Our goal is to visualize participant attributes and the statistical traits and relationships between them in a compact, interpretable, and intuitive way. As a participant attribute, we consider a singular value or semantically meaningful value group for a variable, for example, “the participant was diagnosed with hypertension” or “participant has total cholesterol level above 200 mg/dL.” For the statistical analysis, we use simple metrics, which were found to be intuitive for clinicians [39]. The metrics are calculated for a disease and control group and compared to identify attributes with a large deviation. Thus, in contrast to traditional association rule mining [36], Bayesian networks [29], or Markov models [34], attributes can be selected, which appear more often in the disease group compared to the control group. As we analyze relations of singular attributes instead of associations between variables, our results are methodologically different from correlation analysis, such as chi-square tests [40] or Pearson correlation coefficients [41].

In the AAG, single attributes are captured as nodes and visualized as colored spheres of different sizes. Each node has parameters for the name of the attribute’s variable, its value, and a short description including units of measurement for metric variables. In addition, we assigned labels to each node depending on the broad categories of the represented attribute, for example, Cardiac, Condition, or Medical History.

For metric variables, we calculated reference ranges based on their value distribution within the whole data set. We defined the reference range as all values within SD around the mean. On the basis of reference ranges, we derived 3 additional nodes for the attribute associated with values below, within, and above the reference range. The 3 nodes inherit the parameter’s name and description from the original nodes. They have the value low, normal, or high. In addition, they contain the lower and upper bound of the reference range. All participants are assigned to 1 of the 3 nodes based on their attribute value. Thus, metric values, for example, patient laboratory results, are labeled in comparison to the whole data set and enriched with semantics.

In addition, we enriched the nodes with several statistical measurements of the described participant attribute within the data set. The resulting parameters are given in Table 1. Note that the relative attribute share accounts for the common problem of missing data [42,43] and is an upper bound to the relative total share. By measuring the difference and quotient of relative attribute shares, the distinction in attribute distribution between the 2 groups is expressed. The size and color of the node visualization capture parts of these measurements to support the data exploration with visual highlights.

We assigned a frequency label impacting the node’s size based on the maximum relative attribute share. Therefore, a node’s size indicates how common an attribute is within one of the groups. Let p be the maximum relative attribute share of a node. The node is assigned to 1 of the following 3 frequency label types:

In addition, we assigned a distinction label to each node from which its color is derived. The distinction label, and thus the node color, indicates how much the attribute distribution differs between groups. Here, brighter colors signal a larger distinction. We reuse the symbols in Table 1. Each node is assigned 1 of 5 colors and distinction label types:

Combining size and color, nodes that are displayed largest and brightest represent attributes with high frequency and large distinction between groups. As all parameters calculated for an individual node depend only on data for a single variable, the computation time needed for the calculation of all nodes of the graph scales linearly with the number of variables and linear with the sample size.

In the AAG, edges point from a source node to a target node, indicating the conditional dependence of the target attribute on the source attribute. The edges are displayed as lines with arrows pointing from the source node sphere to the target node sphere. The calculated statistical parameters for the conditional dependence are presented in Table 2. Note that the relative conditional share is conceptually equivalent to confidence in association rule learning [36]. By measuring the difference and quotient of the relative conditional share and the unconditional relative attribute share of the target node, the impact of the added condition is expressed. This impact can be negative if the unconditional relative attribute share is larger than the relative conditional share. We assign a type to each edge to capture the impact of the added condition. In the visualization, the line thickness of the edge is given by its type. We reuse the symbols in Table 2. Each node is assigned to 1 of the following 3 types:

The computation time for the generation of all the AAG’s edges scales quadratically with the number of variables in the data set and linear with the sample size.

In the last step, the nodes and edges are filtered by their statistical parameters to highlight the most relevant attributes and conditional dependencies. A detailed description of the filtering procedure is provided in Multimedia Appendix 1 [41,44,45]. We represented the extracted data in a graph structure using the graph data platform Neo4j [14] and the graphical user interface Neo4j Bloom (Neo4j, Inc) [19]. The graph structure can be navigated by mouse clicking and via a search bar typing prompts in English.

