Introduction
The COVID-19 pandemic has raised awareness of the complex nature of the disease’s impacts beyond healthcare to global networks (e.g., economies, supply chains, politics, socioeconomic factors) in a hierarchy that ranges from nations to individuals to molecules (e.g., vaccines, antibodies, viruses). Humans tend to deal with such complexity by applying reductionistic approaches to cut the problem into pieces that can be better conceptualized and managed. While this makes the approach more tractable, it can limit the ability for solutions to generalize to real-world problems. The need to rapidly digest, evaluate and create policy/recommendations based on the increasing amount of data being generated in COVID-19 studies is constantly challenged by the lack of specificity that results from reductionist labeling. The seemingly simple classification of fully vaccinated, partially vaccinated, and non-vaccinated typifies this issue.
Algorithmic modeling has developed rapidly and can be used both on large complex data sets and on smaller, more quantitative data sets.1 With the current emphasis on the capture and analysis of big data, one of the great challenges is the ability to compare or integrate diverse data types.2 In this study, we choose a network-community-based approach that is founded on an algorithmic model. We implemented and have been exploring the use of community detection algorithms3–5 that can be applied in two ways: (1) identify a target outcome and determine what factors are associated with predicting whether a population will attain that outcome; and (2) identify communities with common characteristics and evaluate their respective outcomes to facilitate better patient management, drug development, and more effective reimbursement policies. In Figure 1, we highlight the difference between these two approaches in the example of heart failure with preserved ejection fraction (HFpEF).
In the United States, heart failure affects approximately 6.2 million individuals, with a prevalence of 2.4–2.6%, and appeared on ∼14% of all death certificates in 2018.6 Heart failure is considered to be a “complex clinical syndrome” characterized by high comorbidity burdens.7 Many of the patients exhibit non-specific symptoms, which makes it difficult to identify heart failure and distinguish it from other conditions. Thus, many patients may have undiagnosed heart failure, or even when diagnosed, other undiagnosed concomitant conditions, such as diabetes which is common in patients with acute heart failure, may confound the heart failure diagnosis. It is important to identify these patients and provide access to appropriate treatment to reduce mortality, improve healthcare, and reduce costs derived from undiagnosed/misdiagnosed diseases.8 Partly due to this difficulty of a clear diagnosis, there currently are no drugs approved for use for HFpEF. The diagnosis and management of HFpEF remain challenging for the physician, drug developers, payers, and ultimately for the patient.
The National Heart and Lung Institute (NHLI) Working Group on Research Priorities for HFpEF identified deep phenotyping as a critical need to address real-world complexity.9 Our thesis is that community detection methods may support HFpEF risk stratification, which would be doubly promising because they are expected to be greatly accelerated by early quantum computers. This work aims to describe our approach and test its ability to identify patient complexity levels and related clinical markers in the trial of a candidate HFpEF drug better than prior methods.
Methods and materials
Study design
This study re-analyzes the data from the Irbesartan in Patients with Heart Failure and Preserved Ejection Fraction (I-PRESERVE) clinical trial (where the initial analysis detected no subpopulation benefiting from the drug), recognizing that the graph representing the patients and medical variables is inherently bipartite and hence the community detection performed on it should reflect that bipartiteness. The data consists of 11 medical variables with a total of 34 categorical values (see Supplementary File 1). The community-detection implementation is also believed to provide better answers due to higher compute intensity, with the added benefit of further improved effectiveness from early quantum computers.
Data
This study was carried out using the baseline data derived from the Irbesartan in Patients with Heart Failure and Preserved Ejection Fraction (I-PRESERVE) clinical trial involving more than 5,000 patients, which began in 2002 and extended over 5 years.10,11 The data were obtained by contacting the I-PRESERVE study authors. Initial trial results showed no benefit over placebo and subsequent multiple subgroup analyses were attempted using traditional statistical clustering approaches with minimal success.12
Clinical guidelines for heart failure
The development of guidelines, commonly by committees based on data from randomized clinical trials, typically reveals limitations both in the assignment of specific diagnoses and their subsequent use in determining appropriate treatment. The development of guidelines for a specific condition ideally includes the recognition of the real-world complexity of the patient and disease with the need to differentiate accurately among both disease and patient sub-groups.
The challenge in the diagnosis of preserved-ejection-fraction heart failure (HFpEF) reflects that of applying clinical guidelines to address a syndromic condition. A gap exists between current clinical practice applied to real-world patients and strict adherence to either European Society for Cardiology (ESC)13 or AHA14 guidelines, which themselves undergo independent, periodic updating. It should be noted that such guidelines are intended to provide informed guidance to clinicians and full compliance is not mandated (nor expected). For example, the threshold level for LVEF as preserved varies among groups and reflects the observation, e.g., in the Framingham study, of limited ability to assign a specific threshold, especially because of the potential that an individual patient’s value may have changed due to pre-treatment between the time of initial diagnosis and enrollment into the I-PRESERVE trial and the more general observation that some patients with LVEF <45% may have HFpEF.15
Inclusion/exclusion criteria for I-PRESERVE
The inclusion and exclusion criteria for the I-PRESERVE study can be found at www.clinicaltrials.gov and are listed in Table 1.
