Aims: Coronary artery disease (CAD) is a highly prevalent disease with modifiable risk factors. In patients with suspected obstructive CAD, evaluating the pre-test probability model is crucial for diagnosis, although its accuracy remains controversial. Machine learning (ML) predictive models can help clinicians detect CAD early and improve outcomes. This study aimed to identify early-stage CAD using ML in conjunction with a panel of clinical and laboratory tests. Methods and results: The study sample included 3316 patients enrolled in the Ludwigshafen Risk and Cardiovascular Health (LURIC) study. A comprehensive array of attributes was considered, and an ML pipeline was developed. Subsequently, we utilized five approaches to generating high-quality virtual patient data to improve the performance of the artificial intelligence models. An extension study was carried out using data from the Young Finns Study (YFS) to assess the results’ generalizability. Upon applying virtual augmented data, accuracy increased by approximately 5%, from 0.75 to –0.79 for random forests (RFs), and from 0.76 to –0.80 for Gradient Boosting (GB). Sensitivity showed a significant boost for RFs, rising by about 9.4% (0.81–0.89), while GB exhibited a 4.8% increase (0.83–0.87). Specificity showed a significant boost for RFs, rising by ∼24% (from 0.55 to 0.70), while GB exhibited a 37% increase (from 0.51 to 0.74). The extension analysis aligned with the initial study. Conclusion: Accurate predictions of angiographic CAD can be obtained using a set of routine laboratory markers, age, sex, and smoking status, holding the potential to limit the need for invasive diagnostic techniques. The extension analysis in the YFS demonstrated the potential of these findings in a younger population, and it confirmed applicability to atherosclerotic vascular disease.

Background: Cardiovascular diseases (CVD) and depression frequently co-occur, yet the biological mechanisms underpinning this comorbidity remain poorly understood. This may reflect complex, non-linear associations across multiple biological pathways. We aimed to identify molecular biomarkers linking depressive symptoms and cardiovascular phenotypes using a network-based integrative approach. Methods: Data were obtained from the Young Finns Study ( N = 1,686; mean age = 37.7 years; 58.3% female), including 21 depressive symptoms (Beck Depression Inventory), 17 CVD-related indicators, 6 risk factors, 228 metabolomic, and 437 lipidomic variables. Mutual information was used to capture both linear and non-linear associations among variables. A multipartite projection network was constructed to quantify how depressive symptoms and cardiovascular phenotypes are biologically connected via shared metabolites and lipids. Biomarkers were ranked by their contribution to these projected associations. Results were validated in an independent cohort from the UK Biobank. Results: Specific depressive symptoms – crying, appetite changes, and loss of interest in sex – showed strong projected associations with diastolic blood pressure, systolic blood pressure, and cardiovascular health scores. Key mediators included creatinine, valine, leucine, phospholipids in very large HDL, triglycerides in small LDL, and apolipoprotein B. Important lipid mediators included sphingomyelins, phosphatidylcholines, triacylglycerols, and diacylglycerols. Replication analysis in the UK Biobank identified many overlaps in metabolite profiles, supporting generalizability. Conclusions: This network-based analysis revealed symptom-specific biological pathways linking CVD and depression. The identified biomarkers may offer insights into shared mechanisms and support future prevention and treatment strategies for cardiometabolic–psychiatric comorbidity.

Higher-order relationships are a central concept in the science of complex systems. A popular method of attempting to estimate the higher-order relationships of synergy and redundancy from data is through the O-information. It is an information–theoretic measure composed of Shannon entropy terms that quantifies the balance between redundancy and synergy in a system. However, bias is not yet taken into account in the estimation of the O-information of discrete variables. In this paper, we explain where this bias comes from and explore it for fully synergistic, fully redundant, and fully independent simulated systems of $n=3$ variables. Specifically, we explore how the sample size and number of bins affect the bias in the O-information estimation. The main finding is that the O-information of independent systems is severely biased towards synergy if the sample size is smaller than the number of jointly possible observations. This could mean that triplets identified as highly synergistic may in fact be close to independent. A bias approximation based on the Miller–Maddow method is derived for the O-information. We find that for systems of $n=3$ variables the bias approximation can partially correct for the bias. However, simulations of fully independent systems are still required as null models to provide a benchmark of the bias of the O-information.

