Positioning relative to prior work.

In contrast to prior surveys, toolkits, and evaluation studies [3–8], this work (i) formalizes widely used XAI metrics using explicit equations and open-source implementations, (ii) pre-specifies a single post-hoc explainee to control model-induced variability, (iii) evaluates post-hoc and ante-hoc methods within a single protocol, and (iv) benchmarks performance across multiple clinical tabular datasets. While prior work has highlighted the need for quantitative evaluation, existing studies remain fragmented: surveys largely provide conceptual definitions without unified operationalization, and toolkits such as Quantus focus on metric collections, primarily in neural network and image-based settings, without a controlled, end-to-end benchmarking protocol. In contrast, this work provides a unified instantiation of commonly cited metrics, explicitly tailored to clinical tabular data, integrating formalized equations, method–metric applicability constraints, and a pre-specified evaluation protocol within a single reproducible framework. A compact comparison is provided in Table 1.

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Table 1. What this work adds vs. representative surveys/toolkits (✓ = provided; – = not a primary focus).

https://doi.org/10.1371/journal.pone.0351473.t001

Scope.

This paper presents a reusable framework for applying auditable, quantitative XAI metrics to clinical tabular tasks, including metric definitions/equations, implementation details, and method–metric applicability. Exhaustive coverage of all explainer families and parameter regimes is left for future extensions.

Families.

We distinguish (i) post-hoc feature-attribution methods, SHAP, which provides local Shapley values that can be aggregated to a global importance profile, and LIME, which is local by design; (ii) rule-based local explainers (Anchors); and (iii) inherently interpretable (ante-hoc) models (EBM, TabNet), both of which yield per-instance signals that can be aggregated to global views (e.g., EBM main-effect shapes; TabNet aggregated importances).

Takeaway.

This literature motivates our emphasis on tree ensembles as competitive tabular baselines and, by extension, on post-hoc explainers commonly paired with them in practice.

Canonical definitions in prior work.

Several metrics already have operational mathematics in the literature: (i) additive local accuracy for SHAP/TreeSHAP with exact reconstruction on tree ensembles [34]; (ii) local surrogate agreement for LIME (weighted regression fit to h in a locality kernel) [16]; (iii) Anchors’ precision and coverage as rule-family metrics estimated against h [17]; (iv) rank-based agreement via Spearman/Kendall for top-k feature sets [8]; and (v) robustness via small input perturbations and explanation-distance sanity checks [36,37].

Our instantiations vs. prior.

Our contribution is not to introduce new metrics but to standardize one auditable instantiation per metric for clinical tabular settings and use them side by side in a single protocol: (1) Fidelity reported as both score- and decision-level; for SHAP/TreeSHAP we use exact additive reconstruction where applicable to avoid surrogate error. (2) Simplicity via a relative importance threshold (sparsity) so values are scale-free across methods/datasets. (3) Consistency as depth-averaged Spearman over top-k (we use k = 5) to stabilize against ties and shallow lists. (4) Robustness as change under small Gaussian perturbations with fixed to make comparisons reproducible. (5) Precision/Coverage restricted to rule-family (Anchors) to avoid cross-paradigm conflation. Where multiple forms coexist in prior work, we justify our single choice for reproducibility and cross-dataset comparability. Formal equations and the method–metric applicability appear in Materials & Methods.

Alternatives and scope.

The rule-based space includes other candidates (e.g., rule lists/sets). Interpretable modeling also spans linear/monotone GAM variants and decision sets. We do not claim exhaustiveness; rather, we provide a reproducible, metric-driven baseline with widely used representatives and release code to ease extension. Counterfactuals and example-based methods are orthogonal families we list for future work (see Limitations).

Methods policy.

This policy reflects the principle, supported in prior XAI literature, that evaluation metrics must be aligned with the structural form and semantics of the explanation, for example numeric attribution vectors versus logical rules, rather than applied uniformly across heterogeneous paradigms [4,8,17]. We compute all metrics on local (per-instance) outputs with fixed parameters and seeds; apply each metric only where it is theoretically meaningful for the explainer family; and run all post-hoc explainers on a single, pre-specified focal predictor to ensure controlled comparability across datasets.

We evaluated five XAI methods spanning post-hoc and inherently interpretable approaches: LIME, SHAP (TreeSHAP for tree ensembles; additive reconstruction is exact [34]. For non-tree models, KernelSHAP yields an additive approximation; the same fidelity equations apply, but we do not evaluate that variant here.), Anchors, EBM, and TabNet. These methods are selected to represent three complementary paradigms, post-hoc attribution, rule-based local explanations, and inherently interpretable models, providing conceptual coverage rather than method-specific focus. This selection is therefore principled and non-arbitrary, ensuring representation of distinct XAI paradigms within a single evaluation protocol. To isolate differences attributable to explainers, all post-hoc methods (LIME, SHAP, Anchors) are applied to a single focal predictor chosen after benchmarking in the Results section. In contrast, EBM and TabNet are assessed via their inherent (ante-hoc) interpretability.