Table 1Inclusion/Exclusion Criteria for I-PRESERVE
| Inclusion Criteria | Exclusion Criteria |
|---|
| a. At least 60 years of age | a. Previous intolerance to an angiotensin-receptor blocker |
| b. Heart failure symptoms | b. Alternative probable cause of the patient’s symptoms (e.g., significant pulmonary disease) |
| c. Left ventricular ejection fraction of at least 45% | c. Any previous left ventricular ejection fraction below 40% |
| d. Required patients to have been hospitalized for heart failure during the previous 6 months | d. History of the acute coronary syndrome, coronary revascularization, or stroke within the previous 3 months |
| e. Current New York Heart Association (NYHA) class II, III, or IV symptoms with corroborative evidence | e. Substantial valvular abnormalities |
| f. If they had not been hospitalized, they were required to have ongoing class III or IV symptoms with corroborative evidence, e.g. | f. Hypertrophic or restrictive cardiomyopathy |
| i. Pulmonary congestion on radiography | g. Pericardial disease; cor pulmonale or other cause of isolated right heart failure |
| ii. Left ventricular hypertrophy or left atrial enlargement on echocardiography | h. Systolic blood pressure of less than 100 mm Hg or more than 160 mm Hg |
| iii. Left ventricular hypertrophy or left bundle-branch block on electrocardiography | i. Diastolic blood pressure of more than 95 mm Hg despite antihypertensive therapy |
| g. Treatment with an angiotensin-converting enzyme (ACE) inhibitor was permitted only when such therapy was considered essential for an indication other than uncomplicated hypertension | j. Other systemic diseases limit life expectancy to less than 3 years |
| k. Substantial laboratory abnormalities (such as a hemoglobin level of less than 11 g per deciliter, creatinine level of more than 2.5 mg per deciliter [221 Î mol per liter], or liver-function abnormalities) |
| l. Characteristics that might interfere with compliance with the study protocol |
Sparseness of real-world (Clinical Trial) data
The current trend/discussion in data analysis, in healthcare and many other domains, focuses on access to and analysis of big data, but it has been long known that there is a constant tension between quantity and quality of data.16 Many current analytic methods, e.g., machine learning and deep learning, are dependent on access to large data sets; this reflects their emphasis on correlative vs causal analysis. For many applications, correlative analysis can provide critical guidance and optimal results but in medicine, unknown biases that may be present in the data may limit the utility of such analyses and even result in incorrect results and interpretation. The reality of real-world clinical data is its sparseness, i.e., measurement of limited numbers of medical variables and rarely in a continuous manner over time. The anticipated transition to digital medicine will help address this issue but will require a significant evolution of clinical practice, physician compliance, and patient adherence so will develop slowly over time despite increasing access to technology. Analytic methods, therefore, will be confronted with sparse data sets for some time and need to be pragmatic in their approach. Clinical trials provide a more controlled environment for the collection of data than typical clinical data, e.g., electronic health records (EHR), because of requirements to follow specific protocols, but even these exhibit significant sparseness in data collection. Table 2 documents the number of patients for whom data was gathered, at each time point in the I-PRESERVE data. We observe, i.e., at Month 18, that for almost all measurements more than half the patients do not have data. In general, high-density data collection is expensive and typically not undertaken without the ability to show value for the effort. In this study, we show how community detection can show increasing value for data integration, even in an incremental manner.
Table 2Data collected for I-PRESERVE at baseline, intermediate, and final times, reflecting the sparsity of current clinical practice
| General | Specific | Exam | Baseline | Wee 2 | Wee 8 | Mon 6 | Mon 10 | Mon 14 | Mont 18 | Mon 30 | Mon 42 | Mon 54 | Mon 66 | Tot |
|---|
| Liver & Kidney Function | Liver function tests | Alanine Aminotransferase (ALT) | 4,302 | 31 | 31 | 24 | 19 | 15 | 18 | 21 | 15 | 20 | 4 | 2,102 |
| Liver & Kidney Function | Liver function tests | Aspartate Aminotransferase (AST) | 4,302 | 32 | 32 | 22 | 19 | 16 | 22 | 26 | 16 | 21 | 4 | 2,104 |
| Liver & Kidney Function | Liver function tests | Bilirubin, Total | 4,302 | 30 | 27 | 17 | 14 | 10 | 9 | 12 | 10 | 16 | 2 | 2,104 |
| Liver & Kidney Function | Kidney function tests | Blood Urea Nitrogen | 4,209 | 27 | 27 | 18 | 14 | 10 | 9 | 9 | 10 | 16 | 2 | 2,058 |
| Liver & Kidney Function | Kidney function tests | Creatinine | 4,361 | 3,811 | 3,703 | 3,552 | 72 | 71 | 2,840 | 2,563 | 1,890 | 915 | 48 | 2,105 |
| Liver & Kidney Function | Kidney function tests | Creatinine Clearance (MDRD) | 4,361 | 3,811 | 3,699 | 3,549 | 71 | 70 | 2,834 | 2,557 | 1,888 | 914 | 46 | 2,105 |
| Other Chemistry Tests | Protein tests | Albumin | 4,302 | 30 | 27 | 17 | 14 | 10 | 9 | 11 | 10 | 16 | 2 | 2,103 |
| Hematology I | Erythroc./Platel. attributes | Hematocrit | 4,153 | 24 | 16 | 10 | 10 | 6 | 6 | 6 | 10 | 16 | 2 | 2,072 |
| Hematology I | Erythroc./Platel. attributes | Hemoglobin | 4,153 | 24 | 16 | 11 | 13 | 6 | 8 | 11 | 10 | 16 | 2 | 2,072 |
| Hematology I | Erythroc./Platel. attributes | Platelet Count | 4,146 | 24 | 15 | 9 | 11 | 5 | 4 | 6 | 11 | 16 | 2 | 2,068 |
| Hematology II | Quantitative WBC | Leukocytes | 4,152 | 24 | 16 | 11 | 11 | 6 | 6 | 6 | 11 | 17 | 2 | 2,072 |
| Hematology II | WBC differential count | Neutrophils (absolute) | 4,125 | 24 | 15 | 9 | 9 | 6 | 4 | 6 | 10 | 13 | 2 | 2,064 |
| Blood | Other testing | NT-proBNP | 3,620 | 32 | 13 | 3,034 | 1,160 | 2,926 | 89 | 7 | 4 | 0 | 0 | 0 |
| Electrolytes | Electrolytes | Potassium, Serum | 4,316 | 3,805 | 3,691 | 3,493 | 72 | 68 | 2,822 | 2,559 | 1,887 | 915 | 47 | 2,093 |
| Electrolytes | Electrolytes | Sodium, Serum | 4,302 | 29 | 27 | 17 | 14 | 11 | 9 | 12 | 10 | 17 | 2 | 2,103 |
The data presented in Table 2 reflect that collected in I-PRESERVE based on the protocol and case report forms. One goal of the analysis is to enable ease of integration of the results into current clinical practice. To facilitate this, the data was further mapped into conventional clinical panels used in the diagnosis and patient management. Note that this results in some observations being present in more than one panel, e.g., Alanine Aminotransferase (ALT, also known as Serum Glutamic Pyruvic Transaminase, SGPT) as shown in Table 3.
