To investigate early lithium-associated renal injury within a controlled and analytically transparent environment, we constructed a synthetic cohort of 1,500 patients designed to emulate the clinical and biochemical profile of individuals receiving long-term lithium therapy. The synthetic dataset was generated using empirically informed distributions aligned with reported epidemiological and nephrological trends [40]-[44]. This approach ensures that feature interactions, marginal distributions, and clinical dependencies reflect plausible physiological behaviour while enabling full control over noise, imbalance, and complexity.

The dataset encompasses demographic variables (age, sex), renal function markers (serum creatinine, baseline eGFR, current eGFR, proteinuria, eGFR decline rate), lithium exposure variables (treatment duration in years, serum lithium concentration, daily dose), comorbidities (hypertension, diabetes, cardiovascular risk), metabolic factors (serum calcium, phosphate, BMI), and inflammatory markers (e.g., IL-6). These variables collectively capture the multidimensional landscape of factors known to modulate susceptibility to lithium-induced nephrotoxicity. To better reflect the nonlinear and synergistic relationships observed in clinical practice, we engineered three interaction features with established relevance in nephrology and psychopharmacology:

1. lithium_duration × lithium_level- representing cumulative toxic load, capturing how long-term exposure at higher serum levels magnifies renal risk far more than either variable individually [45]-[50].

2. age × lithium_duration - modelling the accelerated vulnerability of aging renal tissue under prolonged lithium treatment [51]-[56].

3. eGFR_decline_rate × proteinuria- integrating two primary signatures of early nephron injury, producing a sensitive indicator of progressive CKD trajectory [57]-[60].

The target variable, early kidney damage, was encoded as a binary label reflecting an early-stage CKD phenotype. Although deterministic in generation, the label incorporates stochastic variation to emulate the uncertainty and incomplete observability inherent to clinical diagnostics [61]-[63].

This synthetic design offers several advantages:

Controlled complexity: allowing systematic evaluation of model performance under known interactions [64][65].Balance between realism and tractability: enabling interpretable mechanistic insight without confounding clinical noise [66][67].Reproducibility: ensuring replicable analysis for benchmarking predictive and explainability methods [68]-[70].

Together, the dataset and engineered features form a rigorous foundation for assessing machine-learning based nephrotoxicity prediction and for evaluating the stability and interpretability of explainable AI methods applied to lithium-associated CKD.

2.1.1. Clinical Definition of Early Kidney Damage

To ensure alignment with established nephrology guidelines, the binary outcome variable “early kidney damage” was defined according to KDIGO criteria for early-stage CKD. A patient was labelled as positive (Y = 1) if at least one of the following conditions was met:

Estimated glomerular filtration rate (eGFR) < 60 mL/min/1.73m² persisting for ≥ 3 simulated months,Annual eGFR decline rate ≥ 5 mL/min/1.73m²,Presence of proteinuria exceeding 150 mg/day,Serum creatinine elevation exceeding 1.3 mg/dL (men) or 1.1 mg/dL (women).

To reflect real-world diagnostic uncertainty, stochastic perturbation (Gaussian noise with σ = 0.03) was added to the final probability before thresholding. This ensures that the target variable reflects physiologically grounded CKD definitions rather than a purely deterministic rule.

2.1.2. Synthetic Data Generation Parameters

Synthetic features were generated using multivariate normal and log-normal distributions parameterized according to epidemiological lithium monitoring literature.

Key parameters include:

Age ~ N(52, 14²)Lithium duration (years) ~ Gamma (k = 3.5, θ = 2.0)Serum lithium level ~ N(0.75, 0.15²)Baseline eGFR ~ N(82, 18²)Annual eGFR decline rate ~ N(2.3, 1.2²)Proteinuria ~ LogNormal (μ = 4.8, σ = 0.6)

Feature correlations were imposed using the following covariance structure (partial matrix):

Our goal is to estimate, for each patient, the probability of having early lithium-associated kidney damage given their clinical and treatment profile.

Let,

denote the feature vector for patient i , where p is the total number of predictors (demographics, lithium exposure, renal markers, comorbidities, metabolic and inflammatory variables, plus engineered interactions). The binary outcome is

with y i = 1 indicating early kidney damage and y i = 0 indicating no early damage.