We use six established quantitative evaluation metrics from prior work: fidelity, simplicity, consistency, robustness, precision, and coverage. Although the metrics are not new, we formalize and implement their mathematical definitions for transparency and reproducibility [4,5,8]. Fidelity applies to post-hoc feature-attribution surrogates (LIME, SHAP); precision and coverage apply to rule-based explainers (Anchors); simplicity and robustness apply to all methods; and consistency is reported for methods that yield ranked single-feature importances (EBM (a GA²M) provides per-feature shape functions and optional pairwise interactions [42]; our rank-based consistency metric is defined for single-feature lists. To avoid conflating main effects with interactions [43], we do not compute consistency for EBM, leaving interaction-aware consistency for future work.) (LIME, SHAP, TabNet). Table 2 defines an explicit method–metric applicability mapping, ensuring that each metric is used only where theoretically valid given the structure of the explanation, and preventing invalid cross-paradigm comparisons.

3.10.1. Fidelity.

Fidelity [46] evaluates how accurately an XAI method replicates the behavior of the original predictive model. It is computed in two complementary ways:

• Score fidelity: Measures the similarity between the model’s probability and the explainer’s reconstruction, operationalized as .
• Decision fidelity: Measures the agreement in final class predictions between the predictive model and an explainer-induced approximation (e.g., a local surrogate model where applicable). It reflects how often the label derived from the explainer’s approximation matches the label of the original model. This follows standard definitions of fidelity as agreement between a model and its explanation approximation [38].

The formal equations are:

(1)

(2)

Where:

• is the probability (score) from the trained predictor h at .
• is the surrogate/reconstruction probability produced by the explainer .
• and are the corresponding predicted class labels from h and .
• is the Kronecker delta, returning 1 if a = b and 0 otherwise.

This dual view of fidelity allows both probabilistic closeness and class decision alignment to be assessed, highlighting whether an explanation preserves not just the model’s outcome but its internal confidence as well.

A perfect score of 1.0 indicates that the explainer exactly replicates the model’s predicted probability (score fidelity) or predicted label (decision fidelity); small deviations can arise from ties or probabilistic rounding. Scores closer to 0.0 signify poor alignment between the explainer and the model.

3.10.2. Simplicity (attribution-based).

Simplicity [35] quantifies how concise and interpretable an explanation is, based on the number of features it includes. In high-stakes domains like healthcare, simpler explanations involving fewer features are often preferred to support user trust and rapid decision-making.

For attribution methods, we define simplicity as the average number of features per instance whose relative importance exceeds a threshold . Let be the attribution vector for instance . Features with are counted toward the explanation.

(3)

Where:

• F: set of features (with cardinality |F|).
• : attribution score of feature j for instance .
• : maximum absolute attribution in instance .
• is the threshold value .
• : indicator function, returning 1 if the condition is true, 0 otherwise.

The threshold parameter controls explanation sparsity. Higher thresholds (e.g., 0.1) retain only the most influential features, resulting in simpler, more focused explanations. Lower thresholds (e.g., 0.01) capture weaker attributions, producing denser explanations with more features.

This formulation enables consistent comparison of explanation conciseness across methods and datasets. Lower values indicate simpler explanations involving fewer features, which are generally easier for human interpretation. Higher values may capture more detail but reduce interpretability.

3.10.3. Consistency.

Consistency [8] measures the extent to which explanation methods assign similar relative importance to the same features for a given instance. We use Spearman’s rank correlation because the objective is to compare feature-order agreement rather than absolute attribution magnitudes.

Pairwise consistency is computed across progressive feature depths. For each instance, the top n ranked features from two methods are compared for , where k = 5. The case n = 1 is excluded because rank correlation is not defined for a single ranked item. This formulation focuses on agreement across the most salient part of the explanation while avoiding instability from low-importance feature tails.

The consistency score between two XAI methods M_1,h and M_2,h is defined as:

(4)

Where:

• and : denote the top- n ranked feature lists for instance from methods M_1,h and M_2,h, with feature identities aligned prior to computing the correlation.
• : denotes Spearman’s rank correlation.
• k = 5: the maximum number of top-ranked features considered.

The resulting score lies in the range , where larger positive values indicate stronger agreement in feature ranking, values near zero indicate weak or no rank agreement, and negative values indicate opposing ranking patterns. For comparisons involving TabNet, the score should be interpreted as cross-configuration rank agreement because TabNet explanations are obtained from the native TabNet model, whereas LIME and SHAP explain the selected RF focal predictor.