Table 3Medical variables were tracked in the I-PRESERVE study, by the system
| Blood | Liver | Kidney | Spleen |
|---|
| Age | Age | Age | Age |
| Gender | Gender | Gender | Gender |
| EOS – Eosinophils | ALB – Albumin | ALB – Albumin | ALT – Alanine Aminotransferase (SGPT) |
| HCT – Hematocrit | ALP – Alkaline Phosphatase | ALP – Alkaline Phosphatase | BILI – Bilirubin |
| HGB – Hemoglobin | ALT – Alanine Aminotransferase (SGPT) | BICARB – Bicarbonate | HCT – Hematocrit |
| LYM – Lymphocytes | AST – Aspartase Aminotransferase (GOT) | CL – Chloride | HGB – Hemoglobin |
| MONO – Monocytes | BILI – Total Bilirubin | CREAT – Creatinine | PLAT – Platelets |
| PLAT – Platelets | GGT – Gamma Glutamyl Transferase | K – Potassium | RBC – Red Blood Cell/Erythrocytes |
| RBC – Red Blood Cells/Erythrocytes | GLUC – Glucose | Na – Sodium | SPLEENLEN = Numeric Spleen Length |
| NEUT – Neutrophils | | UR - Urate | |
Current practice
Humans tend to deal with the complexity of many real-world data by applying reductionistic approaches to cut a problem into pieces that can be better conceptualized and managed.17 While this makes the approach more tractable, it can limit the ability for solutions to generalize to real-world problems. The application of reductionism in biology has been shown to be self-limiting.17,18 This is of particular concern when applied to diseases and disease management as the limitations of “naming” (classifying) a condition can have a significant impact on treatment decisions, payer reimbursement, and drug development, all resulting in sub-optimal patient management.
The power of algorithmic modeling has caused researchers to want to combine or integrate diverse types of data, and the novelty of these combinations has further led to a desire to examine data using different algorithms. For example, for data sets that do not necessarily present readily definable clusters, the application of different clustering methodologies may result in variable results which may make any interpretation dependent upon the methodology used.2
In the United States, heart failure affects approximately 6.2 million individuals, with a prevalence of 2.4–2.6%, and appeared on ∼14% of all death certificates in 2018. Globally it is estimated that 64.3 million people are living with heart failure or ∼1–2% of the general population. In the US, the cost of care for heart failure, including direct and indirect costs, is estimated at $43.6B per year and projected to increase to $69.7B by 2030 with ∼70% of these costs going to medical care.6
Heart failure is commonly classified in terms of the Left Ventricular Ejection Fraction (LVEF) into three classes: heart failure with reduced (HFrEF; LVEF <40%, previously known as systolic heart failure), mid-range (HFmEF; LVEF 40–49%), or preserved ejection fraction (HFpEF; previously known as diastolic heart failure, LVEF ≥50%).19 These thresholds may vary among studies and sometimes mid-range is further divided into 40–45% and 45–50%. The actual observed distribution reveals the challenge in defining separable boundaries using only LVEF as the major classifier (or label). The data in Table 420 display the association between simple LVEF classifications, gender, and the causes of death from cardiovascular diseases (CVD), distributed into the coronary heart (CHD) and other diseases.
Table 4Distribution of left-ventricular-ejection-fraction classifications, gender, and disease
Cardiovascular Disease (CVD) Deaths
|
|---|
| LVEF classification by gender | CHD | Stroke | Other CVD | Total |
|---|
| HFrEF male | 45% | 5% | 27% | 77% |
| HFrEF female | 30% | 14% | 26% | 70% |
| HFpEF male | 11% | 3% | 25% | 39% |
| HFpEF female | 15% | 11% | 23% | 49% |
Actual diagnostic guidelines, however, include additional factors and clinical/medical variables, e.g., comorbidities and levels of N-terminal pro-B-type natriuretic peptide, to establish the diagnosis and highlight the complexity of disease presentation. As noted above, the reductionist classification of the disease, based solely on LVEF, does not adequately stratify the disease and patients and hence enables more personalized diagnosis and management and/or development of more effective drugs.
Patients who currently present or have prior symptoms of heart failure are classified as HFpEF. The American College of Cardiology (ACC)/American Heart Association (AHA) classifies these patients in stages C and D, while those patients in stage B are considered to be at risk for developing HFpEF. Additionally, HFpEF must be distinguished from valvular disease, pericardial disease, and cardiac amyloidosis. Currently, approximately 50% of heart failure is HFpEF with a higher prevalence among older patients and females. Moreover, HFpEF diagnosis has increased by 45% over the last two decades.
