Cillian Hourican

Multimorbidity is the co-occurrence of two or more chronic conditions in the same person. Multimorbidity has become the norm rather than the exception in ageing populations. More than half of adults over sixty-five now live with multiple diagnoses. On paper, two patients carrying the same number of conditions may appear comparable; in daily life they often do not. One remains independent while the other struggles with basic tasks. The difference is not because a single disease dominates. The difference is due to symptoms, signs, behaviours, and conditions interacting differently depending on context. A diagnosis list states what a patient has. It does not state what a patient can do, how their burden will evolve, or which factors drive their current limitations. This mismatch between the tidy categories of disease classification and the messy reality of lived function is the starting point of this thesis: Multimorbidity is not merely an accumulation of diseases. It is an interacting system. Clinically, the connections among diseases may matter more than any single condition.

Most analytic tools used to study these systems still rely on pairwise summaries: association networks, conditional-dependence graphs, and additive models. Each factor contributes independently in such representations. These representations capture a great deal. However, they are structurally unable to express when informative patterns emerge only when variables act together. Consider fatigue, poor sleep, and low mood: each symptom on its own may be only weakly predictive of functional decline, yet their co-occurrence can be strongly predictive in a way that no pair of these symptoms achieves alone. Information of this kind, which is available only from the combination and not recoverable from any subset, is called synergy. It stands in contrast to redundancy, in which multiple variables overlap and partly repeat the same signal about an outcome. Partial Information Decomposition (PID) is a framework from information theory. PID makes this distinction formal and quantitative. Given a set of source variables (e.g. symptoms, signs, and diagnoses) and a target (daily functioning), PID separates the joint information into components that are redundant, unique to each source, or synergistic. This thesis develops and applies PID-based methods to identify, interpret, and scale the analysis of higher-order interactions in multimorbidity and symptom systems.

The first contribution of this thesis is to establish why higher-order analysis is needed and how it can be made computationally feasible. Chapter 2 uses synthetic Bayesian networks. Systems are constructed so that their true higher-order structure is known in advance. The network serves as a reference standard. These networks demonstrate that pairwise association networks can both miss critical dependencies and mischaracterise the expected consequences of interventions when the underlying system contains higher-order interactions. The same approach is then applied to clinical data from the EASYcare study. Symptoms, signs, and diseases are combined within a single network. This identifies 184 synergistic triplets represented using a hypergraph. A hypergraph is a network in which edges can connect more than two nodes. Chapter 3 addresses a practical barrier: combinatorial explosion, the fact that the number of possible variable combinations grows unmanageably with system size. This scaling problem makes exhaustive evaluation infeasible for realistic datasets. The chapter develops stochastic search heuristics, namely simulated annealing and particle swarm optimisation. These search heuristics discover high-synergy sets one to two orders of magnitude faster than exhaustive enumeration. It also identifies a previously underappreciated artefact, termed the echo problem, in which redundancy and overlap among variables inflate the apparent number of higher-order findings. A filtering step is proposed to control this inflation before results are interpreted.

The second contribution turns from method to clinical application. It first considers a single endpoint and then extends the analysis across a whole variable set. Chapter 4 applies PID to symptoms, signs, and diseases measured in the Longitudinal Aging Study Amsterdam (LASA) with functional limitations as the target outcome. In a four-variable decomposition, no domain contributed unique information in the total sample. In the multimorbidity subgroup, symptoms were the only domain to contribute unique information. Symptoms accounted for 34.1% of the total information about functional limitations. This information was not carried by signs or diseases. This is consistent with the view that disease labels become informationally saturated as conditions accumulate. Symptom-level assessment may therefore add value precisely where it is most needed. Chapter 5 scales this logic to a set of seventeen LASA variables. It introduces the BUST framework: Breadth, Uniformity, Synergy, and Total. The framework characterises each variable pair along four dimensions. Breadth captures whether a pair’s synergy is distributed across many outcomes (generalist) or concentrated on a few (specialist). Uniformity captures whether synergy remains stable across age, sex, and multimorbidity strata or is context-dependent. Synergy quantifies the magnitude of the information available only when the variables are considered together. Total records overall dependence. The BUST map was applied across 2,040 variable-pair and target triplets in LASA. It summarised the 135 source pairs that carried synergy. This reveals three findings: First, the ten pairs ranked highest by the synergy-based composite share no members with the ten highest-ranked pairs by total mutual information. The two quantities are nevertheless weakly and positively correlated across all pairs (r = 0.31). Second, synergy is concentrated in clinically recognisable cross-domain constellations. These constellations link sleep, pain, mood, physical activity, and body composition. Third, synergy profiles are context dependent. For some pairs, synergy is distributed differently between participants with and without multimorbidity. For other pairs, the distribution differs across sex or age strata. Building on these profiles, the thesis assigns clinical features distinct informational roles. These roles are general indicators, disambiguators, or synergy gates. Each role reflects how a feature’s information is structured relative to different targets and contexts.