Figure 1 [46] shows a minimal fictional example of an AAG with 2 nodes capturing fictional data about history of hypertension and high C-reactive protein (CRP) measurements as well as their relationship in participant group 1 (control group) and 2 (disease group). We conducted a hypothetical data analysis, as we intend the AAG to be used. For CRP measurements (mg/dL), a fictional reference range of 0.0-0.8 was derived. From the difference of the relative total share and relative attribute share, we can infer existing missing values on group 2 for both attributes. In group 1, no missing values exist because relative total share and relative attribute share do not differ. Regarding the quotient of relative attribute shares, we can infer group 2’s participants being almost twice as likely to show a high CRP value. Thus, a CRP measurement >0.8 mg/dL might be highly related to the condition or property of group 2 compared to participants of group 1. A history of hypertension appears approximately 30% more often in group 2, giving a 60% proportional increase. As a result, its node is labeled as highly related to the condition or property of group 2. Viewing the data of the edges, we find that almost all participants with a high CRP measurement also have a history of hypertension in both groups. Therefore, high CRP values could be an indicator for hypertension in both fictional groups. Conversely, only approximately one-third of participants with a history of hypertension also show high measurements of CRP. This pattern of conditional relationship is similar between groups and could thus be independent of the group definitions, for example, medical condition and control group.

To complement the AAG, we generated a dashboard using the NeoDash (Neo4j, Inc) [17] toolkit. With the dashboard, users can investigate the average and distribution of metric variables across participant groups in more detail. In addition to the cardiovascular disease and control cohorts, the group of all participants contained in the Hamburg City Health Study (HCHS) data set was included. We developed 2 different tabs. The first tab allows for comparison of participant groups. We included the sizes of disease and control group. In addition, variable distributions can be compared between groups. For this purpose, we applied the following workflow to all metric variables and participant groups. First, we measured the variable average within the group. Second, we generated a binned distribution by rounding the measurements to multiples of 0.1, 0.5, 1, 5, 10, or 50 depending on the SD within the group. Bins containing <0.5% of the participants or <3 participants are summarized. We removed distributions without any bins fulfilling these requirements. The user can select 2 groups and variables for the distributions shown in the first tab of the dashboard. The averages of all metric variables for all 3 groups are shown in the first tab as well. To make them comparable in a figure, the averages of each variable are normalized by the maximum average of that variable. In the second tab, the user can investigate the relationship between 2 variables within a participant group. For the first variable, the generated binned distribution across the group is shown. For the second variable, we use precalculated averages of participants within a bin. The x-axis of the resulting figure shows the bin values of the first variable, and the y-axis shows the average value of the second variable for participants of that bin.

To evaluate the AAG and dashboard, we used an exemplary data exploration workflow of a large epidemiological cohort study. We compared the results with findings from literature and standard statistical analysis. The HCHS is a single-center, prospective, observational, population-based cohort study of 45,000 randomly selected residents of the metropolitan region of Hamburg, Germany, aged between 45 and 74 years. The study design has been published [47], and the study is registered [48]. The study focuses on major chronic diseases, causes for their development, as well as factors for survival and support for life in survivorship. The study considers >6000 properties per participant. The data are raised from 18 examinations, primarily targeting major organ systems, as well as questionnaires about medical and family history, physical condition, dietary habits, lifestyle, and various other topics. The examinations will be repeated after 6 years to obtain large-scale, long-term assessments. For this analysis, the HCHS committee provided a subset of the whole HCHS data set focusing on cardiovascular and cancer diseases. The subset consists of 524 selected attributes for the first 10,000 participants enrolled in HCHS, including information about laboratory analyses; electrocardiography (ECG); magnetic resonance imaging; vascular ultrasound examinations; blood pressure measurements; cardiovascular and cancer medical history questionnaires; as well as dietary, lifestyle and sleeping habits. We selected 131 (25%) of these 524 attributes, translated their descriptions to English, assigned labels to each variable to broad variable groups, and added Systematized Nomenclature of Medicine Clinical Terms [49] or Logical Observation Identifier Names and Codes [50] codes. When no directly fitting code was found, we chose the code of a related term. A full list of all variables, descriptions, labels, vocabulary codes, and data types can be freely accessed [46]. In some cases, the reference ranges calculated for the AAG deviated from the usual reference ranges known from the literature because of a different value distribution in the HCHS data set. In these cases, we manually adjusted the reference intervals according to the Merck Manual of Diagnosis and Therapy manual [44]. A full list of the adjusted reference ranges can be found in Table S1 in Multimedia Appendix 1. In this work, we focused on participants with a general cardiovascular condition. We included participants in this cohort who met any of the following criteria: showed any pathological cardiovascular findings during the cardiac magnetic resonance imaging examination; had a missing sinus rhythm; had a finding of atrial fibrillation or flutter in the ECG check; or reported a medical history of cardiac infarction, coronary artery disease, angina pectoris, congestive heart failure, myocarditis, or valvular endocarditis in the questionnaire. As a result, the disease cohort contained 1917 participants. In addition, we derived the control group of 8083 participants not exhibiting any of the conditions and findings.