Background: Count scores, disease clustering, and pairwise associations between diseases remain ubiquitous in multimorbidity research despite two major shortcomings: they yield no insight into plausible mechanisms underlying multimorbidity, and they ignore higher-order interactions such as effect modification.Objectives: We argue that two components are currently missing but vital to develop novel multimorbidity metrics. Firstly, networks should be constructed which consists simultaneously of signs, symptoms, and diseases, since only then could they yield insight into plausible shared biological mechanisms underlying diseases. Secondly, learning pairwise associations is insufficient to fully characterize the correlations in a system. That is, synergistic (e.g., cooperative or antagonistic) effects are widespread in complex systems, where two or more elements combined give a larger or smaller effect than the sum of their individual effects. It can even occur that pairs of symptoms have no pairwise associations whatsoever, but in combination have a significant association. Therefore, higher-order interactions should be included in networks used to study multimorbidity, resulting in so-called hypergraphs.Methods: We illustrate our argument using a synthetic Bayesian Network model of symptoms, signs and diseases, composed of pairwise and higher-order interactions. We simulate network interventions on both individual and population levels and compare the ground-truth outcomes with the predictions from pairwise associations.Conclusion: We find that, when judged purely from the pairwise associations, interventions can have unexpected “side-effects” or the most opportune intervention could be missed. The hypergraph uncovers links missed in pairwise networks, giving a more complete overview of sign and disease associations.

In recent years, there has been a notably increased interest in the study of multivariate interactions and emergent higher-order dependencies. This is particularly evident in the context of identifying synergistic sets, which are defined as combinations of elements whose joint interactions result in the emergence of information that is not present in any individual subset of those elements. The scalability of frameworks such as partial information decomposition (PID) and those based on multivariate extensions of mutual information, such as O-information, is limited by combinational explosion in the number of sets that must be assessed. In order to address these challenges, we propose a novel approach that utilises stochastic search strategies in order to identify synergistic triplets within datasets. Furthermore, the methodology is extensible to larger sets and various synergy measures. By employing stochastic search, our approach circumvents the constraints of exhaustive enumeration, offering a scalable and efficient means to uncover intricate dependencies. The flexibility of our method is illustrated through its application to two epidemiological datasets: The Young Finns Study and the UK Biobank Nuclear Magnetic Resonance (NMR) data. Additionally, we present a heuristic for reducing the number of synergistic sets to analyse in large datasets by excluding sets with overlapping information. We also illustrate the risks of performing a feature selection before assessing synergistic information in the system.

In the context of multimorbidity, clinical features seldom act in isolation: symptoms, signs and behaviours form interdependent systems in which joint effects on function can be demonstrated only when features are considered together. We introduce an open, reusable workflow that detects and interprets these “together-only” interactions using bivariate Partial Information Decomposition (PID; two sources to one target), linking synergy-based dependence to the broader network of clinical variables rather than to a single target. The workflow estimates synergy with small-sample bias correction and summarises each pair in a Breadth–Uniformity–Synergy–Total (BUST) map: breadth of synergy across target variables (broad “generalist” vs narrow “specialist” patterns), cross-stratum uniformity across age, sex and multimorbidity (uniform vs subgroup-specific), synergy strength, and total shared information. Simple diagnostics contrast observed targets with additive expectations, revealing the specific joint configurations through which non-additive effects arise. Applied to data from the Longitudinal Ageing Study Amsterdam, we treated all health-related variables—covering symptoms, clinical signs, behaviours, lifestyle factors, and self-rated health indicators—as both sources and targets in the PID framework. This symmetric design permits synergy to be quantified for every pair of variables with respect to every other variable. The workflow identifies synergistic constellations that additive models miss. Multidomain cliques involving subjective health, pain, cognition and grip strength showed multiple non-additive configurations, whereas pairs such as alcohol use with grip strength exhibited focused, narrow but uniform synergy. Notably, the pairs with the strongest synergistic contributions were largely distinct from those with the highest total mutual information, indicating that synergy captures dependency structure overlooked by conventional association measures. Rather than a new measure, this work provides a bias-aware workflow that makes higher-order dependence visible and transferable. Our results support synergy-aware mapping as a practical complement to conventional multimorbidity analyses: it highlights specific combinations of routinely assessed features whose joint states may be especially informative across multiple health targets and therefore candidates for prioritised joint assessment and future multi-domain intervention studies.