversarial domain adaptation to align datasets from different labs or distributions.
  • Feature Extraction & Variance Isolation:
  • PALMO: Performs variance decomposition to isolate which features are "stable" versus "dynamic" over time. You run this before integration to trim noise.
  • W-CFS: A correlation-based feature selection wrapper to prune high-dimensional omics datasets before feeding them to an integrator.
  • gWQS (generalized Weighted Quantile Sum regression): An environmental mixture method used to handle highly correlated exposures over time (repeated measures). In multi-omics, it is often used prior to integration to compress dozens of correlated environmental chemicals into a single "WQS Index," which can then be safely fed into a multi-omics model without overpowering it.

 

4. Tools to Help AFTER Integration (Causal, Network, & Post-hoc Explainers)

These tools take the output of your integration (or the generated multi-omics networks) mapping causal directions and removing confounders.

 

Post-hoc Explainability & De-confounding:

  • METALICA: A suite of post-hoc tools used after network inference. It mathematically "unrolls" the network to find hidden intermediate genes/metabolites and removes spurious edges caused by environmental batch effects (de-confounding).
  • Mime: A flexible machine-learning framework used to evaluate, benchmark, and visualize the output features of predictive models.

 

Mediation & Causal Inference:

  • HIMA (High-dimensional Mediation Analysis): Used to identify which specific omics features (e.g., CpG sites) mathematically mediate the relationship between an exposure and a disease.
  • BKMR-CMA: Bayesian Kernel Machine Regression for Causal Mediation (evaluates non-linear mixtures of exposures).
  • TABU / HC (Hill-Climbing) / GraSP: Causal Structure Discovery algorithms. Once you know which multi-omics features are important, you use these to build Directed Acyclic Graphs (DAGs) to infer the directional flow of causality.

 

Network Visualization:

  • netOmics: Used post-integration to infer and visually map the learned cross-modality connections between variables.

 

Detailed cross-cutting methodological checklist for each framework.

A detailed methodological comparison for each of the idiosyncrasies and challenges of data integration methods by algorithm taxonomic group from studies that work with exposome data is available for download in docx format by clicking this icon Word icon