2.2.1. CatBoost as Nonlinear Risk Function

We use CatBoost as the main predictive model. Conceptually, CatBoost can be seen as a flexible nonlinear function [71]-[73]

Here, f ( x i ) is the model’s output in the log-odds scale (also called “logit”), not yet a probability. To convert this into a clinically interpretable probability of early kidney damage, we apply the logistic (sigmoid) function [74][75]:

If f ( x i ) = 0 , then P ( y i = 1 | x i ) = 0.5 .If f ( x i ) > 0 , the probability is greater than 0.5 (higher risk).If f ( x i ) < 0 , the probability is less than 0.5 (lower risk).

CatBoost itself is an ensemble of many decision trees, trained sequentially (boosting). Each new tree tries to correct the errors of previous trees, allowing the model to capture complex nonlinear interactions among features (e.g., the joint effect of lithium duration and serum lithium level) [76][77].

2.2.2. Shapley Additive Explanations (SHAP)

While CatBoost can learn complex patterns, the raw function f ( x i ) is not directly interpretable. We therefore use SHAP (SHapley Additive exPlanations) to decompose the prediction for each patient into feature contributions.

a) Additive decomposition of the prediction

For each patient i , SHAP approximates the model output as:

where:

ϕ 0 is the baseline value, equal to the expected log-odds of early kidney damage over the whole training dataset. Intuitively, this is the model prediction before seeing any patient-specific information. ϕ i j is the Shapley value for feature j in patient i . It measures how much feature j moves the prediction for patient i away from the baseline.

If ϕ i j > 0 , then feature j increases the log-odds (and thus the probability) of early kidney damage for that patient. If ϕ i j < 0 , then feature j decreases the risk for that patient.

The key point:

SHAP converts a complicated black-box prediction into a sum of interpretable feature-level effects.

b) Patient-specific risk score

To quantify how “strongly” the model uses the features for a given patient, we define a simple patient-level risk score based on the magnitude of all SHAP values:

If R i is large, many features are making strong contributions (positive or negative), meaning the model is very confident and the patient is far from the baseline.If R i is small, the patient is close to the baseline risk, and no single feature has a strong effect.

This risk score is in the same “logit space” as the model output but is specifically measuring total explanatory activity around patient i .

c) Global feature importance

To understand which features are important overall, not just for one patient, we average the absolute SHAP values across all patients:

Here, I j is the global importance of feature j :

If I j is large, feature j frequently has a big impact on predictions.If I j is small, feature j rarely affects the model decision.

This is what you plot in the SHAP bar plots and summary plots to rank lithium duration, eGFR decline, proteinuria, etc.

2.2.3. Bootstrap Confidence Intervals for Feature Importance

Simply ranking features by I j (mean |SHAP|) is not enough; we also want to know how stable these importance scores are. To do this, we use bootstrap resampling.

For each feature j :

1. We perform B bootstrap iterations (here B = 1000 ).

2. In each iteration b , we sample patients with replacement from the test set, re-compute mean |SHAP| for feature j , and get a bootstrap replicate I j ( b ) .

3. After B iterations we have a distribution { I j ( 1 ) , I j ( 2 ) , ⋯ , I j ( B ) } .

We then compute a 95% confidence interval:

Interpretation:

If the lower bound of the CI is greater than zero, the feature’s importance is statistically robust and unlikely to be a random artifact.If the CI is wide and includes zero, we treat the feature’s importance as less stable.

This is exactly what you visualize in the error-bar plots: features with tight, strictly positive intervals are marked as reliably influential.

2.2.4. Permutation Test for Model Significance

Finally, we want to ask:

Is the model’s performance (AUC) significantly better than what we’d get by chance?

To answer this, we use a permutation test:

1. Compute the baseline AUC of the model on the real data:

2. For each permutation k = 1 , ⋯ , K (e.g. K = 100 ):

Randomly shuffle the outcome labels y true to obtain y perm ( k ) .Recompute the AUC using the same predicted probabilities:

3. This gives us a null distribution of AUC values expected if there were no real relationship between features and labels.

4. The p-value is the proportion of permuted AUCs that are greater than or equal to the real AUC:

If this p-value is small (e.g. p < 0.05 ), we conclude that the model’s AUC is statistically significant and unlikely to arise just by random alignment of labels and features.

To rigorously evaluate predictive performance and ensure robustness across different algorithmic families, we trained four supervised learning models: Random Forest, XGBoost, Logistic Regression, and CatBoost. Each model represents a distinct methodological class bagged trees, gradient boosting machines, linear classifiers, and ordered boosting respectively allowing us to compare performance across diverse representational capacities.

2.3.1. Cross-Validation Strategy

Because the dataset exhibits a severe class imbalance (≈98.8% early kidney damage vs. 1.2% no damage), naive data splitting could lead to folds lacking examples of the minority class. To prevent this, we employed stratified 5-fold cross-validation, ensuring that each fold preserved the original class distribution as closely as possible.

