Fig 1.
Flowchart of the clinical decision support system and the interpretable tropical geometry-based fuzzy neural network algorithm.
Fig 1A describes the system and training strategy: The EHR dataset is collected from Michigan Medicine and then the patient selection and outcome definition were performed. The data is split into training and test sets. Five-fold cross-validation is performed on the training dataset. Rules extracted from five-folds are ensembled. The model is then retrained on the whole training dataset with ensembled rule initialization. The trained model is later validated on the test set. Fig 1B depicts the structure of tropical geometry-based fuzzy neural network: The encoding layer encodes the input features into ‘low’, ‘medium’ and ‘high’ fuzzy concepts. The rule layer combines different concepts to generate several rules and decisions are made at the final inference layer by leveraging all rules. The edges between modules are trainable parameters to optimize the model. xi: continuous variables; : low concept membership function;
: medium concept function;
: high concept membership function; A: attention matrix; M: connection matrix; W: inference matrix.
Table 1.
Demographic characteristics of patients requiring HT/LVAD evaluation (“Positive”) and those too well for HF advanced therapies (“Negative”).
Displayed are mean (standard deviation) for continuous variables or N (%) for categorical variables.
Table 2.
Performance of machine learning models on HF dataset using 5-fold cross validation.
Models are referred to as transparent if they can explain their recommendations in a way understood by humans. The column ‘Interpretability’ indicates whether the feature importance can be provided with the model. Although Random Forest, XGBoost and SVM are listed as interpretable, these models can only be interpreted using external approach such as SHAP (SHapley Additive exPlanations). The column “Rules” refers to whether the model provides a set of clinical rules by which to explain its prediction.
Table 3.
Performance of machine learning models on the HF test dataset.
Fig 2.
Clinical rules extracted from the network: In the heatmap, each column represents a rule, while each row represents one concept of a clinical feature.
The number beneath every rule measures the contribution of the rule. The color shades on the heatmap indicate the importance of individual concepts for each rule. Rule 1 can be written as: IF Systolic Blood Pressure is low AND Left Ventricular Ejection Fraction is low, THEN refer for heart transplantation/ LVAD. KEY: BMI = body mass index; BNP = brain natriuretic peptide; CREAT = creatine; HGB = hemoglobin; LVEF = left ventricular ejection fraction; MAP = mean arterial pressure; SBP = systolic blood pressure; SOD = sodium.
Fig 3.
Membership function visualization: Continuous clinical features are encoded into three concepts: ‘‘low’, ‘medium’ and ‘high’.
Membership values range from 0 to 1. The x-axis of each membership function represents the range of possible values, while the y-axis represents the degree of membership of each value in the corresponding fuzzy set, ranging from 0 to 1. The X-coordinates of the intersection of two membership functions indicate where the transition from one concept to another occurs KEY: SBP = systolic blood pressure; MAP = mean arterial pressure; SOD = sodium; HGB = hemoglobin; BMI = body mass index; CREAT = creatine.
Table 4.
Critical values of membership functions learned from the study cohort by the algorithm.
These critical values indicate the potential threshold where adjacent concepts transition.
Fig 4.
Profile for a patient in the test dataset, showing the composite rules that fired.