The other 50% of heart failure is classified as HFrEF. Similar clinical manifestations appear in HFrEF and HFpEF including peak oxygen uptake (VO2) and neurohumoral activation. Many comorbidities are common between HFrEF and HFpEF including hypertension, atrial fibrillation, diabetes mellitus, metabolic syndrome, obesity, chronic obstructive pulmonary disease (COPD), chronic kidney disease, and anemia.
Angiotensin-converting enzyme inhibitors (ACEIs), angiotensin receptor blockers (ARBs), beta-blockers, mineralocorticoid receptor antagonists (MRAs), and diuretics form the basis of first-line pharmacological management of left ventricular heart failure with reduced ejection fraction (i.e., HFrEF). However, until 2021, no drugs had been approved for use in HFpEF although there were 17 active clinical trials involving 14 unique agents and testing 14 endpoints, involving 10 distinct classes of mechanism of action, and thus there was great interest in finding an effective drug. In 2021, based on analysis of the PARAGON-HF trial,21 sacubitril/valsartan (Entresto™, Novartis) received a broad heart failure indication that reached into the normal range of ejection fraction. It was noted that most benefits remained in the HFrEF population despite missing its primary endpoint. Significance was shown in subgroup analysis involving patients with an ejection fraction at or below the median of 57%. (Note: More recently, a sodium-glucose cotransporter-2 (SGLT2) inhibitor (Farxiga™) has shown a positive effect in HFpEF patients in the Emperor-Preserved study.22)
The main tests that comprise the initial HFpEF diagnosis remain Doppler echocardiography and serum natriuretic peptide levels. Further diagnostic scoring of patients currently utilizes two scores, H2FPEF and HFA-PEFF, which include some degree of subjectivity in the evaluation and interpretation.23 H2FPEF includes evaluation of body mass index, hypertension, atrial fibrillation, pulmonary hypertension, age, and filling pressure. HFA-PEFF the incorporates assessment of major and minor criteria within functional, morphological, and biomarker categories. In general, however, the use of multi-variable scores can obscure critical heterogeneity in patient groups. It has been noted that current HFpEF diagnoses are confounded by the presence of several significant subtypes.
Modularity-based community detection
The goal of this study was to classify or stratify patients using community detection algorithms that were objectively data-driven, i.e., which identified patient groups based on similarity of clinical presentation. This was done differently from conventional subgroup analysis that would select a target characteristic, e.g., response to a specific therapy, and then identify the characteristics that were common among those patients. In addition, the community detection method requires no pre-determination of how many patient groups, how many medical variables were needed to define these groups, whether each group reflected different values of the same medical variables, or even if the same set of variables was used to define the individual groups based on their values. The community detection algorithms were evaluated using both unipartite and bipartite graphs.
Modularity-based community detection (mCD) was first described and implemented by Newman and Girvan3 based on their insight that communities in a graph are best defined as “a statistically surprising arrangement of edges”. Their analysis converted the general problem of finding communities into a graph-based constrained optimization problem, where the metric to be maximized is modularity, and there are constraints for every node to be in exactly one community. Modularity is defined as a difference of two terms: (1) the density of edges inside communities as compared to edges between them, minus (2) the same measure for the corresponding null model, i.e., a graph where each node has the same number of edges as the original graph, but the connected nodes are randomized.
Finding the globally optimal answer to a modularity maximization problem is NP-hard, meaning its computational cost on a classical computer grows exponentially with the number of nodes. Thus, many implementations, including Newman-Girvan’s, are greedy heuristic algorithms that make locally optimal decisions each iteration, with no guarantee they will be able to find the globally optimal solution. Quantum computers, whose quantum bits (qubits) work in the exponentially larger quantum problem space than bits of classical computers, are expected to be able to find globally optimal answers for many classes of NP-hard problems efficiently, and there is vigorous research into quantum algorithms even though practical hardware implementations for real-world sized problems are still years away.24 Researchers at Los Alamos National Laboratory (LANL) describe a quantum implementation for mCD in Negre et al.25 that targets the globally optimal answer, though real-world samplers are currently heuristic. If there are N nodes in the graph, searching for K communities requires N * K variables, or qubits if the problem is being solved on a quantum computer. In the case of the current study, N = (3,935 patients + 34 medical variables) and K = 5, which requires ∼20,000 densely connected qubits. This is well beyond the capability of the largest available quantum annealing computer, the D-Wave Advantage™ system, with 5,600 sparsely connected qubits, and even further beyond the capability of the largest available gate-model quantum computer, the IBM Eagle processor, with 127 sparsely connected qubits. The effectiveness of early quantum computers in solving constrained optimization problems like mCD was discussed by Hen and Spedalieri26 and Hadfield et al.27
Note that our hypothesis consists of two primary tenets: that mCD will give better clustering than prior methods, and that quantum computers will accelerate the performance of mCD. While we provide conceptual arguments supporting the latter, only the first of these is tested in this paper.
Community detection for unipartite and bipartite graphs
The simplest graphs are unipartite, i.e., they consist of only one type of node. An example would be to consider the atoms in a protein molecule as the nodes of a graph, with the strength of their connections equal to the pairwise atomic-level forces between them. mCD can identify a community of atoms for each amino acid in the protein. Unipartite graphs were what Newman and Girvan originally studied, and many software systems only consider this type of graph.
However, in the real world, many graphs are bipartite graphs, which are defined as having nodes of two types and edges that only join opposite types of nodes. Communities for unipartite graphs are often described informally as having high connectivity within communities and lower connectivity between communities. That mental model does not hold for bipartite graphs, where there is, by definition, no connectivity between same-type nodes within a community, so we must depend more explicitly on the definition of modularity. To bring the bipartite model to a concrete example, we view humans, not as atoms; they do not generate their own connections. They are connected by the events they attend, the papers they co-author, the movies they act in, etc., and so they are typically found in bipartite graphs. One standard example studied in the literature is the Southern women graph documented by Davis et al.,28 consisting of 18 women and the 14 events they attended in the 1930s. The women are connected to the events they attended, and the events are connected to the women who attended them. Figure 2 illustrates the best assignment of communities found by Liu and Murata29 for the Southern women graph. Each community (to the left and right of the vertical blue bar, respectively) contains both events (white nodes with black text) and women (black nodes with white text).