The HCHS study was approved by the Ethics Committee of the Hamburg chamber of physicians (PV5131) and has been registered at ClinicalTrial.gov (NCT03934957).

We have generated the AAG for the disease and control group within the HCHS data set based on our definition of a general cardiovascular disease. In this paragraph, we give an exemplary data analysis using the graph and some aspects of the dashboard. This analysis was conducted by the authors of this work independently of the exploration of users during the usability test. The analysis is meant to showcase the usability of the graph representations and is by no means exhaustive. The Neo4j database dumps, configuration files, and user guide can be freely accessed [46]. In addition, the software tool used to generate AAGs was made publicly available [57] and will be presented in an upcoming publication. To assess the compatibility of the presented methods with standard statistical inference, we calculated Pearson correlation coefficients [41], 1-tailed CIs at the confidence level of 95% using the Fisher transformation [45], and P values for 1-tailed null hypothesis testing of statistical independence for all associations discussed in the following data analysis. The results can be found in Table S2 in Multimedia Appendix 1.

For brevity, we define the cardiovascular disease group as group A and its control group as group B. Group A contains 1917 participants, and group B contains 8083 participants. The generated AAG is shown in Figure 2 [14,46]. The nodes labeled as related or highly related form a cluster in the middle of the graph with the highest density of edges between them. Most of the inverse and highly inverse labeled nodes are primarily located on the periphery of the graph with many interconnections but few connections to the inner cluster. This observation indicates a clear distinction highlighted by the graph between the attributes based on their cooccurrence with cardiovascular disease within the HCHS data set.

