Historically, nephrology has relied on manual analysis, which presents challenges when dealing with complex data sets, often leading to diagnostic errors and suboptimal treatment choices. The ongoing advancements in numerical algorithms and artificial intelligence offer new opportunities to enhance kidney health monitoring. This progress allows for greater diagnostic accuracy and more precise treatment strategies. The synergy between expert medical knowledge and the automation capabilities of algorithms is paving the way for systems that can effectively address complex nephrological challenges.

Glomerular diseases, a subset of kidney conditions, specifically target the glomeruli-tiny structures in the kidneys that filter blood and produce urine. These diseases can arise from various causes, including infections, autoimmune disorders, hypertension, diabetes, and other metabolic conditions. This article provides a comparative approach to different AI algorithms that can be used in risk classification of patients with a nephrological disease called idiopathic membranous nephropathy (IMN). The concept is to create an extended and multi-task expert system that would be tasked with supporting nephrologists' decisions in their daily work in treating patients with kidney diseases. The risk classification module is therefore crucial from the perspective of the domain expert, who can determine the further course of action based on the patient's assignment to a specific group. The range of algorithms ranges from simple linear approaches to complex and advanced gradient solutions. The expertise of nephrologists is also leveraged along with advances in engineering. Focusing on specific applications, our goal is to show how these advances can impact the standards of patient care, ultimately improving the outcomes of traditional approaches. Figure 1 provides a general outline of the methodology, scope of the study and the approach used to address the problem.

The next section will provide a detailed literature review and an overview of the state of the art.

This literature review examines the use of automation, artificial intelligence, and classification systems in the field of nephrology. It delves into how these advanced technologies streamline processes, increase diagnostic precision, and improve patient outcomes. Through a critical analysis of the current literature, the goal is to uncover trends and identify gaps, thereby guiding future research toward innovative solutions in the field of nephrology.

Advancements in artificial intelligence, innovation, and transformative technologies are pivotal in nephrology and dialysis [2][3][4]. Additionally, the future prospects of AI and modern technologies in managing kidney diseases are extensively reviewed [5,6]. Research focusing on numerical models and machine learning techniques also holds considerable importance [7][8][9].

A key area in nephrology research is the integration of acute kidney injury (AKI) with AIdriven predictive algorithms [10,11]. Another significant focus includes the development of predictive models in the context of personalized medicine [12]. AI-based clinical applications in nephrology are explored in works by [13] and [14]. Furthermore, ethical considerations surrounding AI applications are discussed in [15] and [16].

Recent research underscores the integration of AI and machine learning within nephrology. For instance, [17] develops short-term prognosis prediction models for severe AKI patients undergoing PIRRT (Prolonged Intermittent Renal Replacement Therapy), utilizing algorithms such as Naive Bayes and Random Forest, and highlighting the critical role of serum electrolyte management. Another study [18], introduces Sugeno's fuzzy inference system for regression problems involving numerous variables and limited data, demonstrating superior performance over traditional methods.

In addition, [19] presents health-disease phase diagrams (HDPDs) for visualizing disease onset probabilities, while [20] develops CKD.Net, a hybrid model that achieves high accuracy in predicting CKD stages. Other significant contributions include [21], which focuses on precise kidney volume measurement using AI, and [22], which addresses PRCC (Papillary Renal Cell Carcinoma) stage classification. Furthermore, [23] showcases the importance of machine learning in predicting AKI and diagnosing PDAC (Pancreatic Ductal Adenocarcinoma).

A study derived and validated an ML risk score for predicting diabetic kidney disease (DKD) progression using biomarker and electronic patient data [24]. Research into interpretable ML for early AKI prognosis emphasizes model interpretability benefits [25]. ML has also been utilized to predict primary nephrotic syndrome pathology without biopsy and identify hub genes in membranous nephropathy [26,27]. A model for predicting idiopathic membranous nephropathy prognosis is discussed in [28]. ML models predicting rituximab underdosing in membranous nephropathy show high accuracy, sensitivity, and specificity [29]. Another study reports a machine learning framework for diagnosing membranous nephropathy from wholeslide images, achieving a 97.32% F1-score [30].