The data were partitioned into five equally sized subsets. For each fold:

1. Four subsets were used for training.

2. One subset was used for validation.

3. The process was repeated five times, each subset acting once as the validation fold.

This provides a reliable estimate of the generalization performance and reduces sensitivity to a particular train-test split.

2.3.2. Evaluation Metrics

Given the extreme imbalance, accuracy alone is misleading (a model predicting “early damage” for all patients would reach ~99% accuracy). Thus, we assessed models using a suite of complementary metrics:

AUC (Area Under the ROC Curve): Measures discrimination across all thresholds; robust to imbalance.Precision: Fraction of predicted positives that are true positives.Recall (Sensitivity): Fraction of actual positives that are correctly identified.F1-Score: Harmonic mean of precision and recall; penalizes imbalance in either measure.Accuracy: Reported for completeness but interpreted cautiously.

AUC is the primary metric because it remains stable even under highly skewed prevalence.

2.3.3. Handling Class Imbalance

To prevent the classifiers from being dominated by the majority class (“early damage”), we applied class weighting during training:

so that misclassifying a rare healthy patient (negative class) incurred a higher penalty than misclassifying a positive case. This ensures the model maintains sensitivity to detecting the minority class.

For tree-based models (RF, XGBoost, CatBoost), built-in parameters were used to adjust class weights. For logistic regression, a weighted loss function was applied to ensure balanced gradient updates.

2.3.4. Selection of the Final Model

Across the four evaluated models:

Logistic Regression achieved the strongest cross-validated AUC but generalized modestly.Random Forest and XGBoost performed moderately but showed larger variance across folds.CatBoost demonstrated the highest test AUC (0.785), strongest stability across folds, and best F1-score, reflecting robust discrimination in the presence of nonlinear relationships and interactions.

Because of its superior predictive performance, stability under imbalance, and compatibility with high-resolution explainability techniques (especially SHAP), CatBoost was selected as the final model for in-depth interpretability analyses.

A central objective of this study is not only to achieve accurate prediction of lithium-associated renal impairment but also to expose the mechanistic structure of the model’s reasoning in a clinically interpretable manner. To accomplish this, we developed an integrated explainability pipeline combining global, local, and statistical interpretability methods. This multi-layered framework ensures that both population-level patterns and individual patient predictions can be understood, audited, and clinically validated.

2.4.1. Global Explainability

Global explainability methods provide insight into how the model behaves on average across the entire population revealing dominant predictors, interaction structures, and systemic trends relevant to nephrotoxicity risk [78]-[80].

SHAP Summary Plots:We used Shapley Additive Explanations (SHAP) to compute the marginal contribution of each feature across all patients. Two forms of summary visualizations were generated:

1. Beeswarm summary plot: Illustrates how every feature influence model output across the cohort, with colour encoding raw feature values and horizontal dispersion indicating effect size.

2. Mean |SHAP| bar plot: Provides a ranked, magnitude-based assessment of global feature importance.

Together, these plots reveal which biological and treatment variables exert the strongest influence on predicted CKD risk.

SHAP Interaction Plots:Given the importance of synergistic effects in nephrology (e.g., age × duration), we computed pairwise SHAP interaction values, enabling decomposition of total predictive contribution into:

main effectsinteraction terms

These plots clarify whether a feature’s risk contribution depends on the level of another feature critical for understanding cumulative lithium toxicity and multifactorial renal decline.

Feature Category Mapping:To enhance clinical interpretability, features were grouped into domain-relevant categories:

Lithium exposureRenal functionComorbiditiesMetabolic markersInflammatory markersDemographicsEngineered interactions

For each category, aggregated SHAP importance scores were computed, providing a structured overview of which physiological systems are most implicated in lithium-associated CKD.

Risk Distribution Analysis:Using patient-level SHAP decomposition, we derived an individualized risk score:

Population-level histograms and density curves illustrate the distribution of predicted risk across the cohort. Median and interquartile ranges characterize the overall risk landscape and facilitate detection of outlier subpopulations.

2.4.2. Emphasizes Individual/Patient-Level Focus + Dual Methodology (SHAP + LIME)

Local Explainability:Local interpretability methods dissect individual predictions, enabling clinician-facing explanations suitable for decision support.

SHAP Waterfall Plots:For representative high-risk patients, we generated waterfall plots that sequentially display how each feature shifts the log-odds from the baseline expected value toward the final patient-specific prediction. This clarifies:

the magnitudethe directionthe ordering

of each contributing factor to a patient’s predicted renal risk.