For a more detailed analysis of this AAG, we focused on the laboratory results data shown in Figure 3 [14,46]. Within the graph, 3 nodes are labeled as highly related, along with several adjacent nodes labeled as related. The nodes representing glomerular filtration rate <60 mL/min/1.73 m² (“GFR-CKD, low”) and creatinine levels >1.2 mg/dL (“creatine, high”) are identified as highly related and are interconnected. Furthermore, they are also connected to the node representing elevated potassium levels >4.15 mmol (“potassium, high”) through high conditional difference relationships. The presence of a low glomerular filtration rate, high creatinine, and elevated potassium levels are all correlated with chronic kidney disease [58], which in turn is a risk factor for the development of cardiovascular conditions [58,59]. Thus, all 3 laboratory results are associated with heart disease in clinical settings [60], which coincides with the findings presented in this graph. The respective 95% CIs lie fully above 0 for creatine and potassium levels and fully below 0 for the glomerular filtration rate. The relative attribute share of the nodes for glomerular filtration rate <60 mL/min/1.73 m² (“GFR-CKD, low”) in group A is, with 12%, more than twice as high as the relative total share. This indicates missing values for glomerular filtration rate measurements in participant with a cardiovascular condition. The related node in the center of Figure 3 (“proBNP, high”) represents elevated N-terminal prohormone of B-type natriuretic peptide (proBNP) levels >125 ng/L, which were identified as a biomarker for cardiac diseases [61]. With 47%, group A has a 1.7-fold increased relative attribute share for this attribute compared to group B. The associated CI for the Pearson correlation coefficient is strictly positive. The node has 3 incoming edges of high conditional difference. Of these 3 edges, 2 describe the relationship between low glomerular filtration rate and high creatinine levels to elevated proBNP levels. Participants of group B with 1 of these properties are at least 1.6-fold more likely to show elevated proBNP levels >125 ng/L compared to general patients of group B. The same pattern can be observed in group A, which is consistent with the impact of worsening kidney function on proBNP concentration [62,63]. The CIs of the Pearson correlation coefficient of proBNP and glomerular filtration rate is strictly negative, and the CI for creatinine and proBNP levels is fully positive. The third incoming edge is of type high conditional difference. It indicates a relationship between hemoglobin levels <13 g/dL (“HBKC, low”) and elevated proBNP measurements. Although the node for low hemoglobin levels is labeled as unrelated, measurements <13 g/dL appear with a 1.4-fold increase in group B compared to group A. The associated CI is close to, but fully above, 0. Interestingly, participants of both groups with low hemoglobin levels are approximately 1.5-fold more likely to exhibit high proBNP measurements compared to general participants of their group, a phenomenon observed in other studies [64-66]. The Pearson correlation coefficient CI for proBNP and hemoglobin levels are close to, but fully below, 0. Overall, these 3 relationships confirm that while elevated proBNP levels serve as a biomarker for cardiac conditions, other factors may also contribute to its elevation.

Figure 4 was extracted from the dashboard and discloses the relationship of hemoglobin and proBNP levels across the whole data set in more detail. Average proBNP values increase for participants with hemoglobin levels <13 g/dL. Interestingly, proBNP levels also increase in participants with high hemoglobin values >17 g/dL. For further investigation, we returned to the graph and inspected the node (“HBKC, high”) for high hemoglobin levels >15.5 g/dL. This threshold is exceeded by 21.5% of the participants in group A and by only 15.3% of the participants in group B. These observations align with the calculated, strictly positive CI and findings of other studies associating high hemoglobin concentrations with cardiovascular disease [67,68]. The third node (“cholesterol, low”), which is labeled as highly related, can be seen in the lower center of Figure 3. It represents total cholesterol levels <150 mg/dL, which is exhibited by 16.3% of group A and only 5.5% of group B. Conversely, total cholesterol levels >200 mg/dL are observed in 47.3% of group A and 61.2% of group B. As a result, the corresponding node (“cholesterol, high”) is labeled as inversely related.

However, in Figure 5, we can observe that the highest number of participants in both groups exhibit a slightly elevated total cholesterol level of 210 mg/dL. Next, we inspected the 2 nodes (“CholLDL, normal” and “CholLDL, high”) for low-density lipoprotein (LDL) cholesterol levels. Measurements >130 mg/dL (“CholLDL, high”) appear with a 1.3-fold increase in group B. LDL cholesterol levels <130 mg/dL (“CholLDL, normal”) appear in 68.1% of group A and 59.7% of group B. These observations are peculiar because elevated total and LDL cholesterol are commonly recognized as important risk factors for cardiovascular diseases [69-73]. A similar pattern can be inferred from the 2 nodes (“CholHDL, low” and “CholHDL, high”) for measurements of high-density lipoprotein (HDL) cholesterol. Levels <45 mg/dL appear with a 1.7-fold increase in group A, whereas measurements >83 mg/dL showed a 1.8-fold increase in group B. This observation coincides with the widely accepted inverse association of HDL levels with cardiovascular diseases [74,75]. It is noteworthy that the nodes for high LDL and HDL cholesterol levels share an edge with the node for high total cholesterol levels. The same holds true for low HDL, normal LDL, and low total cholesterol measurements. These edges are all labeled with “high conditional difference.” The CIs for all 3 cholesterol measurements and the membership to group A are strictly negative. The CIs for total cholesterol levels and HDL as well as LDL cholesterol measurements are strictly positive, with the correlation coefficient of LDL and total cholesterol being close to 1. In summary, reduced overall cholesterol, LDL cholesterol, and HDL cholesterol levels appear more often in the cardiovascular disease group compared to the control group and are associated with each other. As stated earlier, this observation contradicts the commonly accepted association of elevated overall and LDL cholesterol with cardiovascular diseases. It could be attributed to the widely used therapy with statins [76], which mainly targets the reduction of LDL and overall cholesterol [77]. On the basis of this idea, the high conditional difference relation between elevated creatinine levels and low total cholesterol measurements found in Figure 3 and the associated strictly negative CI for the Pearson correlation coefficient could be explained by statin-associated muscle symptoms [78]. However, additional information about the medication history of the participants would be required and could be a starting point for further investigation.

