Translating biomarkers between multi-way time-series experiments

Translating potential disease biomarkers between multi-species ‘omics’ experiments is a new direction in biomedical research. The existing methods are limited to simple experimental setups such as basic healthy-diseased comparisons. Most of these methods also require an a priori matching of the variables (e.g., genes or metabolites) between the species. However, many experiments have a complicated multi-way experimental design often involving irregularly-sampled time-series measurements, and for instance metabolites do not always have known matchings between organisms. We introduce a Bayesian modelling framework for translating between multiple species the results from ‘omics’ experiments having a complex multi-way, time-series experimental design. The underlying assumption is that the unknown matching can be inferred from the response of the variables to multiple covariates including time.

💡 Research Summary

The paper tackles a fundamental challenge in cross‑species “omics” research: how to translate biomarkers when experiments involve multiple covariates, irregularly sampled time‑series, and no pre‑defined mapping of variables (genes, metabolites) between species. Existing approaches are limited to simple healthy‑vs‑diseased comparisons and rely on orthology information, which is often unavailable for metabolites. The authors propose a unified Bayesian framework that simultaneously (i) reduces dimensionality through regularized factor analysis, (ii) models multi‑way covariate effects (e.g., disease, gender, treatment) in a latent factor space, (iii) aligns irregular time points using a hidden Markov model (HMM) that captures latent metabolic development states, and (iv) learns unknown projections from the latent spaces of each species to their observed data spaces, thereby discovering shared clusters of variables without any a priori matching.

In the model, each species’ high‑dimensional observation vector (x for species X, y for species Y) is generated from a low‑dimensional latent vector (x_lat, y_lat). The latent vectors are influenced by shared effects (α_s for aligned time, β_b for disease, and the interaction (αβ)_sb) as well as species‑specific effects (α_x_s, β_x_b, etc.). The shared effects are projected into the observed spaces via unknown functions f_x and f_y, which are inferred jointly with all other parameters using Gibbs sampling. The central translational question becomes whether a particular dimension of x_lat responds to the covariates in the same way as a dimension of y_lat; if so, that pair of dimensions represents a cross‑species biomarker cluster.

Matching of clusters is treated as a combinatorial problem. An iterative Metropolis‑based algorithm proposes to link or unlink a pair of clusters, evaluates the likelihood of the shared multi‑way model versus an average random pairing, and accepts or rejects the move according to a Metropolis criterion. Over many iterations, posterior probabilities of each possible pairing are obtained, providing a principled measure of confidence for each inferred cross‑species match.

The authors validate the approach on synthetic data and on a real lipidomic time‑series study of human patients (some progressing to type‑1 diabetes) and a mouse model. Synthetic data were generated with known shared temporal effects and shared disease‑time interaction effects across two data sets with different numbers of variables and latent dimensions. The model correctly recovered the two shared clusters, aligned the irregular time points into the correct HMM states, and identified species‑specific clusters. In the real data, the HMM successfully aligned irregular clinical visits into five latent metabolic states, and the Bayesian model discovered clusters of metabolites in humans and mice that exhibited similar responses to disease progression over time, despite the absence of any orthology information.

Key contributions of the work are: (1) a Bayesian multi‑way ANOVA‑type model that integrates heterogeneous, high‑dimensional data from multiple species; (2) simultaneous learning of latent time alignment (via HMM) and covariate effects; (3) an unsupervised mechanism for discovering shared variable clusters without pre‑defined mappings; and (4) a probabilistic assessment of matching confidence, which is essential for translational biomarker discovery. By embedding dimensionality reduction, covariate modeling, and time alignment within a single probabilistic framework, the method overcomes the limitations of previous meta‑analysis, canonical correlation, and iterative pairing approaches, offering a powerful tool for cross‑species translational medicine.