A belief rule-based system for diagnosing primary membranous nephropathy shows significant reliability with 98% sensitivity, 96.9% specificity, 97.8% accuracy, and an AUC of 0.93 [31]. A predictive model for long-term renal function impairment post-minimally invasive partial nephrectomy has a concordance index of 0.75 [32]. The use of AI and ML in dialysis is reviewed, focusing on diagnostics, prognosis, and treatment optimization [33]. Guidelines for proper application and transparent reporting of ML models in biomedical research emphasize best practices [34]. Recent literature highlights the crucial role of clinical prediction models in modern healthcare, emphasizing challenges and the need for transparent reporting to assess their quality [35]. The literature underscores the importance of understanding diagnostic and prognostic prediction models, addressing issues such as model development, validation, and sample size considerations to improve clinical decision-making [36][37][38], as well as valuable research [39,40].

This section explores the development of an expert system for diagnosing and treating idiopathic membranous nephropathy, focusing specifically on the risk classification module. The system is structured as a hierarchical decision tree that integrates clinical data, diagnostic criteria, and therapeutic guidelines to assist nephrologists in managing IMN.

The expert system consists of several key components, which are shown in Figure 2 and briefly described below:

1. Diagnostic Module -the diagnosis of (IMN) is confirmed through a combination of patient history, diagnostic tests, and kidney biopsy. The evaluation also considers the likelihood of progression to stage 5 chronic kidney disease (CKD5) by analyzing glomerular filtration rate, levels of proteinuria, and serum albumin concentrations. 2. Risk Stratification -patients are classified into four distinct risk categories -low, intermediate, high, and very high -based on factors such as estimated glomerular filtration rate (eGFR) and proteinuria levels. Each category is associated with specific management strategies tailored to the risk profile. 3. Therapeutic Module -treatment recommendations vary from conservative management to more aggressive immunosuppressive therapies, depending on the risk category. Options include ACE inhibitors or ARBs, rituximab, calcineurin inhibitors, cyclophosphamide, and corticosteroids.

patient response to treatment is re-evaluated after six months. Based on clinical indicators, the treatment plan may be continued, modified, or altered. Protocols are provided for deciding on the appropriate course of action. 5. Follow-up Module -guidelines are provided for the long-term monitoring and management of patients who achieve partial or complete remission, including strategies for addressing treatment resistance and managing relapses. 6. User Interface -the system includes a user-friendly graphical interface designed for ease of use by healthcare professionals. In this article, we focus solely on the Risk Stratification Module (see Fig. 2) of the expert system, which plays a crucial role in assigning patients to specific risk groups for targeted management. The comparative analysis involves various AI algorithms, from basic linear methods to advanced gradient-based solutions, alongside traditional expert approaches. The details will be explained in the following sections of the article.

The remaining components of the system -such as diagnostic, therapeutic, and followup modules -will be explored in future research. This initial focus on risk classification aims to demonstrate how AI advancements can enhance traditional nephrological practices and improve patient outcomes.

This subsection details the process of modeling the classification system, presenting the input variables and their corresponding output classifications. The classification model processes clinical parameters to categorize IMN patients into risk groups using a Multi Input Single Output (MISO) framework. The authors used the information provided in the guidelines in [41]. The 11 inputs to this model, detailed below, include a range of variables:

1. eGFR (Estimated Glomerular Filtration Rate) -a measure of kidney function estimating how well the kidneys filter blood. 2. Proteinuria -the level of protein present in the urine. 3. Serum Albumin Concentration -the concentration of albumin in the blood. 4. Response to ACEi/ARB Treatment -the percentage reduction in proteinuria after 6 months of treatment with ACE inhibitors or ARBs. 5. Serum anti-PLA2R Concentration -the level of anti-PLA2R antibodies in the serum. 6. Urinary α1-microglobulin Concentration -the concentration of α1-microglobulin in the urine. 7. Urinary IgG Concentration -the concentration of IgG in the urine. 8. Urinary β2-microglobulin Concentration -the concentration of β2-microglobulin in the urine. 9. Selectivity Index -the ratio of different urinary protein components indicating the selectivity of proteinuria. Selectivity Index > 0.20 g.

Very High Risk h.

Life-threatening nephrotic syndrome symptoms OR • Rapidly progressive renal impairment not caused by other diseases.