LIME Explanations:To complement SHAP, which is model-consistent but computationally intensive, we applied Local Interpretable Model-agnostic Explanations (LIME). LIME constructs local surrogate models around selected instances and highlights the top features contributing to predictions.

We produced LIME analyses for:

High-risk patients (top predicted probabilities)Medium-risk patients (around median risk levels)

These provide intuitive rule-based explanations that clinicians can read without specialized ML background.

2.4.3. Emphasizes Statistical Rigor + Three Validation Methods

Statistical Validation of Explainability:Explainability must be statistically reliable not merely descriptive. Therefore, we implemented multiple validation procedures to assess stability and significance.

Bootstrap Confidence Intervals:We computed 1,000 bootstrap resamples to estimate variability in global feature importance. For each feature j , a 95% confidence interval was calculated:

Features whose intervals exclude zero are considered stable contributors across resamples.

Stability Assessment of LIME Explanations (Rewritten Properly)

To quantify the stability of LIME attributions, we performed repeated local perturbation resampling with M = 200 runs per selected patient. For each feature j , we computed the empirical standard deviation of its LIME weight across perturbations:

where:

w j ( m ) is the LIME weight for feature j in perturbation run m , w ¯ j = 1 M ∑ m = 1 M w j ( m ) is the mean LIME weight for feature j , M is the total number of perturbation samples.

Features satisfying:

were considered locally stable.

Across high-risk patients, dominant exposure and renal features particularly lithium duration × level, age × duration, and eGFR decline rate consistently exhibited low attribution variance, confirming the robustness of the local surrogate explanations.

Permutation Testing:To assess whether the observed performance could arise by random chance, we generated a null distribution of AUC scores by permuting outcome labels while keeping features fixed. The proportion of permuted AUCs exceeding the real AUC yields a p-value.

In our results, the permutation test produced:

p = 0.030, indicating statistically significant predictive power (p < 0.05).

Feature SHAP Correlation Analysis:For each feature, we computed Pearson correlations between the raw feature value and associated SHAP contribution:

This analysis reveals:

Whether a feature is positively or negatively associated with predicted risk.The strength of that association.Whether nonlinear patterns require further stratification.

The combined use of global SHAP maps, interaction effects, individualized waterfall plots, LIME local models, and rigorous statistical validation forms a comprehensive and clinically grounded interpretability ecosystem. This pipeline ensures transparency, reproducibility, and clinical trustworthiness in predicting lithium-associated CKD.

Figure 1 provides a comprehensive four-panel evaluation of the predictive models, following the structured visual organization used in the reference methodological paper. Each subfigure isolates a fundamental performance dimension discrimination, calibration, metric balance, and class-level behaviour allowing a multidimensional understanding of model behaviour in the lithium-associated CKD prediction task.

Figure 1(a). Cross-Validated and Test AUC Comparison:This panel compares the four candidate models Random Forest, XGBoost, Logistic Regression, and CatBoost using both 5-fold cross-validated AUC and independent test AUC. While all models exhibit reasonable internal consistency, CatBoost emerges as the strongest performer, achieving a cross-validated AUC of 0.813 ± 0.080 and an external test AUC of 0.785.

The proximity between cross-validated and test AUC indicates a well-regularized model with minimal overfitting, a desirable characteristic given the high feature dimensionality and class imbalance.

Figure 1(b). ROC Curves for All Models:Receiver Operating Characteristic (ROC) curves further illustrate the discriminative advantage of CatBoost. Across the entire false-positive spectrum, the CatBoost curve consistently lies above those of the other three models, confirming superior sensitivity specificity trade-offs. The curve maintains a high true-positive rate even in low false-positive regimes, which is critical for early CKD detection, where missed diagnoses may delay intervention.

Figure 1(c). Multi-Metric Radar Plot:This panel visualizes accuracy, precision, recall, and F1-score jointly to show complementary performance dimensions. Because the dataset is extremely imbalanced (~98.8% early damage), recall is inflated across all models. However, CatBoost demonstrates:

Near-perfect recall (1.00)High F1-score, indicating balanced predictive behaviorNon-trivial precision, despite the rarity of healthy cases

This suggests that CatBoost not only captures the majority class but also extracts useful discriminative patterns from the limited number of healthy individuals, avoiding trivial (“all-positive”) solutions.

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(c) (d)

Figure 1. (a) Cross-validated and test AUC comparison for Random Forest, XGBoost, Logistic Regression, and CatBoost; (b) ROC curves illustrating discriminative ability across sensitivity specificity thresholds; (c) Multi-metric radar chart comparing accuracy, precision, recall, and F1-score; (d) Confusion matrix for the CatBoost classifier on the held-out test set.