3.10.4. Robustness (attribution-based).

Robustness [36] evaluates how stable a feature-based explanation remains when small input perturbations are introduced. In this study, it is operationalized using the fixed Gaussian-jitter protocol described above.

We introduce Gaussian noise to each instance, drawn from with , applied element-wise to the numerically encoded input representation with no model refitting. Robustness is computed as the average change between explanation vectors before and after a small perturbation (We use the norm; results are qualitatively similar with . We do not divide by |F| so robustness reflects the total attribution shift per instance.):

(5)

Where:

• : element-wise perturbation.
• : explanation vector from method for input .

Lower values indicate higher robustness, i.e., explanations remain stable even under small input perturbations. A value of 0 means the explanation is entirely unchanged. These values therefore quantify explanation sensitivity under the benchmark perturbation protocol.

3.10.5. Transition to rule-based explainers.

The metrics discussed thus far apply to explainers that yield numeric, per-instance feature-importance vectors. In contrast, rule-based explainers such as Anchors produce logical decision rules, for which precision and coverage are native evaluation criteria [17]. This necessitates a distinct set of metrics tailored to symbolic conditions and coverage-based evaluation. We now describe four such metrics used to evaluate rule-based explanations.

3.11.1. Notation reminder (rule-based).

In this subsection denotes the set of feature conditions (literals) in the rule for ; primes (e.g., ) indicate the rule after a small perturbation of .

Rule-based XAI methods, such as Anchors, generate explanations in the form of logical if-then rules composed of discrete feature conditions (e.g., “Age > 40 AND Gender = Female”). These rules differ fundamentally from numeric feature attributions and thus require tailored evaluation metrics. We define four such metrics: precision, coverage, simplicity, and robustness, detailed below.

3.11.2. Precision and coverage.

Precision measures how often the black-box predictor agrees with the explained-instance prediction on the samples covered by the rule, and coverage is the fraction of instances to which the rule applies [17]. Tightening the precision threshold typically increases reliability while reducing coverage (the canonical precision–coverage trade-off).

Let be the prediction of h on the explained instance , and let be the indicator. Then

(6)

(7)

Where:

• z denotes a generic instance in the dataset X.
• .
• N is the dataset size used for coverage.

These metrics are computed using the Anchor package’s inbuilt estimators and reflect how reliably and broadly each generated rule captures the model’s behavior.

A perfect precision score is 1.0 (i.e., 100% correct on all covered instances). Coverage values range from 0 to 1, where 1 indicates full dataset applicability.

Higher thresholds (e.g., 0.99) enforce stricter rule precision, producing explanations with near-perfect reliability. However, this typically reduces coverage, as the rules apply to fewer data instances. This trade-off is particularly relevant in healthcare: while high-precision rules improve trust in local predictions, their narrow applicability must be weighed against the need for generalizability across diverse patient groups.

3.11.3. Simplicity (rule length).

Simplicity equals rule length (number of literals) (E.g., “Age > 45 AND BMI > 30” has length 2; adding “Smoker = Yes” gives length 3.).

(8)

Where:

• : the set of features used in the rule that explains .

A smaller simplicity score may be desirable in clinical settings to support quick comprehension and decision-making.

3.11.4. Robustness (rule-based).

Robustness for rule-based explanations reflects the stability of the rule features under the same fixed perturbation protocol. If different rules are generated from perturbed inputs, this indicates lower rule stability. We introduce small Gaussian noise to the input instance, drawn from , with , before recomputing the rules.

Following the same perturbation approach as attribution methods [36], we measure robustness via the Jaccard dissimilarity (We use Jaccard dissimilarity on rule feature sets in Eq. (9); other set distances (e.g., Hamming on binary literal vectors) produce qualitatively similar trends.) between pre- and post-noise rule feature sets, as defined in Eq. (9).

Let be the set of features used in the rule for instance , and the rule after applying small Gaussian noise to the input . Then:

(9)

Where:

• is the set of feature conditions in the rule for , and is the corresponding set after a small perturbation is applied to (i.e., ).

Lower scores indicate greater stability of the rule structure under the fixed perturbation protocol. A robustness score of 0.0 means the rule remains identical after perturbation.

3.11.5. Framework components and extensibility.

The framework comprises: (i) explicit equations for six established metrics; (ii) a pre-specified focal-model protocol to control model-induced variance; (iii) a metric–method applicability map; and (iv) open-source code. New explainers or metrics can be added by implementing the metric interface (inputs/outputs documented in the repository) and extending the applicability map; the protocol remains unchanged.