In the current study, there are two types of nodes – patients and medical variables – so it is also a bipartite graph. Medical variables do not connect directly to other medical variables and patients do not connect directly to other patients; they only connect indirectly through common medical data.
The null model for a unipartite graph is not correct for a bipartite graph, because it assumes any two nodes can be randomly connected by an edge, and so it connects nodes of the same bipartite type in violation of the definition. Barber30 presents the correct null model for a bipartite graph, where nodes are randomly connected only to nodes of the opposite type. See Calderer and Kuijjer31 and Ganji32 for more discussion of when unipartite or bipartite mCD is appropriate.
The current study did the initial mCD analysis33,34 using the Gephi implementation of the Louvain method.35 Gephi is an open-source graph visualization tool,36 which uses a heuristic algorithm that is limited to the computational resources present where it is executing, usually a user’s laptop/desktop system. That limitation directly affects the quality of the community assignments it can find. Gephi calculates modularity only for unipartite graphs. We calculated bipartite modularity for the Gephi unipartite solution by running it through Qatalyst’s bipartite modularity calculation.
The Qatalyst quantum-acceleration platform, by Quantum Computing Inc., samples binary constrained optimization problems using classical and quantum processors, with quantum-ready heuristic formulations; the best results are currently obtained running purely classically, with no quantum contribution.37,38 Graph-based mCD is readily expressed as a constrained optimization problem25 that Qatalyst can effectively sample. Qatalyst runs on AWS servers, with the compute-intense classical quadratic-unconstrained-binary-optimization (QUBO) sampler executing on thousands of cores. The current study used Qatalyst for both unipartite and bipartite calculations.
Selection of data for analysis: framing the question
Understanding the complexities of data like those present in this study has led to much development and application of methods such as deep learning. Our focus on moving from correlative towards causal analysis and the ability to calculate real-world results has led us to enable the evaluation of specific models that are readily applied in current clinical practice. Several example models include:
Disease Model 1 (Patient Demographics and anamnesis): Age, Gender, BMI, Age at Diagnosis, Number of years post HF diagnosis (entry into the trial), Atrial Fibrillation by ECG, Left Bundle branch block by ECG, Left Ventricular Hypertrophy by ECG, Peripheral Edema, Left Ventricular Ejection Fraction, Etiology;
Disease Model 2 (Clinical History): Age, Gender, BMI, Age at Diagnosis, Number of years post HF diagnosis (entry into the trial), History of COPD, History of Diabetes, History of Atrial Fibrillation, Heart Failure within previous 6 months, Jugular Venous Distension, Lung Sounds, Left ventricular hypertrophy or Left Atrial Enlargement, NY Heart Association Functional Classification;
Hematologic Profile (Clinical Data): Age, Gender, BMI, Albumin, Hematocrit, Hemoglobin, Platelet Count, Leukocytes, Neutrophils (absolute), NT-proBNP;
Liver & Kidney Function. (Clinical Data): Age, Gender, BMI, ALT, Aspartate Aminotransferase (AST), Bilirubin (total), Blood Urea Nitrogen (BUN), Creatinine, Serum Potassium, Serum Sodium, Creatinine Clearance (MDRD);
NT-proBNP (Clinical Data): At the time of initiation of I-PRESERVE, levels of NT-proBNP were not incorporated into clinical guidelines for the diagnosis of heart failure but were added in subsequent studies and are currently used as a threshold for diagnosis of heart failure;
Longitudinal/Temporal analysis (Clinical Data): Initial analysis of patient progress during the study was planned to develop patient trajectories, e.g., patterns of progression both with treatment and placebo, for purposes of comparative analysis. Longitudinal/Temporal analysis was limited by data sparsity.
We choose to define a single model for liver function and kidney function, based on evidence for co-existing liver and kidney pathology in patients with chronic liver disease. Chronic liver disease is associated with primary and secondary kidney disease and impacts markedly on survival.39 Moreover, we define the Hematologic model including NT-proBNP data as most HFpEF patients have elevated NT-proBNP levels. The NT-proBNP concentrations were related to baseline characteristics generally associated with worse outcomes for HF patients.40
For example, the clinical data for both the Liver & Kidney panel and the Hematologic panel are provided (in Supporting Material) where the categorization was based on observed medical-variable ranges in patients and also includes gender-based differences. We initially developed categorical boundaries, i.e., cutpoints, for each medical variable based on current laboratory standards. These boundaries were further refined based on cardiologist input as potentially relevant to the study population. These boundaries also reflect the expected differences between male and female patients, and where appropriate, reflected a high/normal/low classification. A result is several categories that defined individual nodes: for example, BMI is defined into 5 categories Underweight (<18.5; BMI-L), Normal weight (18.5–24.9; BMI-N), Overweight (25.0–29.9; BMI-H-OV), Obese (30.0–34.9; BMI-H-OB), Morbidly obese (>35; BMI-H-OB*); ALT is defined by 3 categories for male (H high, N normal, L low), ALT-L <0, ALT-N between 0 and 55, ALT-H: >55 and 3 categories for female, ALT-L <0, ALT-N between 0 and 40, ALT-H >40.
Benefits of community detection for this analysis
Despite some observations being present in more than one panel, e.g., ALT, the data was readily incorporated into this community-detection analysis.