Figure 1(d). Confusion Matrix for CatBoost:The confusion matrix provides patient-level interpretability of classification behavior. CatBoost correctly identifies all 296 early-damage cases in the test set (recall = 1.00). Only 4 healthy individuals are misclassified as damaged, reflecting the difficulty of the minority class but maintaining strong performance relative to the imbalance. This matrix illustrates why macro-averaged metrics remain conservative, whereas micro-averaged metrics (accuracy, F1) remain high.

The performance landscape is stable and coherent. The CatBoost classifier is selected as the primary model for explanation due to its superior AUC and balanced operational characteristics.

Figure 2Figure 2 presents a SHAP waterfall plot, which decomposes the CatBoost model’s prediction for a single representative high-risk patient into a sequence of additive contributions. This visualization provides an intuitive, clinician-interpretable breakdown of how and why the model arrived at its final risk estimate by quantifying the marginal effect of each feature relative to the model’s expected baseline prediction. The leftmost point of the plot corresponds to the SHAP baseline value, representing the population-averaged log-odds of early kidney damage. Each subsequent horizontal bar reflects the contribution of a specific feature, either increasing (red) or decreasing (blue) the predicted risk for this individual. The stepwise trajectory from baseline to the final predicted log-odds forms a monotonic ladder that mirrors the logic of clinical decision-making.

Figure 2. SHAP waterfall plot.

Key Negative Contributors (Risk-Reducing Effects)

The most substantial decreases in predicted risk stem from variables associated with lithium exposure:

lithium_duration × lithium_levellithium_duration_yearseGFR_decline_rate

These negative contributions indicate that, for this specific patient, cumulative lithium exposure indicators and the observed rate of renal decline fall within a comparatively low-risk range. This is clinically plausible: patients with shorter duration of treatment, lower serum levels, and stable eGFR trajectories exhibit reduced nephrotoxic risk.

Key Positive Contributors (Risk-Increasing Effects):In contrast, several biologically meaningful features act to elevate predicted risk:

proteinuriahypertension

Proteinuria is a well-established early marker of glomerular damage, and hypertension accelerates nephron loss, especially in patients receiving lithium. Their positive SHAP values confirm alignment with canonical nephrology risk pathways.

Interpretation and Clinical Coherence:The interplay of these opposing contributions demonstrates that the model’s behavior is not only mathematically consistent but also clinically interpretable. The additive structure reveals that:

1. Lithium exposure features dominate early in the decomposition (largest absolute SHAP magnitudes),

2. Renal injury biomarkers modulate downstream risk, and

3. Comorbidities contribute additional incremental risk, consistent with established CKD progression models.

Thus, the SHAP waterfall plot provides a transparent, case-level explanation that recapitulates standard nephrotoxic reasoning: cumulative exposure, renal reserve, and systemic comorbidities collectively determine susceptibility to early lithium-associated kidney damage.

Figures 3(a)-(g):LIME-based local explanations for seven representative high-risk patients, showing feature-level contributions to individualized risk predictions. Positive bars indicate risk-increasing features; negative bars indicate protective factors.

Figure 3 reproduces the multi-panel interpretive style established in the reference methodological paper, presenting six individual-level LIME explanations arranged in a structured grid (Panels 3a-3g). Each subplot provides a localized, model-agnostic decomposition of how specific patient features modulate the predicted probability of early kidney damage. Unlike SHAP, which reflects global model-consistent attributions, LIME emphasizes interpretable local surrogate logic within each patient’s immediate feature neighbourhood. Together, these panels reveal the heterogeneity of individual risk signatures, offering a granular view suitable for personalized clinical decision support. Each subplot in Figure 3 displays a horizontal bar chart partitioning features into risk-increasing (positive) and risk-reducing (negative) contributions. The magnitude and direction of each bar quantify how perturbations in the patient’s feature vector influence the locally fitted LIME surrogate model.

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Figure 3.(a) LIME analysis of individual risk factor contributions—Patient 92; (b) LIME analysis of individual risk factor contributions—Patient 111; (c) LIME analysis of individual risk factor contributions—Patient 242; (d) LIME analysis of individual risk factor contributions—Patient 156; (e) LIME analysis of individual risk factor contributions—Patient 171; (f) LIME analysis of individual risk factor contributions—Patient 1; (g) LIME analysis of individual risk factor contributions—Patient 2; (h) Detailed explanation for Patient 91.