The third contribution extends PID from local variable sets to full symptom networks. It does so through approximation rather than exact decomposition. When every other symptom serves as context, a complete multivariate decomposition becomes infeasible. The number of information atoms grows faster than exponentially with the number of sources. Chapter 6 addresses this barrier through embedding-based PID (ePID). The method compresses all other symptoms into a single summary variable that preserves information most relevant to the target. A tractable two-source PID is then applied to the focal symptom, the compressed summary, and the target. Compression uses an Agglomerative Conditional Information Bottleneck. This groups the joint states of the remaining symptoms into a small number of categories that are chosen to retain target-relevant structure. The method is benchmarked against synthetic networks with three to five sources, where the ground-truth decomposition is known. The embedding tracks synergistic information closely (r = 0.92). The empirical applications embed a larger remainder than this validated range. The reported atom fractions should therefore be read as approximate. In UK Biobank and the Xinxiang student sample, the PHQ-9 depression data show that most pair-to-target dependence is shared with the remainder. This occurs through two channels: redundancy and remainder-unique information. Redundancy alone accounts for 45 to 51 per cent of the decomposed information. Synergy constitutes a small component. This highlights specific symptom configurations where interaction-aware modelling may be needed rather than additive approaches alone. The composition of information channels replicates across cohorts. Spearman correlations are 0.59 for redundancy, 0.68 for remainder-unique information, and 0.78 for synergy. This supports the generalisability of the decomposition. It also suggests that higher-order structure in depressive symptom networks is not an artefact of a single sample. The same decomposition protocol is applied to a contrasting instrument, the 28-item Interpersonal Reactivity Index. Here, the pipeline returns a synergy-dominated decomposition. This indicates that embedding-based PID registers synergy dominance where it is present rather than imposing either pattern.

These three contributions form an integrated framework whose progression from motivation through discovery, application, interpretation, and scaling reflects the practical arc of making higher-order dependence a computable object rather than a conceptual curiosity. The common thread is an information-theoretic weighting and interpretation programme for clinical systems. Each chapter adds a layer: a demonstration that pairwise representations are structurally incomplete, search heuristics that make synergy discoverable without exhaustive enumeration, structured summaries that compress high-dimensional interaction landscapes into interpretable maps, and embedding-based approximations that extend the decomposition to full symptom networks. The thesis begins from the mismatch between disease lists and lived function; the framework developed here offers a way to make that hidden structure visible, quantifiable, and clinically interpretable. Rather than replacing existing analytic tools, the approach complements them by exposing a mode of dependence that additive and pairwise representations cannot express by construction. Important limitations remain: all analyses are cross-sectional and observational, PID decompositions depend on the choice of redundancy measure and the included variable set, and treatment processes, which shape the symptom landscape in multimorbidity populations, are not included as sources or conditioning variables.

The broader significance of this work lies in making context visible and computable in precisely those settings where measurements span multiple clinical domains and decisions must be made for individual patients. In such settings, the operative question is not whether a variable is associated with an outcome, but whether additional measurements provide genuinely new information for a given person or subgroup, or whether they largely repeat existing signal. By providing a principled way to separate redundancy from synergy, and by developing computational scaffolding that makes these quantities discoverable and interpretable at scale, the thesis contributes a step towards a more operational notion of personalised medicine: not merely predicting outcomes, but understanding which combinations of measurements are informative, for whom, and under what conditions. The methods introduced here have been tested on ageing-cohort, cardiovascular-risk, metabolomic, psychiatric-symptom, and psychometric data across several independent samples, namely LASA, the Cardiovascular Risk in Young Finns Study, the UK Biobank metabolomics panel, UK Biobank mental-health data, and the Xinxiang student sample, together with an online sample completing the Interpersonal Reactivity Index; whether they generalise to other clinical domains and data modalities remains an empirical question. The present work provides the conceptual and computational foundation on which that broader validation can proceed.