We believe that the use of the community detection method described in this report can effectively address critical issues in clinical medicine, going beyond correlation to approach causality. Perhaps the leading example of these issues is that the use of the panels outlined in Table 3 provides a convenient assessment of a patient’s status along with specific pathophysiologic domains through the highlighting of “outliers” from normal lab values:
The “normal” ranges for these medical variables may be dependent on an individual’s clinical history, co-morbidities, diet, etc., and thus require “personalized” evaluation;
While individual outliers may suggest diagnostic and therapeutic intervention, including lifestyle and/or medication, e.g., low hemoglobin suggesting anemia, it is not uncommon for multiple medical variables to be non-normal with the increased complexity being less commonly observed and with reduced indications for management;
Temporal changes in an individual’s multiple medical variables may be much more informative of a patient’s status than single-point-in-time measurements. Such temporal patterns may involve clinical medical variables that never individually trigger an “abnormal” classification;
Higher level complexity in temporal measurements, i.e., patterns involving more than one clinical variable, would be very difficult to detect but may be critical to define a more accurate diagnosis and staging of a specific condition.
Results
Unipartite analysis
Our first mCD-based analysis of the data viewed the problem as unipartite. The resulting communities via the Gephi implementation are described below in terms of disease characteristics’ association and patient numerosity; the number of nodes always includes patients’ and characteristics’ nodes. With the unipartite Gephi implementation, the best results were obtained for K = 5 communities with modularity = 0.061 (Fig. 3).
Pink community
This group is composed of 1,125 nodes (1,116 patients). It aggregates Females aged 60–69, obese and morbidly obese (BMI-H-OB and BMI-H-OB*), showing several high serum values (Alanine Aminotransferase – ALT-H, Aspartate Aminotransferase – AST-H, Sodium – SOD-H) and normal values of Potassium (K-N) and Bilirubin (BILI-N).
Cyan community
It is the biggest community, composed of 1,177 nodes (1,168 patients). It aggregates Males, Overweight (BMI-H-OV), aged 70–79, with mildly reduced kidney function (KIDFUN-MIL) characterized by low values of BILI and K (BILI-L, K-L) and normal values of Blood Urea Nitrogen (BUN-N), Creatinine (CREAT-N), and SOD.
Green community
It is composed of 393 nodes (390 patients). It aggregates patients with normal weight (BMI-N) and low values of SOD (SOD-L), and normal values of AST (AST-N).
Red community
Composed of 999 nodes (990 patients), it aggregates the oldest patients (≥80), underweight (BMI-L) with severely or moderately reduced kidney function (KIDFUN-SEV, KIDFUN-MOD), and several abnormal values: high values of Bilirubin, Blood Urea Nitrogen, Creatinine, and Potassium (BILI-H, BUN-H, CREAT-H, K-H) and low values of Alanine Aminotransferase (AST-L), with normal values of Alanine Aminotransferase (ALT-N).
Yellow community
This is the smallest community, composed of 276 nodes (272 patients). It aggregates the youngest patients (<60) with normal kidney function (KIDFUN-NOR), and low values of BUN and CREAT (BUN-L, CREAT-L).
To evaluate the clinical significance of these communities, we compared them using conventional survival analysis with the outcome of death/survival, neither of which had been included in the derivation of these communities. In terms of the quality of the patterns we can observe that the Red curve (representing the Red community) refers to the patients with shorter life expectancy; the Yellow curve (representing the Yellow community) shows the patients with higher life expectancy. This is coherent with the Liver & Kidney communities’ composition. Moreover, the performed log-rank test (Bonferroni adjustment for multiple comparisons) revealed statistical significance: a) the Green curve has statistical significance concerning the Yellow (p = 0.003); b) the Red curve concerning the Yellow, Cyan, and Pink curves (Red vs Yellow p < 0.001; Red vs Cyan p < 0.001; Red vs Pink p < 0.001).
Using the same data, Qatalyst finds an optimal answer of K = 4 communities with modularity = 0.144 and finds a slightly smaller modularity (=0.142) for K = 5 communities (greater modularity indicates stronger communities). These values are graphically represented in Figure 3. Looking at the Kaplan-Meier survival curves in Figure 4, the lines for two of the five communities (Cyan and Pink) almost completely overlap, lending weight to the finding of four communities as being globally optimal.
Table 5 explores the overlap between the 5-community solutions found by Gephi and Qatalyst. Each entry is a pair of numbers (m, p), where m is the number of medical variables and p is the number of patients in the community: so, by example, (3,390) to the right of “Green (m, p)” indicates that in the Green community of the Gephi solution there are 3 medical variables and 390 patients. The outer values are the counts for the two solutions, horizontal values come from the Qatalyst solution and vertical values come from the Gephi solution. The values in the box represent the overlap of patients between pairs of communities. The assignment of numbers to communities is arbitrary, so even if the same solution was found twice, the community numbers assigned could be different. In this case, we see that a majority of Gephi Community 2 (the Red community) wound up as the majority of Qatalyst Community 5 (data in italic).
Table 5Comparison of unipartite communities found by Gephi and Qatalyst; (m, p), m = number of medical variables; p = number of patients
| Qatalyst Communities | Community 1 (m, p) | Community 2 (m, p) | Community 3 (m, p) | Community 4 (m, p) | Community 5 (m, p) |
|---|
| Gephi Communities | | (3, 296) | (11, 1,208) | (2, 327) | (8, 1,149) | (10, 955) |
| Green (m, p) | (3, 390) | (0, 14) | (0, 59) | (1, 98) | (1, 137) | (1, 82) |
| Red (m, p) | (9, 990) | (0, 28) | (0, 148) | (0, 70) | (1, 228) | (8, 515) |
| Pink (m, p) | (9, 1,116) | (3, 182) | (5, 473) | (1, 78) | (0, 210) | (0, 173) |
| Yellow (m, p) | (4, 272) | (0, 5) | (4, 231) | (0, 8) | (0, 23) | (0, 5) |
| Cyan (m, p) | (9, 1,168) | (0, 67) | (2, 297) | (0, 73) | (6, 551) | (1, 180) |
Bipartite analysis
Realizing that the data of the current study is inherently bipartite, with patients and medical variables comprising the two separate sets of entities, we performed the calculations again treating the graph as bipartite.