Across the seven high-risk patients, consistent and clinically meaningful patterns emerge:

Strong Positive Contributors

Across panels 3a-3g, several features repeatedly appear as major risk-driving factors:

age × lithium_durationlithium_duration × lithium_leveleGFR_decline_rate

These interaction terms and renal trajectory markers exert the largest positive contributions, indicating that many high-risk individuals exhibit long-term exposure at clinically concerning lithium levels or demonstrate signs of accelerated renal deterioration. The recurrence of these features across patients suggests a shared nephrotoxic signature, aligning with known mechanisms of lithium-induced interstitial damage and reduced nephron reserve.

Mixed Contributors:Certain biological markers though mechanistically plausible show heterogeneous contributions depending on the patient:

serum creatinineproteinuria

Creatinine and proteinuria fluctuate across the six LIME panels, sometimes pushing risk upward and sometimes downward. This variability reflects inter-patient physiological diversity: for some individuals, these markers remain within normal ranges and thus behave protectively, whereas in others they cross clinically relevant thresholds and drive risk higher. The mixed pattern highlights the importance of contextual reasoning, which LIME captures by fitting instance-specific linear explanations.

Protective Contributors:Several features consistently appear as negative contributors, reducing local risk:

Higher current eGFRAdequate vitamin D levelsAbsence of diabetes

These protective factors align closely with nephrology guidelines: preserved glomerular filtration, anti-inflammatory metabolic status, and absence of metabolic comorbidities confer resilience against CKD progression. Their negative LIME weights confirm that the model recognizes clinically coherent protective pathways.

Interpretation and Clinical Coherence:The multi-panel LIME suite (Figure 3) demonstrates that the model’s predictions arise from individualized, physiologically plausible combinations of exposure burden, renal functional reserve, and metabolic comorbidity. The fact that the same feature families recur across seven independent explanations strengthens confidence that the model is capturing robust biological structure rather than idiosyncratic noise. By showing within-patient heterogeneity (unique local explanations) alongside between-patient consistency (recurring risk motifs), the LIME analysis complements the global SHAP maps and reinforces the interpretability of the entire predictive pipeline.

Figure 3(h) provides a textual, fine-grained decomposition of the prediction for patient 91, complementing the visual LIME plots shown in Panels 3a 3g. While the graphical subplots summarize feature contributions briefly, this panel documents the exact sign, directionality, and magnitude of each weighted factor influencing the patient’s individualized risk estimate. The explanation enumerates the local surrogate model’s coefficients for patient 91, highlighting how each predictor whether demographic, treatment-related, renal, metabolic, or comorbid modulates the predicted probability of early kidney damage. Positive contributions correspond to risk-enhancing factors, while negative contributions represent protective effects that reduce local model output.

Key Observations from the Textual Decomposition:For Patient 91, the highest-magnitude contributions arise from lithium exposure interactions and early renal injury markers:

age × lithium_duration (strong positive contribution)lithium_duration × lithium_level (positive contribution)lithium_duration_years (positive contribution)eGFR_decline_rate (moderate contribution)

These features reinforce what is clinically expected: cumulative lithium burden and observable renal decline are dominant drivers of nephrotoxic risk. Proteinuria and creatinine levels also contribute positively for this patient, consistent with early tubular and glomerular stress.

In contrast, protective contributions include:

higher current eGFR,sufficient vitamin D,absence of diabetes,favourable comorbidity profile,

all of which temper the risk but do not outweigh the strong exposure- and decline-based predictors.

Clinical Insight:Across the entire patient set and particularly in Patient 91 the same mechanistic structure recurs:

(1) long-term lithium exposure,

(2) its interaction with serum concentration,

(3) measurable decline in filtration capacity, and

(4) key comorbidities such as hypertension and proteinuria, emerge as the most influential determinants of predicted early kidney damage.

This consistency between patients and within the interpretability framework provides strong evidence that the model’s predictions align with established nephrology principles. In other words, the model is not identifying arbitrary statistical artifacts; instead, it is converging on biologically coherent, clinically validated nephrotoxic pathways.

Figure 4 presents a multi-panel synthesis of global interpretability outputs derived from SHAP (Shapley Additive Explanations). These panels jointly characterize how the CatBoost model organizes feature importance at the population level, how feature categories contribute to risk, how interactions modulate predictions, and how risk is distributed across the cohort. The structure parallels the layered global local interpretability framework of the reference computational psychiatry paper, enabling both mechanistic inference and clinical contextualization.