The participants indicated a work experience in the current field ranging from 1 to 10 years, with an average of 5.8 years. The data exploration tools mostly used by the participants were SPSS (IBM) [79], R [80], and Microsoft Excel (Microsoft) [81]. No users mentioned any prior experience with graph-based statistical analysis tools. The results of the user test can be found in Multimedia Appendix 3.

In Figure 6, the results of the SUS questionnaire are shown and range from 62.5 to 85.0. The mean of 70.5 indicates the passing of usability criteria [82] and a rating of “good” usability [83]. In addition, physicians rated the user-friendliness on a scale from 1 (very bad) to 10 (very good), with a mean of 7.0 in accordance with the SUS results.

In Figure 7, the percentage of the 10 participants with successful completion is shown for each user task. The average score across all tasks is 81.4%, with 6 (86%) of 7 navigation tasks being correctly completed by all participants. However, only 20% (2/10) of participants queried successfully for the 10 nodes most statistically associated with the disease group by the quotient of relative attribute shares. Regarding the description tasks of category 1, all but 1 task of reproducing label and parameter meaning was completed by at least 70% (7/10) of users. An exception was task C3.2 where participants should describe the meaning of the edge parameter for the difference of relative conditional share and relative attribute share of the target node. This task was only completed correctly by 30% (3/10) of the participants. In addition, only 30% (3/10) of the participants found the parameter names for nodes understandable, and only 10% (1/10) of the participants classified the edge parameter names as clear.

During the free data exploration, all participants noticed the unusually low levels of total and LDL cholesterol in the cardiovascular disease group compared to the control group, which is also discussed during the exemplary data analysis conducted by the authors. In addition, 40% (4/10) of the participants suspected this association to be caused by medication not represented in the data set. Overall, 60% (6/10) of the participants discussed ECG signals, and 60% (6/10) of the participants discussed kidney metabolism. Moreover, 70% (7/10) of the physicians mentioned the results of their data exploration to be plausible, except for total and LDL cholesterol unprompted. Regarding the answers to the open feedback questions, 80% (8/10) of the participants mentioned the colors and sizes of nodes to be helpful, and 40% (4/10) of the participants referred to the display of attribute connections as edges becoming apparent. Moreover, 30% (3/10) of the participants mentioned the benefit of initial data exploration without the need for numerical values. As to disadvantages of the AAG, 30% (3/10) of the users mentioned the edge definitions being hard to understand, 20% (2/10) assessed the graphs to be too crowded to get a good overview, and 20% (2/10) stated that they would need more practice to use the tool efficiently.

In this work, we presented the AAG for visual exploration of medical data sets using disease and control cohorts. The graph structure represents attributes as nodes and identifies as well as visually highlights attributes, which are linked to the observed disease by robust statistical metrics. Relations between attributes are captured as edges by conditional frequencies. As a result, attributes associated with the observed disease are visually clustered and clearly separated from attributes, which are associated with the control group. The graph structure detects and handles missing values without the need for data deletion.