Qatalyst implements Barber’s bipartite modularity calculation, which gives the unipartite Gephi solution bipartite modularity that is substantially higher than its unipartite modularity, a result due solely to the different null models. Maximizing bipartite modularity, Qatalyst again finds a solution with notably higher modularity than Gephi, i.e., modularity = 0.146 for K = 4 communities, as shown in Figure 5, with different communities than it found when ignoring the bipartite structure. For Qatalyst, the modularity difference between K = 4 and K = 3/K = 5 is larger using the bipartite null model than the unipartite, but the differences are still small.
Comparing the community assignments in detail between Qatalyst results for bipartite K = 4 and unipartite K = 5 in Table 6, we see a strong overlap between bipartite Community 1 and unipartite Community 5, as well as bipartite Community 3 and unipartite Community 2 (both in italic). Most of the small bipartite Community 4 winds up in unipartite Community 1, but bipartite Community 2 is redistributed across the unipartite communities.
Table 6Comparison of unipartite and bipartite communities found by Qatalyst; (m, p) m = number of medical variables; p = number of patients
| Qatalyst | Bipartite | Community 1 (m, p) | Community 2 (m, p) | Community 3 (m, p) | Community 4 (m, p) |
|---|
| Unipartite | | (13, 1,208) | (9, 1,479) | (11, 1,187) | (1, 61) |
| Community 1 (m, p) | (3, 296) | (2, 134) | (0, 114) | (0, 5) | (1, 43) |
| Community 2 (m, p) | (11, 1,208) | (0, 44) | (2, 269) | (9, 895) | (0, 0) |
| Community 3 (m, p) | (2, 327) | (1, 137) | (1, 134) | (0, 52) | (0, 4) |
| Community 4 (m, p) | (8, 1,149) | (1, 51) | (5, 895) | (2, 193) | (0, 10) |
| Community 5 (m, p) | (10, 995) | (9, 842) | (1,67) | (0, 42) | (0, 4) |
Comparing the characteristics that describe the communities found between Qatalyst unipartite and bipartite approaches (see Fig. 5), we see that some communities have similar characteristics, such as the Orange unipartite and the Mustard bipartite community, but there are still some significant differences between the two. The difference in the obtained results demonstrates the importance of using the correct null model for the type of mCD problem being solved.
Discussion
In this study, we have applied a novel approach to stratification of HFpEF patient data to objectively elucidate the HFpEF subtypes using a hypothesis-free, data-driven approach and outlined the method and results.
In the last few decades, various technological and cultural changes have contributed to exposing the limitations of the hypothesis-driven approach to knowledge discovery.41 First, all scientific disciplines are nowadays required to tackle increasingly challenging, nonlinear problems and systems, some of which are very difficult, if not impossible, to model with theories based on first principles. Moreover, many newly interesting phenomena, for various reasons ranging from intrinsic randomness to inaccessibility for measurement, are characterized by a high level of uncertainty, limiting the effectiveness of traditional statistical approaches. All this is in the context of an exponential increase in data availability and complex relations among different data collected on the same statistical unit, in particular, if it is the real-world patient. The imprecision of many common diagnostic categories implies the need of specifying inclusion/exclusion criteria in more detail for a clinical trial, along with scientific and commercial considerations. This leads to significantly differentiating the patient recruited for the trial from the real-world patient and limiting the ability to directly compare results among independent trials.42,43
The large amounts of data being captured in COVID-19 studies and the urgency of processing that data into information usable by laypeople have highlighted the lack of specificity that results from reductionist labeling. The seemingly simple classification of fully vaccinated, partially vaccinated, and non-vaccinated typifies this issue. For the mRNA vaccines, Pfizer and Moderna, does this mean 2 shots? And do boosters create a 3-shot vaccination program? Does this include a two-week post-shot period for the immune response to develop? For non-mRNA vaccines, e.g., Johnson and Johnson, is it a 1-shot course or does it require a booster? And with a booster or multiple-shot protocols, how should the mixing of vaccines be considered as well as the length of time between shots? This complexity is further compounded when these events concern subjects in a frail state, even if temporary, as happens to women during pregnancy, i.e., during the pre-conception, gestation, or post-partum periods, as to their impact on the baby or the mother. While the application of simple classifications facilitates statistical significance to be evaluated for such groupings, as Rose stated,18 “…ideological reductionism manifests…confusion of statistical artifact with biological reality”. Traditionally, there are two considerations in the use of statistical modeling to derive subgroup conclusions from the data. One assumes that the data are generated by a given stochastic data model. The other uses algorithmic models and treats the data dependency as being unknown.
We have used community detection to emphasize the difference between model-driven analysis and data-driven analysis. In the former, data is evaluated as to how well it may fit an existing model or how to refine the model to fit the data. In the latter, we are using an objective analysis of the data to identify what models may exist within the data.
Because of our focus on driving towards causality versus correlation and our intention to establish ease for clinical utility, we further incorporate clinical processes and pathways into the analysis. We distinguish our application of community detection from conventional unsupervised learning methods as we are developing and implementing complex functional models, e.g., following clinical practice, to help identify and better manage potential gaps and biases that may exist in the data.