3.12.1. Why a single explainee?.

Fixing one competitive predictor for post-hoc comparisons controls model-induced variance so that differences are attributable to the explainer rather than to changes in the underlying decision function [7,37]. Selecting a different best-performing predictor for each dataset, or applying all post-hoc explainers to all candidate predictors, would introduce an additional experimental axis and shift the study from controlled metric evaluation toward explainer–model interaction analysis. This latter question is important but outside the scope of the present framework demonstration.

3.12.2. Hyperparameter policy and reproducibility.

Because our primary goal is to benchmark explainability, not to maximize predictive accuracy, we adopt library defaults with a fixed global seed and avoid extensive per-dataset hyperparameter optimization. This standardization reduces model-induced variability so that observed differences are attributable to the explainers themselves, in line with recent guidance on rigorous and transparent XAI evaluation and reproducible ML workflows [7,47,48]. Moreover, explanation quality is known to be sensitive to modeling and procedural choices, which motivates controlling additional sources of variance introduced by heavy hyperparameter optimization [37]. For Random Forests specifically, prior work shows diminishing returns once the number of trees is sufficiently large and argues that treating the tree count as a major tuning parameter is often unnecessary; performance typically plateaus around ∼100–200 trees [49,50]. Accordingly, we use defaults with a fixed seed for all models and a conventional tree count for RF (Settings used in all experiments: random_state = 42 for all models; RF: n_estimators = 100, n_jobs; GBC: scikit-learn defaults; XGB: library defaults; EBM: library defaults; TabNet: seed = 42, verbose = 0. Full configuration files and code are available.).

3.12.3. Software environment and packages.

All experiments were conducted in Python 3.11.7. Explainability methods were implemented using established open-source libraries. Specifically, LIME explanations were generated using the lime, SHAP values were computed using the shap, rule-based explanations were generated using the anchor-exp, EBM were implemented via interpret, and TabNet models were trained using the pytorch-tabnet package. The full software environment, including all Python dependencies, was captured using pip freeze and is released as a requirements.txt file alongside the source code to support exact reproducibility.

Model selection rule (pre-specified).

As outlined in the Experimental setup, the single focal explainee for post-hoc XAI is selected by best average rank on F1 across datasets (primary), with average rank on accuracy as a tie-breaker if needed.

Selection outcome.

Applying the rule yields “Random Forest (RF)” as the focal post-hoc explainee (see Table 4): RF ranks first on two datasets (PDHS, ESDRPD), second on Breast cancer, and fifth on Diabetes retinopathy, giving the best average F1 rank (2.25). The accuracy tie-breaker was not required. RF is not the best-performing classifier on every dataset, particularly Diabetes retinopathy. The focal-model protocol therefore selects a competitive aggregate explainee for controlled post-hoc comparison, rather than a per-dataset optimal classifier.

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Table 4. Per-dataset F1 ranks (1 = best) and average rank used for model selection.

https://doi.org/10.1371/journal.pone.0351473.t004

Implication for XAI.

Having selected RF by a pre-specified, data-driven rule, we compute post-hoc explanations (SHAP, LIME, Anchors) on RF to control for model-induced variability. EBM and TabNet are reported via their inherent interpretability.

Evaluation of XAI methods aggregated over local explanations.

The explanation outputs were assessed using predefined metrics: fidelity, simplicity, consistency, robustness, precision, and coverage. The results, averaged over local instance explanations, summarize explanation behavior across the different datasets. The XAI results should be interpreted according to the method–metric applicability design in Table 2. LIME, SHAP, and Anchors explain the selected RF focal predictor, whereas EBM and TabNet are evaluated through their native model-specific interpretability mechanisms. Thus, mixed-family comparisons involving EBM or TabNet describe method–predictor configurations rather than explanations of a common underlying predictive function. These results should therefore be read alongside the corresponding predictive performance in Table 3.

Evaluation of feature importance-based XAI methods.

Fidelity: The fidelity scores for LIME and SHAP are reported in Table 5. In this context, fidelity is assessed using two complementary criteria: Score fidelity, which measures agreement in predicted probabilities, and Decision fidelity, which measures agreement in predicted class labels.

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Table 5. Fidelity of LIME and SHAP explanations, reported as mean ± standard deviation over test instances. The highest numerical values are marked with ^†; for SHAP (TreeSHAP on tree ensembles), score fidelity of 1.000 reflects exact additive reconstruction rather than a comparative surrogate approximation outcome. Standard deviations are not shown when they round to 0.000.

https://doi.org/10.1371/journal.pone.0351473.t005

SHAP, using TreeSHAP, obtained score fidelity of 1.000 across all datasets with zero variance. This reflects the local accuracy property of TreeSHAP for tree ensembles, where additive feature attributions exactly reconstruct the model output [15,34]. It should therefore be interpreted as an expected property of the RF–TreeSHAP pairing, rather than as an empirical superiority result under comparable surrogate-approximation conditions. In contrast, LIME’s fidelity reflects the quality of a local surrogate approximation and can vary across instances. Minor deviations in decision fidelity can still occur due to thresholding and rounding effects when converting probabilities into class labels (e.g., 0.994 ± 0.076 for Diabetes retinopathy), despite near-identical probability reconstruction.