Machine learning algorithms are excellent at identifying complex interactions between multiple input variables that may not be apparent with rule-based logic alone. This leads to a more nuanced understanding of a patient's risk profile. The guidelines above provide a framework for categorizing data, but they cannot account for every possible combination of lab results and other factors. Nor could a rule-based system easily provide a way to determine which output category values fall into. This gives AI and ML methods an advantage in these types of tasks.

Machine learning models leverage historical patient data to identify patterns and correlations that enhance the precision of risk classification predictions. This approach, driven by data, refines decision boundaries and reduces the likelihood of misclassification. A key benefit of machine learning models is their capacity to adapt and become more accurate as new data is introduced. Furthermore, certain machine learning models offer insights into the probability of data belonging to specific classes.

The next section will describe in detail the considered algorithms.

In any problem where automatic classification of collected data is needed, selecting the right AI models and numerical algorithms is a key step in developing a robust classification system. Seven AI and ML-based models were selected and tested to provide the best solution to the task. The models feature different algorithms used, such as tree-based methods, ensemble techniques, support vector machines, and neural networks. By using different methods, a comprehensive evaluation and comparison is provided. It also provides researchers with an answer as to which model performs best in classifying the risk of IMN patients. Below is a brief description of each algorithm: This chapter briefly introduces seven different AI and ML models for their usefulness in classifying the risk of IMN patients. The models reviewed include K-Nearest Neighbors, Decision Trees, Random Forests, Support Vector Machines, Adaptive Boosting, LightGBM, and the Multi-layer Perceptron Classifier. Each model offers unique strengths: KNN is straightforward but computationally intense, DTs are interpretable but prone to overfitting. RFs improve stability and generalization, SVMs excel in high-dimensional spaces and AdaBoost focuses on hard-to-classify examples but can be sensitive to noise. LightGBM provides efficiency and scalability for large datasets, and MLPs capture complex patterns but require extensive tuning.

The next chapter will detail the training process of these models and provide a discussion of the results obtained from their application to the classification task.

In this section, we present the insights gained from the analysis and the results of classifying nephrology patient data using various machine learning models described in Section 4.

The original dataset included laboratory results relevant to IMN risk classification. To mitigate class imbalance and improve model performance, synthetic data augmentation was applied, generating new data points that mirror the distribution and features of the existing data. For model training, 200 datasets were used, evenly distributed among the four risk categories: low, medium, high, and very high, with 50 datasets in each category. An identical number of datasets were allocated for testing. This approach ensured that the models had ample data for training and a reliable set for evaluation.

The comparison of precision scores (see Fig. 3) across various machine learning models in the context of nephrology risk classification reveals important insights into their performance on the dataset prepared and described in the preceding sections. By analyzing the results in Figure 3, we can discuss in detail the results and implications of each classifier:

1. MLP Classifier -the MLP classifier achieved a high precision score of 0.96, indicating its robustness in accurately predicting the positive class in the IMN risk classification task. This model's architecture, which simulates the neural networks found in biological brains, has proven effective in capturing the complex, non-linear relationships inherent in the clinical dataset. 2. LightGBM -in contrast, the LightGBM model exhibited a notably lower precision score of 0.11. This result is surprising given LightGBM's reputation for efficiency and high performance in many classification tasks. The poor performance may suggest that the specific characteristics of the nephrology dataset, or the hyperparameters used, do not align well with the strengths of this gradient boosting framework. Further investigation into feature importance and model tuning would be necessary to understand this anomaly. 3. AdaBoost -Adaptive Boosting yielded a precision score of 0.89, demonstrating its capability to enhance weak classifiers by focusing on misclassified instances. This performance indicates that AdaBoost effectively leveraged the synthetic data augmentation and was able to generalize well across the test dataset. 4. Support Vector Machine -the SVM classifier, with a precision score of 0.93, performed robustly, confirming its strength in high-dimensional spaces, where it constructs optimal hyperplanes to segregate different risk classes. This suggests that the SVM is particularly well-suited to handle the complexity of the feature space derived from nephrology patient data. 5. Random Forest -the RF model achieved the highest precision score of 0.98. This ensemble method's exceptional performance underscores its ability to manage the variability within the dataset by combining the predictions of multiple decision trees, thereby enhancing overall predictive accuracy. 6. Decision Tree -the single DT model also performed well, with a precision score of 0.96.