We note a fundamental problem in all analyses that attempt to identify “subgroups” of patients, namely that missing data may present a challenge that big data alone cannot overcome. We have several studies underway that focus on identifying symptoms that indicate missing critical data, although they do not necessarily identify what specific data may be missing. In addition, parallel development of the comprehensive functional model enables the identification of data that may bias analytic results and their interpretation.
The integration of a functional model that includes the complexity of disease processes, clinical practice, and the complexity of a patient, e.g., lifestyle, environment, and genomics, is kept coherent by a knowledge graph that supports ongoing evolution as new concepts and relationships are identified, as well as a data model for functional integration of data from any source. The community detection algorithms described in this work operate on this knowledge graph.
Data enables an objective evaluation of its contents or any subset that may be selected to evaluate specific hypotheses. For example, communities can be identified that are based on data collected from EHRs and be compared with communities based on claims data to highlight the difference in perspective of these two data sources and their ability to describe a patient and their disease. Such a comparison could provide significant value to both the clinical community for improving patient management and the payer community for improving reimbursement policies, with both efforts yielding better outcomes for the patient.
While the application of our community detection approach introduced in this study has been focused on healthcare and a specific disease, HFpEF, it should be apparent that it represents an expanded view of how to address complex systems both in medicine and in many other fields. Community detection’s ability, with properly binned data, to discover and return the medical variables that define each community, rather than them being specified by an analyst, delivers a valuable unsupervised capability. The integration of community detection algorithms with a model of the true complexity of the problem space should be viewed as being potentially generalizable across many domains and not limited to medicine, although it can provide a unique opportunity to improve clinical care and patient outcomes across most diseases and conditions.
Strengths and limitations
The potential clinical meaning underpinning the found communities has not been validated. Based on evidence for existing both liver and kidney pathology in patients with chronic liver disease, we defined the “Liver & Kidney data model” instead of two separate ones, a “Liver data model” and a “Kidney data model”. Moreover, the absence of specific exam measurements suggested the combining of medical variables in a single data model. Specific exams for the Liver (Gamma Glutamyl Transferase, Glucose, ALP Alkaline phosphatase) were not present in the original data; other specific values for Kidney (Bicarbonate, Chloride, Urate) were absent too. Lastly, potential time points for the longitudinal analysis were excluded because of many missing data during the different periods of the trial. By running frequencies on laboratory values collected in different periods (Baseline, Week 2 and 8; Month 6, 10, 14, 18, 30, 42, 54, 66, 72) we found the highest frequencies at Baseline and Month 72. For this reason, longitudinal analysis was done considering two time points only, presenting weaknesses in the sustainability of the results.
Despite the limitations above, we found that community detection techniques applied in this study are well suited to analyze complex phenomena involving large amounts of information; we had a significant number of subjects with associated data, approximately 4,000, and with many (complex) relationships to disease characteristics about these subjects. The application of community detection methods has identified critical aspects derived from over-connected portions of the network; the assessment of the quality of the resulting aggregation involved consultation with clinicians and domain experts.
Future directions
We believe that the results of this study can be generalized for redefining the concept of phenotype to incorporate the patient’s progression through disease. We are currently applying this approach to several other diseases/conditions: multiple sclerosis, triple-negative breast cancer, and prematurity/infant-maternal morbidity and mortality. We believe that the next stage for refinement of diagnosis and both patient and disease stratification will require such evolution from current practice both for research and improved patient management and outcome.
Conclusions
This study has examined the application of community detection approaches to clinical trial data using algorithms applied to the I-PRESERVE study data. The resulting objective identification of specific subgroups, without the need to initially establish the number of subgroups or the number and identity of medical variables to include in the analysis, is a significant strength of this approach. In this manner, the data drives the analysis, and in the common situation where sparse data might be involved, is not limited in its ability to establish initial hypotheses about potential subgroups. The ability to incorporate disparate data without pre-selection also appears to potentially support a more integrative approach to clinical data analysis that can be used to improve disease stratification. These characteristics have the potential to enhance both the analysis of completed clinical trials, but of even greater significance, contribute to better clinical trial design and rates of success. The goal of this study was to review current limitations in disease stratification based on the need to apply reductionist considerations to achieve statistical significance and the potential to establish a data-driven, graph analytics approach that can lead to new study designs and hypotheses. We are currently applying these approaches in several other conditions and exploring the use of these results to further stratify HFpEF in clinical studies and patient management.
Abbreviations
- CD:
community detection
- mCD:
modular community detection
- HFpEF:
heart failure with preserved ejection fraction
- HFrEF:
heart failure with reduced ejection fraction
- LVEF:
left ventricular ejection fraction
- ARB:
angiotensin receptor blocker
- ALT:
alanine aminotransferase
- BMI:
Body mass index
- ECG:
electrocardiogram
- BILI:
bilirubin
- CREAT:
creatinine
- AST:
aspartate aminotransferase
- SOD:
sodium
Declarations
Acknowledgement
The authors would like to acknowledge ongoing discussions with Nicholas Sarlis, MD, Ph.D., and Michael Montgomery, MD.
Data sharing statement
The original data used in this work may be obtained from the I-PRESERVE study authors. The curated data for community detection is available from the authors.
Funding
Funding was provided through internal resources contributed by IPQ Analytics, CNR, and QCI.
Conflict of interest
ML is a technical advisor to QCI. ML has been an editorial board member of Exploratory Research and Hypothesis Medicine since February 2020. MW and SR were at the time of this work QCI employees. The authors have no other conflicts of interest to report.
Authors’ contributions
ML envisioned the whole experiment and ensured the connection to clinical usefulness. SP, MF, LF, MS, and SM prepared the data and did the initial unipartite-mCD analysis. MW performed the later bipartite-mCD analysis. SR provided analytic coherence and relevance for quantum computers. All authors have made a significant contribution to this study and have approved the final manuscript.