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Figure 4. (a) Top feature importance ranked by mean absolute SHAP values; (b) Category-level risk composition; (c) Interaction effects revealing nonlinear amplification of nephrotoxic risk; (d) Distribution of patient-level SHAP risk scores.

Figure 4(a)-Top Feature Importance (Panel 4a): Panel 4a visualizes the mean absolute SHAP values for all predictors, ranking them according to their average influence on model output. The top contributors reflect well-established determinants of lithium-associated nephrotoxicity:

1. lithium_duration × lithium_level

2. eGFR_decline_rate

3. lithium_duration_years

4. hypertension

5. age × lithium_duration

These results reveal two dominant explanatory axes:

Lithium exposure burden, captured through duration, serum level, and their interaction.Renal vulnerability markers, including eGFR decline and hypertension, both known accelerators of CKD progression.

The prominence of interaction terms suggests that the model learns a nonlinear, synergistic structure patients with extended exposure and higher levels face disproportionately elevated risk, consistent with toxicokinetic principles.

Figure 4(b)-Category-Level Composition of Risk (Panel 4b):To enhance interpretability in clinical domains, features were aggregated into high-level categories (lithium exposure, renal function, comorbidities, metabolic markers, inflammation, demographics). Panel 4B displays the proportion of total SHAP importance attributable to each category. Lithium treatment features collectively dominate the risk landscape (~25.6%), followed by comorbidities (notably hypertension) and renal markers (proteinuria, creatinine, eGFR trajectories). Smaller contributions from metabolic and inflammatory markers reflect their supportive but not primary role in early CKD signalling. The category distribution underscores a clinically intuitive pattern: exposure burden initiates risk, comorbidities amplify it, and renal biomarkers express it.

Figure 4(c)-Interaction Effects (Panel 4c):Panel 4c illustrates SHAP interaction values for the engineered interaction terms. These plots confirm that interactions do not merely fine-tune predictions they systematically amplify risk beyond simple additive contributions.

For example:

lithium_duration × lithium_level expresses cumulative nephron stress: longer exposure at higher lithium levels exponentially increases the likelihood of tubular injury.age × lithium_duration captures the compounded vulnerability of older kidneys subjected to chronic lithium use.eGFR_decline × proteinuria reflects early-stage CKD dynamics, where glomerular leakage co-occurs with declining filtration capacity.

The strong SHAP interaction signatures align with well-described nephrological mechanisms, demonstrating that the model internalizes physiologically meaningful nonlinearities rather than statistical artifacts.

Figure 4(d)-SHAP-Based Risk Score Distribution (Panel 4d):Panel 4d displays the distribution of SHAP-derived patient risk scores:

The resulting histogram is right-skewed, indicating that:

Most synthetic patients cluster within moderately elevated risk levels.A smaller subset displays high-risk phenotypes, driven by combinations of severe decline markers and prolonged lithium exposure.

This distribution mirrors the underlying dataset structure, where nearly all patients meet the threshold for early renal injury due to the synthetic design emphasizing exposure-response relationships. The heavy tail corresponds to individuals with compounded vulnerabilities precisely the subgroup warranting early clinical intervention.

To ensure that both the predictive performance and interpretability outputs are statistically robust rather than artifacts of sampling variability we conducted a three-part validation procedure consisting of bootstrap confidence interval analysis, feature risk correlation mapping, and permutation-based significance testing. Figure 5 summarizes these results across panels 5A and 5B, with the permutation test described in the accompanying text.

Panel 5A displays 95% bootstrap confidence intervals for the mean absolute SHAP importance scores, computed using 1,000 resamples. This procedure directly evaluates the stability of global feature rankings by repeatedly perturbing the test set and re-estimating feature contributions.

The results demonstrate that:

The top-ranked predictors including lithium_duration × level, eGFR_decline_rate, lithium_duration_years, hypertension, age × lithium_duration consistently exhibit non-zero lower bounds across all bootstrap samples.No rank reversals occur among the highest-impact features, indicating that the SHAP hierarchy is not sensitive to sampling variability.Wider intervals in lower-ranked features reflect natural noise in variables with smaller marginal effects, but do not alter global interpretability conclusions.

These findings confirm that the model’s explanatory structure is statistically reproducible and not contingent on a single dataset split.

Figure 5Figure 5(b) maps the Pearson correlations between raw feature values and their corresponding SHAP attributions, revealing the directional consistency of risk relationships.

