Representing multimorbid disease progressions using directed hypergraphs

Objective To introduce directed hypergraphs as a novel tool for assessing the temporal relationships between coincident diseases, addressing the need for a more accurate representation of multimorbidity and leveraging the growing availability of electronic healthcare databases and improved computational resources. Methods Directed hypergraphs offer a high-order analytical framework that goes beyond the limitations of directed graphs in representing complex relationships such as multimorbidity. We apply this approach to multimorbid disease progressions observed from two multimorbidity sub-cohorts of the SAIL Databank, after having been filtered according to the Charlson and Elixhauser comorbidity indices, respectively. After constructing a novel weighting scheme based on disease prevalence, we demonstrate the power of these higher-order models through the use of PageRank centrality to detect and classify the temporal nature of conditions within the two comorbidity indices. Results In the Charlson population, we found that chronic pulmonary disease (CPD), cancer and diabetes were conditions observed early in a patient’s disease progression (predecessors), with stroke and dementia appearing later on (successors) and myocardial infarction acting as a transitive condition to renal failure and congestive heart failure. In Elixhauser, we found renal failure, neurological disorders and arrhythmia were classed as successors and hypertension, depression, CPD and cancer as predecessors, with diabetes becoming a transitive condition in the presence of obesity and alcohol abuse. The dynamics of these and other conditions changed across age and sex but not across deprivation. Unlike the directed graph, the directed hypergraph could model higher-order disease relationships, which translated into stronger classifications between successor and predecessor conditions, alongside the removal of spurious results. Conclusion This study underscores the utility of directed hypergraphs as a powerful approach to investigate and assess temporal relationships among coincident diseases. By overcoming the limitations of traditional pairwise models, directed hypergraphs provide a more accurate representation of multimorbidity, offering insights that can significantly contribute to healthcare decision-making, resource allocation, and patient management. Further research holds promise for advancing our understanding of critical issues surrounding multimorbidity and its implications for healthcare systems. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This study is based on work originally funded by the Medical Research Council (MRC) (Grant No.: MR/S027750/1) and supported by Health Data Research UK (Grant No.: HDR-9006), which receives its funding from the UK Medical Research Council, Engineering and Physical Sciences Research Council, Economic and Social Research Council, Department of Health and Social Care (England), Chief Scientist Office of the Scottish Government Health and Social Care Directorates, Health and Social Care Research and Development Division (Welsh Government), Public Health Agency (Northern Ireland), British Heart Foundation (BHF) and the Wellcome Trust; and Administrative Data Research UK, which is funded by the Economic and Social Research Council (Grant No.: ES/S007393/1). ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: Information Governance Review Panel of the SAIL Databank and Swansea University gave ethical approval for this work. I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes The data used in this study are available in the SAIL Databank at Swansea University, Swansea, UK. All proposals to use SAIL data are subject to review by an independent Information Governance Review Panel (IGRP). Before any data can be accessed, approval must be given by the IGRP. The IGRP carefully considers each project to ensure the proper and appropriate use of SAIL data. When approved, access is gained through a privacy-protecting trusted research environment (TRE) and remote access system referred to as the SAIL Gateway. SAIL has established an application process to be followed by anyone who would like to access data via SAIL https://www.saildatabank.com/application-process. This study has been approved by the IGRP as project 1392.