LIME generally exhibited lower fidelity and substantially higher variability across instances. For example, in the Diabetes retinopathy dataset, LIME achieved a score fidelity of 0.832 ± 0.118 and a markedly lower decision fidelity of 0.538 ± 0.499, indicating unstable local approximations at the instance level. Comparable patterns are observed in ESDRPD (0.791 ± 0.145 for score fidelity and 0.917 ± 0.276 for decision fidelity), highlighting LIME’s sensitivity to complex or non-linear decision boundaries. These findings underscore that LIME’s linear approximation of decision boundaries often sacrifices an accurate reflection of model behavior.

Simplicity: The simplicity of LIME, SHAP, EBM, and TabNet is measured by the number of features involved in the explanations, as reported in Table 6. Results are summarized using mean ± standard deviation over test instances to capture both the typical explanation size and its variability across instances.

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Table 6. Simplicity of XAI method–predictor configurations, measured as the number of features in the explanation and reported as mean ± standard deviation over test instances. LIME and SHAP explain the selected RF focal predictor, whereas EBM and TabNet are evaluated through native model-specific interpretability. Lowest values are marked descriptively with ^† and should be interpreted alongside the corresponding predictive performance in Table 3. Standard deviations are not shown when they round to 0.000.

https://doi.org/10.1371/journal.pone.0351473.t006

The thresholds (0.1, 0.05, and 0.01) represent different levels of feature-importance cutoffs used to determine which features are included in an explanation. Specifically, the threshold indicates a fraction of the maximum absolute feature-attribution value in a given instance. A feature is included in the explanation if its absolute value exceeds the threshold multiplied by the maximum absolute value in that instance. Higher thresholds therefore result in fewer features and simpler explanations, while lower thresholds admit more features and yield more detailed explanations. Because the maximum absolute feature value varies across datasets and instances (i.e., practitioners assess which threshold appears most suitable based on the dataset.), the resulting explanation sizes also vary, as formalized in Eq. (3).

Within the method–predictor interpretation described above, TabNet frequently produced compact native explanations, particularly at lower thresholds (0.05 and 0.01). However, these compactness results should not be interpreted independently of predictive performance. In particular, TabNet’s simplicity values on Breast cancer and ESDRPD should be read cautiously given its weak classification performance on those datasets in Table 3. LIME produced compact RF-based local explanations in some settings and, at lower thresholds, often converged to a fixed number of selected features with near-zero deviation. SHAP explanations were generally denser, while EBM generated more feature-rich native explanations across thresholds.

The reported standard deviations highlight important differences in instance-level behavior. TabNet and SHAP exhibit higher variability in explanation size, reflecting adaptive feature selection that can change substantially across instances, whereas LIME often produces explanations of consistent size once the threshold constraint becomes binding. Overall, these results describe an explanation compactness–detail trade-off across the evaluated method–predictor configurations, rather than a model-independent ranking of XAI methods.

Consistency: The consistency scores between LIME, SHAP, and TabNet are reported in Table 7. Results are summarized using mean ± standard deviation over test instances to capture both average agreement and instance-level variability in feature rankings.

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Table 7. Consistency between explanation-producing configurations measured using Spearman rank correlation over , with k = 5, reported as mean ± standard deviation over test instances. LIME and SHAP explain the selected RF focal predictor, whereas TabNet rankings are obtained from the native TabNet model. Highest values within each dataset are marked descriptively with ^†.

https://doi.org/10.1371/journal.pone.0351473.t007

LIME and SHAP produced the highest pairwise consistency scores in all four datasets, indicating stronger agreement between the two RF-based post-hoc attribution methods than between either method and TabNet. The strength of this agreement varied across datasets: it was highest for ESDRPD (0.66 ± 0.32), moderate for PDHS (0.46 ± 0.23), and weaker for Breast cancer (0.16 ± 0.42) and Diabetes retinopathy (0.08 ± 0.49).

Comparisons involving TabNet produced negative mean consistency scores across datasets. Because TabNet rankings are obtained from the native TabNet model, whereas LIME and SHAP explain the selected RF focal predictor, these values should be interpreted as cross-configuration rank divergence rather than disagreement among explainers applied to the same predictive function.

Overall, the consistency results suggest that LIME and SHAP provide the strongest observed feature-ranking alignment under the RF focal predictor, while TabNet yields a distinct ranking profile under its native model configuration.