References

  1. Bodein, A., Scott-Boyer, M. P., Perin, O., Lê Cao, K. A., & Droit, A. (2022). timeOmics: an R package for longitudinal multi-omics data integration. Bioinformatics, 38(2), 577-579.
  2. Yamaguchi, K., Abdelbaky, S., Yu, L., Oakes, C. C., Abruzzo, L. V., & Coombes, K. R. (2025). PLASMA: Partial LeAst Squares for Multiomics Analysis. Cancers, 17(2), 287.
  3. Van Loon, W., Fokkema, M., Szabo, B., & De Rooij, M. (2020). Stacked penalized logistic regression for selecting views in multi-view learning. Information Fusion, 61, 113-123.
  4. Argelaguet, R., Arnol, D., Bredikhin, D., Deloro, Y., Velten, B., Marioni, J. C., & Stegle, O. (2020). MOFA+: a statistical framework for comprehensive integration of multi-modal single-cell data. Genome biology, 21(1), 111.
  5. Velten, B., Braunger, J. M., Argelaguet, R., Arnol, D., Wirbel, J., Bredikhin, D., ... & Stegle, O. (2022). Identifying temporal and spatial patterns of variation from multimodal data using MEFISTO. Nature methods, 19(2), 179-186.
  6. Zhao, Y., Jia, Q., Goodrich, J. A., & Conti, D. V. (2025). LUCIDus: An R Package For Implementing Latent Unknown Clustering By Integrating Multi-omics Data (LUCID) With Phenotypic Traits. R J., 16(2), 4-27.
  7. Gliozzo, J., Soto Gomez, M. A., Bonometti, A., Patak, A., Casiraghi, E., & Valentini, G. (2025). miss-SNF: a multimodal patient similarity network integration approach to handle completely missing data sources. Bioinformatics, 41(4), btaf150.
  8. Wang, L., Nie, R., Miao, X., Cai, Y., Wang, A., Zhang, H., ... & Cai, J. (2024). InClust+: the deep generative framework with mask modules for multimodal data integration, imputation, and cross-modal generation. BMC bioinformatics, 25(1), 41.
  9. Nambiar, A., Melendez, C., & Noble, W. S. (2026). Unified imputation of missing data modalities and features in multi-omic data via shared representation learning. bioRxiv.
  10. Larizgoitia, J. I. A., Partel, G., Venturelli, L., Zhang, W., Spotbeen, X., Vanuytven, S., ... & Sifrim, A. (2025). Multi-omics integration and batch correction using a modality-agnostic deep learning framework. bioRxiv.
  11. Liu, Z., & Park, T. (2024). DMOIT: denoised multi-omics integration approach based on transformer multi-head self-attention mechanism. Frontiers in Genetics, 15, 1488683.
  12. Yang, T., & Chen, Z. (2026). MOTGNN: interpretable graph neural networks for multi-omics disease classification. ArXiv, arXiv-2508.
  13. Rifat, J. I. M., Tabashum, T., Rahman, M. M., Mokter, M. F., Engala, S., & Bozdag, S. (2025). BioLM-NET: an interpretable deep learning model combining prior biological knowledge and contextual LLM gene embeddings on multi-omics data to predict disease. In Biocomputing 2026: Proceedings of the Pacific Symposium (pp. 644-663).
  14. Liao, K., Du, D., Li, J., Huang, J., Fan, X., Chen, C., ... & Li, H. (2026). Interpretable integration of unpaired multi-omics for Alzheimer’s diagnosis via cross-modal transformer reconstruction. PLOS Computational Biology, 22(3), e1014074.
  15. Li, Y. C., Wang, L., Law, J. N., Murali, T. M., & Pandey, G. (2022). Integrating multimodal data through interpretable heterogeneous ensembles. Bioinformatics advances, 2(1), vbac065.
  16. Castellano-Escuder, P., Zachman, D. K., Han, K., & Hirschey, M. D. (2025). GAUDI: interpretable multi-omics integration with UMAP embeddings and density-based clustering. Nature Communications, 16(1), 5771.
  17. Yang, Y., Zha, K., Chen, Y., Wang, H., & Katabi, D. (2021, July). Delving into deep imbalanced regression. In International conference on machine learning (pp. 11842-11851). PMLR.
  18. Arteaga, M., Gacto, M. J., Galende, M., Alcalá-Fdez, J., & Alcalá, R. (2023). Enhancing soft computing techniques to actively address imbalanced regression problems. Expert Systems with Applications, 234, 121011.
  19. Baena-Miret, S., Reverter, F., & Vegas, E. (2024). A framework for block-wise missing data in multi-omics. Plos one, 19(7), e0307482.
  20. Ugidos, M., Tarazona, S., Prats-Montalbán, J. M., Ferrer, A., & Conesa, A. (2020). MultiBaC: A strategy to remove batch effects between different omic data types. Statistical Methods in Medical Research, 29(10), 2851-2864.
  21. Choi, J. M., & Chae, H. (2026). A unified framework for correcting batch effects and integrating multi-omics data. Scientific Reports, 16(1), 12341.
  22. Vasaikar, S. V., Savage, A. K., Gong, Q., Swanson, E., Talla, A., Lord, C., ... & Li, X. J. (2023). A comprehensive platform for analyzing longitudinal multi-omics data. Nature Communications, 14(1), 1684.
  23. Ling, Z., Wu, J., Zhang, Y., Zhou, P., Jiang, B., Yu, K., & Wu, X. (2024). Causal feature selection with imbalanced data. IEEE Transactions on Emerging Topics in Computational Intelligence, 9(2), 1610-1626.
  24. Gennings, C., Midya, V., Renzetti, S., & DeFelice, N. (2025). Weighted quantile sum (WQS) mixed-effects model. MethodsX, 103580.
  25. Ruiz-Perez, D., Gimon, I., Sazal, M., Mathee, K., & Narasimhan, G. (2024). Unfolding and de-confounding: biologically meaningful causal inference from longitudinal multi-omic networks using METALICA. Msystems, 9(10), e01303-23.
  26. Liu, H., Zhang, W., Zhang, Y., Adegboro, A. A., Fasoranti, D. O., Dai, L., ... & Li, X. (2024). Mime: A flexible machine-learning framework to construct and visualize models for clinical characteristics prediction and feature selection. Computational and structural biotechnology journal, 23, 2798-2810.
  27. Zhang, H., Zheng, Y., Hou, L., & Liu, L. (2025). HIMA: An R Package for High-Dimensional Mediation Analysis. Journal of Data Science, 1-15.
  28. Devick, K. L., Bobb, J. F., Mazumdar, M., Claus Henn, B., Bellinger, D. C., Christiani, D. C., ... & Valeri, L. (2022). Bayesian kernel machine regression‐causal mediation analysis. Statistics in medicine, 41(5), 860-876.
  29. Kitson, N. K., & Constantinou, A. C. (2025). Stable structure learning with HC-Stable and Tabu-Stable algorithms. International Journal of Approximate Reasoning, 186, 109522.
  30. Bodein, A., Scott-Boyer, M. P., Perin, O., Lê Cao, K. A., & Droit, A. (2022). Interpretation of network-based integration from multi-omics longitudinal data. Nucleic acids research, 50(5), e27-e27.