Despite its simplicity compared to ensemble methods, the decision tree's interpretability and effectiveness in handling this particular dataset are evident from its high score. 7. K-Nearest Neighbors -KNN classifier attained a precision score of 0.88. While KNN is often sensitive to the local structure of the data and can be affected by noise, its performance in this scenario indicates a reasonable degree of success in classifying risk levels among nephrology patients.

In summary, the Random Forest model emerged as the most effective classifier in terms of precision, followed closely by the Decision Tree and MLP classifiers. The unusually low precision score of LightGBM warrants further exploration to identify potential causes and corrective measures. These findings will inform future work in refining model selection and optimization for nephrology risk classification tasks. The F1-score evaluation of different classifiers (see Fig. 4), as presented in the nephrology risk classification study, provides deeper insights into the balance between precision and recall across various models. Here, we discuss the performance of each classifier in terms of its F1score, which is particularly useful in assessing the model's effectiveness in dealing with the complexities of an imbalanced dataset:

1. MLP Classifier -F1-score of 0.96 confirms strong capability in managing complex, nonlinear classification, balancing precision and recall effectively 2. LightGBM -low F1-score of 0.16, suggesting significant struggles with both precision and recall, making it less suitable for this task. 3. Adaptive Boosting -F1-score of 0.84 reflects good performance, particularly in enhancing classification of difficult instances in imbalanced data. 4. Support Vector Machine -SVM scored 0.89 in F1, indicating strong performance with well-balanced precision and recall, effectively separating risk classes. 5. Random Forest -excelled with an F1-score of 0.99, showcasing superior performance by combining multiple decision trees to minimize errors. 6. Decision Tree -DT achieved a high F1-score of 0.94, demonstrating effective classification by accurately partitioning the feature space. 7. K-Nearest Neighbors -F1-score of 0.79 indicates moderate performance, reflecting challenges in balancing precision and recall, particularly with imbalanced data.

In conclusion, the Random Forest classifier once again proved to be the most effective model in terms of the F1-score, closely followed by the MLP and Decision Tree classifiers. The consistently low performance of LightGBM, as reflected in both precision and F1-score, warrants further exploration. Overall, these results provide clear guidance on the most appropriate machine learning models for nephrology risk classification tasks, with a particular emphasis on the effectiveness of ensemble methods and neural network-based approaches. In summary, the Random Forest model again demonstrated the highest reliability with its near-perfect recall score, followed closely by the MLP and Decision Tree classifiers. The low recall score of LightGBM, similar to its performance in other metrics, suggests that it struggled significantly with this specific task. The confusion matrices (see Fig. 6) presented in the provided figure summarize the performance of four different machine learning algorithms -KNN, LightGBM, RF, and DT. The results presented in Figure 6 clearly indicate that the RF algorithm in the classification model achieved the best results in the course of the study. On the other hand, LightGBM, similarly to the graphics presented in Figures 3-5, performed the worst, which is confirmed by the result on the confusion matrix. In the case of the other two algorithms -KNN and DT, their efficiency in the task of risk classification of patients with IMN is confirmed to be decent, but not as good as for RF.

The comparative analysis of various artificial intelligence and machine learning algorithms for the classification of idiopathic membranous nephropathy risk demonstrates the potential of these technologies in enhancing traditional nephrological practices. The study evaluated seven different AI models, including K-Nearest Neighbors, Decision Trees, Random Forests, Support Vector Machines, Adaptive Boosting, LightGBM, and Multi-layer Perceptron Classifier.

The results indicate that ensemble methods such as Random Forests outperform other models, achieving a precision score of 0.98, demonstrating their robustness in handling the variability within nephrological data. The MLP Classifier and Decision Tree also showed high precision scores (0.96), suggesting their capability in capturing complex relationships within the clinical dataset. In contrast, LightGBM's performance was unexpectedly low, with a precision score of 0.11, indicating that further tuning and investigation into model parameters are required for this specific application.

The study highlights that AI models, particularly ensemble methods, can significantly improve the accuracy of risk classification in nephrology, potentially leading to better patient outcomes. However, the results also underscore the importance of selecting appropriate models and fine-tuning them to the specific characteristics of medical datasets. Future research should focus on optimizing these models and exploring their integration into clinical decision support systems to assist nephrologists in managing kidney diseases more effectively.

Overall, this work provides a foundation for the continued exploration and application of AI in nephrology, emphasizing the need for further validation and refinement to achieve reliable and clinically applicable tools.