Robustness: The robustness scores for LIME, SHAP, EBM, and TabNet are reported in Table 8. Results are summarized using mean ± standard deviation over test instances to capture both average sensitivity and variability of explanations under small input perturbations.

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Table 8. Robustness of XAI method–predictor configurations measured as sensitivity of explanations to input perturbations, reported as mean ± standard deviation over test instances. LIME and SHAP explain the selected RF focal predictor, whereas EBM and TabNet are evaluated through native model-specific interpretability. Lowest values are marked descriptively with ^†. Standard deviations are not shown when they round to 0.000.

https://doi.org/10.1371/journal.pone.0351473.t008

EBM and TabNet showed low sensitivity scores in their native model-specific explanation configurations under the fixed Gaussian-jitter protocol. EBM in particular exhibited near-zero mean sensitivity with negligible variance, indicating stable native explanations under this numerical perturbation setting. TabNet also produced low sensitivity scores in most datasets, although these results should be interpreted alongside its dataset-specific predictive performance, particularly for Breast cancer and ESDRPD (see Table 3).

For the RF focal predictor, SHAP generally showed low sensitivity, with moderate variability in Diabetes retinopathy and Breast cancer. In contrast, LIME was more sensitive to the perturbation and exhibited larger standard deviations, indicating greater instance-level instability in its local surrogate explanations.

Overall, the robustness results provide a comparative view of explanation sensitivity under a fixed numerical perturbation protocol. They should be interpreted as benchmark stability scores rather than as evidence of robustness under domain-valid clinical perturbations.

Evaluation of rule-based XAI method.

Precision, coverage, simplicity, and robustness: The quantitative results for Anchors are reported in Table 9, summarizing how rule-based explanations vary with different precision thresholds. All metrics are reported as mean ± standard deviation over test instances to capture both average behavior and instance-level variability. In Anchors, the threshold controls the minimum acceptable precision for a rule to be extracted. While higher thresholds increase rule reliability (precision), they reduce the number of data points covered (coverage) and typically increase rule complexity (simplicity), as more conditions are needed to meet the stricter criteria.

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Table 9. Precision, coverage, simplicity, and robustness of Anchors across datasets, reported as mean ± standard deviation over test instances. Standard deviations are not shown when they round to 0.000.

https://doi.org/10.1371/journal.pone.0351473.t009

Across all datasets, increasing the threshold improves rule precision, often reaching values of ≥0.99, but leads to a substantial reduction in coverage, in some cases explaining as little as 1% of instances (e.g., Diabetes retinopathy). This highlights that very precise rules typically apply only to a small subset of instances. Importantly, the relatively small standard deviations observed for precision indicate that Anchors reliably enforces the desired precision expectation level across instances once a threshold is fixed.

Coverage, in contrast, exhibits low mean values and modest variability across datasets, particularly for Diabetes retinopathy, where coverage remains consistently low across thresholds. This suggests that the narrow applicability of Anchors rules is not driven by a few outlier instances, but is a systematic consequence of enforcing high-precision constraints. In contrast, datasets such as PDHS and Breast cancer retain moderate coverage at lower thresholds, indicating that broader rules can be obtained when the underlying decision structure is simpler.

As thresholds increase, rule length generally increases, reducing compactness and requiring more feature conditions to satisfy stricter precision requirements. The reported standard deviations indicate substantial instance-level variability in rule length, particularly for datasets exhibiting higher heterogeneity, such as Diabetes retinopathy and PDHS, where simplicity standard deviations are comparable to or larger than the mean. This indicates that while some instances can be explained using relatively compact rules, others require substantially more conditions to achieve the same precision level, which has implications for human interpretability and practical usability.

Robustness generally remains moderate and, in some datasets, worsens slightly at stricter precision thresholds (lower values indicate higher robustness against noise), suggesting increased sensitivity of longer rules to small perturbations. The moderate standard deviations observed for robustness suggest that this sensitivity varies across instances, reflecting heterogeneity in how tightly rule conditions bind to individual patient profiles. Compared with the low sensitivity observed for native EBM explanations, Anchors rules showed greater perturbation sensitivity, particularly at higher thresholds.

Overall, these results reinforce a fundamental trade-off in rule-based explainability: precision versus coverage versus simplicity versus robustness. Anchors excels at producing human-readable, high-precision rules for narrowly defined subpopulations, but at the cost of limited coverage, variable rule complexity, and reduced robustness under noise. Compared to attribution-based methods such as LIME and SHAP, Anchors offers more actionable (human-readable) rule-based explanations, but for a smaller and more selective set of cases.

Scope and interpretation.

This subsection reports a descriptive plausibility check of global feature profiles. It is intended to contextualize model behavior by comparing aggregated explanation summaries with risk factors reported in prior literature. This is not a clinical validation analysis: no clinician-led review, external validation, causal assessment, or subgroup analysis was conducted. Accordingly, the results should be interpreted as descriptive face-validity evidence only, not as evidence of clinical utility, clinical significance, or medical decision validity.