The usability of the AAG and dashboard was assessed using an exemplary data analysis. All but 1 association of laboratory measurements and cardiovascular diseases extracted from the HCHS data set are in line with findings from the literature. The exceptions are unusually low total and LDL cholesterol levels in participants with cardiovascular disease, which might be caused by lipid-lowering therapy. All results extracted from the AAG were confirmed by standard statistical inference using null hypothesis testing and CI for the Pearson correlation coefficient. In addition, a user test with physicians was conducted using the standardized SUS questionnaire, nonstandardized open feedback questions as well as user tasks, and a free data exploration. The SUS score of 70.5% and average successful task completion of 81.4% show a general acceptance and good usability of the AAG. After the initial 30-minute preparation period, all users were able to navigate the graph and could extract medical knowledge that they considered plausible and meaningful. In addition, all participants identified the unusual lipid levels in participants of the cardiovascular disease group and some suspected medication not represented in the data set to be the cause. The encoding of statistical results by color, size, and clustering of nodes as well as thickness of edges was seen as helpful by the users. The users regarded the tool as useful for accessible hypothesis formation during the initial research phase.

Other existing data-driven approaches based on graph structures focus mainly on the connection of different data sources as knowledge graphs [23,24,26] or direct clinical decision support through outcome prediction [27,31,35,38,84-86]. To our knowledge, a graph structure capturing statistical measurements of a medical data set using disease and control cohorts with a clear focus on interpretability and visualization is a novel approach. In addition, as our proposed methods consider single attributes and pairs of attributes, they are robust to high-dimensional data, which pose a problem for many other statistical models applied to the medical domain [87]. We believe that the usability of graph-based visualizations in the medical field is rarely assessed using standardized tests such as the SUS questionnaire. The only other results known to the authors reported a slightly lower SUS score of 64.4 [25].

Regarding the graph-based statistical framework, we see our work closest related to Bayesian networks [29] and association rule learning [36]. While Bayesian networks can hold strong predictive power [88], the choice of prior distribution and sensitivity to data quality can be challenging for clinicians [89]. In association rule learning, conditional relationships between attributes are partially expressed through the confidence parameter, which is quite similar to our methodology in that regard. However, we enrich the added condition with semantics by calculating difference and quotient to the unconditional relative frequencies. Finally, none of the 2 methods measure statistical differences between disease and control cohorts. We believe this to be vital in our approach for generation of insight and adoption in the medical domain.

We intended the AAG and dashboard as a compact visualization for data exploration in the initial phase of research projects. We aimed to incorporate easily interpretable, robust metrics in the form of conditional and unconditional absolute and relative frequencies as well as their deviations between disease and control cohorts. However, because of this choice of metrics, the accuracy could be lower when used in prediction tasks compared to, for example, Bayesian networks or other nonlinear models. In addition, CIs and null hypothesis significance testing play a key role in statistical inference of medical data [90]. They are not incorporated into the methods presented here but could be a follow-up to the initial exploration using the AAG. Finally, temporal data cannot be handled with the proposed methodology in the current form, and Markov models [33] could be applied instead.

Regarding the usability of the visualization, the results of the user test indicate a need for simplification of the parameter names regarding the statistical measurements. In addition, the comparison of conditional and unconditional frequencies captured in the edges of the graph structure was not accessible enough for the users. Moreover, the prompt for retrieval of nodes most associated with one of the groups was considered too lengthy by the users. The authors will incorporate this valuable feedback in the next update iteration of the presented methods.

In this work, we introduced the AAG, a novel graph-based representation of statistical data combined with a dashboard. These structures can be visually explored and allow for data analysis tailored to the needs of the medical domain. The usability of the graph structure and dashboard was confirmed by user tests conducted with physicians. In addition, the validity of the incorporated statistical analysis was assessed through an exemplary data analysis of a large epidemiological study, and its compatibility with standard statistical methodology and findings from the literature was established. For the future, it might be of interest to enable clinicians in generating their own AAGs without the need for programming experience as an extension to their existing data analysis workflow. To achieve this, we developed a software package [57], which will be presented in an upcoming publication. We think that accessible data analysis and intuitive presentation for clinicians and patients is the way forward in a world of ever-growing data availability and complexity.