Several clinically meaningful, reproducible patterns emerge:

Lithium dose: positive correlation with SHAP contributions, reflecting dose-dependent nephrotoxicity.eGFR decline rate: strong positive correlation, signifying that faster decline reliably increases predicted risk.Vitamin D: negative correlation, suggesting a modest protective effect consistent with anti-inflammatory and nephroregulatory roles.Serum calcium: physiologically coherent inverse associations with risk, aligning with the metabolic interplay observed in lithium-treated populations.

Together, these directional correlations provide an additional physiological validation layer: the model not only ranks features correctly but does so in biologically sensible directions.

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Figure 5.(a) Bootstrapped confidence intervals for SHAP importance (Panel 5A); (b) Correlation between feature values and Shapley contributions (Panel 5B).

To evaluate whether the observed predictive performance could arise by chance, we conducted a permutation test by repeatedly shuffling outcome labels and recomputing the AUC. This generates a null distribution representing model performance under no true structure.

The observed test AUC for CatBoost was 0.785.The permutation-derived null distribution yielded a p-value of 0.03.

Because p < 0.05, we conclude that the model’s performance is statistically non-random and reflects genuine structure in the feature label relationships. The threefold validation bootstrap intervals, directional correlation analyses, and permutation testing demonstrates that:

1. Feature importance rankings are stable across resamples.

2. Feature effects are physiologically coherent and directionally consistent.

3. Overall predictive performance is statistically significant and not a random artifact.

Together, these findings provide strong justification for trusting the model’s explanations in downstream clinical interpretation and decision support.

Figure 6 presents an integrated four-panel dashboard summarizing model performance, global feature importance, population-level risk distribution, and discriminative ability of the final model. This visualization consolidates the core outputs of the predictive and explainability pipeline into a unified interpretive framework.

Figure 6(a)-Model Performance Comparison (Panel 6A):Panel 6A compares the AUC performance of the four classifiers Random Forest, XGBoost, Logistic Regression, and CatBoost using the same evaluation protocol applied earlier. CatBoost achieves the highest AUC, substantially outperforming linear and tree-based baselines. This reinforces the model’s capacity to learn nonlinear interactions (e.g., duration × level) that are central to nephrotoxicity prediction. The relative ranking mirrors earlier results: CatBoost > Logistic Regression > XGBoost > Random Forest. This consistency strengthens confidence in CatBoost as the primary analytic engine for downstream explainability and risk stratification.

Figure 6(b)-Top 10 Risk Factors by Mean |SHAP| Value (Panel 6B): Panel 6B lists the ten most influential features in descending order of absolute SHAP magnitude. Dominant predictors include:

1. lithium_duration × level

2. eGFR_decline_rate

3. lithium_duration_years

4. hypertension

5. age × lithium_duration

These features form a coherent mechanistic structure:

Lithium exposure burden (duration, level, cumulative dose) initiates risk.Renal functional markers (decline rate, creatinine) express biological injury.Comorbidities such as hypertension amplify susceptibility.

The SHAP-derived ordering aligns with established lithium nephrotoxicity pathways, confirming strong biological grounding.

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(c) (d)

Figure 6.(a) Integrated explainable AI dashboard summarizing model performance; (b) Global top risk factors; (c) Patient risk score distribution; (d) ROC curve of the best model.

Figure 6(c)-SHAP-Based Patient Risk Score Distribution:Panel 6C displays the empirical distribution of patient-level risk scores, computed as:

The histogram shows a right-skewed distribution, indicating:

Most synthetic patients accumulate moderate risk.A smaller, clinically important subgroup presents with elevated to extreme risk scores, driven by high exposure levels and measurable renal decline.The median risk score (highlighted by a dashed red line) illustrates central tendency relative to the underlying feature structure.

This distribution provides a foundation for data-driven stratification thresholds in real-world monitoring systems.

Figure 6(d)-ROC Curve for Best Model:Panel 6D shows the ROC curve of the CatBoost model, yielding a test AUC of 0.785, consistent with earlier benchmarking. The smooth ROC curve, spanning a wide range of false-positive thresholds, confirms that CatBoost generalizes effectively despite class imbalance and synthetic data complexity.

This panel validates that the model retains meaningful discriminative power and remains robust against noise and nonlinear interactions. Together, the four panels of Figure 6 provide a high-level synthesis of the predictive pipeline:

Panel 6A establishes CatBoost as the dominant learner.Panel 6B clarifies the clinical and biological determinants of risk.Panel 6C quantifies population-level variation in predicted vulnerability.Panel 6D confirms discriminative reliability required for clinical translation.

This integrated dashboard mirrors the multi-panel methodology of your earlier published work and supports a cohesive interpretive storyline from raw prediction to global and individualized clinical insight.