To contextualize model behavior, we examined global feature-importance outputs from EBM, SHAP, and TabNet across the four healthcare tabular datasets. For the RF focal explainee, we also compared conventional RF global importances, permutation importance (PFI) and Gini/MDI, with the corresponding global explanation summaries as a descriptive cross-check of top-ranked signals (see S1 Appendix, Figs 3–10). Below, we summarize the main feature groups highlighted by each method and relate them cautiously to prior clinical literature.

PDHS (C-section) dataset.

EBM: Key features include Births in the last five years & Had Previous C-section, Had Previous C-section, Number of household members & Mothers BMI, and Age of Mother & Number of ANC Visits.

SHAP: Important features highlighted are Had Previous C-section, Suffered by Domestic Violence, Number of ANC Visits, and Type of place of residence.

TabNet: Significant features identified are Births in the last five years, Reading Newspaper or Magazine, Had Previous C-section, and Household Toilet Facility.

RF baseline (tree importances): The RF summaries place Had Previous C-section among the dominant signals, with Number of ANC Visits and maternal-demographic factors also appearing prominently. This broadly overlaps with the EBM and SHAP summaries, while SHAP also assigns high importance to Domestic Violence, a socio-behavioural variable not always ranked at the top by RF split-based summaries (S1 Appendix, RF: Fig 3; SHAP/EBM/TabNet: Fig 4).

These features are qualitatively consistent with factors reported in maternal health research. For instance, prior C-sections and antenatal care have been associated with surgical delivery outcomes, while domestic violence and household conditions reflect broader socioeconomic risks [25,51,52].

Diabetes retinopathy dataset.

EBM, SHAP, TabNet: EBM, SHAP, and TabNet all highlight variants of ma (microaneurysms) and ex (exudates) features, such as ma0.5, ex0.5, and exm1, among the dominant signals.

RF baseline (tree importances):.

RF PFI and Gini/MDI also highlight lesion-related features, including microaneurysms (ma*) and exudates (ex*), as important signals. This provides a descriptive cross-check against the SHAP/EBM/TabNet summaries, which similarly emphasize retinal lesion features (S1 Appendix, RF: Fig 5; SHAP/EBM/TabNet: Fig 6).

This pattern is consistent with prior literature on diabetes retinopathy, where microaneurysms and retinal exudates are reported as important diagnostic indicators [53,54].

Breast cancer dataset.

EBM, SHAP, TabNet: EBM, SHAP, and TabNet highlight geometric and morphological features, including Mean/Worst concave points, Texture, Area, and Perimeter.

RF baseline (tree importances): RF importances (PFI and Gini/MDI) surface geometric/morphological variables, concave points (mean/worst), area, perimeter, and texture-related measures, consistent with EBM/SHAP rankings. This overlap with morphology-related variables provides descriptive face-validity for the global signals (S1 Appendix, RF: Fig 7; SHAP/EBM/TabNet: Fig 8).

These features are consistent with breast cancer literature on malignancy-related morphology, including concavity, area, perimeter, and texture measures [55,56].

ESDRPD dataset.

EBM, SHAP, TabNet: EBM, SHAP, and TabNet highlight symptom-related features such as Polyuria, Polydipsia, Gender, and Partial paresis, with TabNet additionally emphasizing features such as Muscle stiffness and Sudden weight loss.

RF baseline (tree importances): RF PFI and Gini/MDI also rank classic symptom variables, including Polyuria, Polydipsia, Gender, and Partial paresis, among the leading contributors, with occasional emphasis on related neurological or metabolic features. This provides a descriptive cross-check against the symptom profile highlighted by the global explanation summaries (S1 Appendix, RF: Fig 9; SHAP/EBM/TabNet: Fig 10).

These symptoms are consistent with prior literature on early diabetes indicators and diabetes-related complications [57–59].

Overall, the global explanation summaries from EBM, SHAP, TabNet, and RF importances provide descriptive numerical context for model behavior. In several cases, different methods highlight broadly similar feature groups; in others, they emphasize distinct signals. Such convergence and divergence should be interpreted as exploratory evidence for further investigation, not as validated clinical findings. The qualitative consistency with previously reported risk factors supports a face-validity or plausibility interpretation, but does not establish clinical validity, causal relevance, subgroup generalisability, or usefulness in medical decision-making. Figures supporting these descriptive analyses are presented in the S1 Appendix (see Figs 3–10).

Fidelity.

SHAP obtained score fidelity of 1.000 across all datasets (Table 5). This reflects the expected exact additive reconstruction property of TreeSHAP for tree ensembles, rather than an empirical superiority finding over surrogate-based methods. In contrast, LIME’s fidelity reflects the approximation quality of its local surrogate model, which can vary across instances and datasets.

Simplicity.

The simplicity results describe explanation compactness across method–predictor configurations rather than a strict ranking of methods under a common predictive function. TabNet produced compact native explanations in several settings, particularly at lower thresholds (0.01 and 0.05), but these results should be interpreted alongside its dataset-specific predictive performance. LIME produced compact RF-based local explanations in some settings and often saturated at a fixed number of selected features once the threshold constraint became binding. SHAP explanations were generally denser, while EBM produced more feature-rich native explanations (Table 6). Among rule-based explanations, Anchors produced short rules in several datasets (Table 9), but rule length varied substantially across instances and coverage remained limited at higher precision thresholds.

Consistency.

LIME and SHAP showed the highest pairwise rank agreement across datasets, although the magnitude of agreement was dataset-dependent. Agreement was strongest for ESDRPD and PDHS, but weaker for Breast cancer and Diabetes retinopathy (Table 7). Comparisons involving TabNet were consistently negative, reflecting divergence between RF-based post-hoc rankings and native TabNet rankings. These findings suggest that inter-explainer consistency is useful as a diagnostic measure of rank alignment, but should not be interpreted as evidence of explanation correctness.

Robustness.

Robustness scores should be interpreted as numerical sensitivity measures under the fixed perturbation protocol and in relation to the underlying predictor. EBM and TabNet showed low perturbation sensitivity in their native explanation configurations, whereas SHAP and LIME were evaluated on the selected RF focal predictor (Table 8). For RF-based explanations, SHAP generally showed lower sensitivity than LIME, while LIME exhibited larger variability across instances. Anchors also showed non-trivial sensitivity under perturbation (Table 9), with robustness varying across datasets and thresholds. These results support the usefulness of robustness as a comparative stress test for explanation stability, but not as a model-independent or clinically validated ranking of explanation methods.

Fig 2 demonstrates this instability using two LIME explanations for the same ESDRPD instance, once with the original input and once with a minor perturbation. While the predicted class remains the same, the explanations shift significantly in content and magnitude. This perturbation was applied by adding small Gaussian noise () to the original input instance, as described in the Materials and methods section under Robustness. The example therefore illustrates local explanation instability under the benchmark perturbation protocol, rather than instability under clinically realistic patient change.

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Fig 2. Original and perturbed LIME explanations for an ESDRPD instance.

(A) Original LIME explanation. (B) LIME explanation after element-wise Gaussian jitter, , applied to the numerically encoded input representation with no model refitting.

https://doi.org/10.1371/journal.pone.0351473.g002

In parallel, Anchors generated different rule sets for the same instance under noise:

• Original Anchor Rule: AND AND AND Gender > 0.00 AND Itching > 0.00
• Noisy Anchor Rule: Polydipsia > 0.00 AND Irritability > 0.00 AND AND Age > 58.00

These results show that post-hoc explainers relying on local sampling (LIME) or greedy rule induction (Anchors) can be fragile under perturbation, especially in datasets with closely correlated features or small decision boundaries.

Precision and coverage.

Anchors excelled in producing precise rules with interpretable conditions, making it valuable in applications like subgroup-style model auditing. However, the cost of this precision is low coverage, limiting its utility for broad model auditing (Table 9). Reporting mean ± standard deviation clarifies that these behaviors are systematic rather than driven by a few outliers: precision shows relatively small variability once a threshold is fixed, whereas coverage is consistently low (and only modestly variable), especially in Diabetes retinopathy. Rule complexity (simplicity) exhibits large instance-level dispersion in some datasets (e.g., PDHS and Diabetes retinopathy), indicating that some instances can be captured by compact rules while others require substantially longer rules to meet the same precision threshold. Robustness also shows moderate variability, suggesting heterogeneous stability under perturbations across instances. This trade-off should be considered when using Anchors for local model auditing or subgroup-style interpretation in healthcare tabular settings.

Triangulation with traditional tree importances.

Across datasets, RF PFI and Gini/MDI broadly corroborate the global signals surfaced by SHAP/EBM/TabNet: (i) PDHS (C-section), strong emphasis on Had Previous C-section with ANC visits/maternal-demographic factors also high; SHAP further lifts socio-behavioral risk (Domestic Violence). (ii) Diabetes retinopathy, lesion markers (ma*, ex*) dominate across RF and SHAP/EBM. (iii) Breast cancer, geometric/morphological variables (concave points, area, perimeter, texture) agree across methods. (iv) ESDRPD, classic symptoms (Polyuria, Polydipsia, Gender, Partial paresis) align. Where differences arise, they are typically in the ordering of secondary factors rather than complete disagreement, and may reflect known properties of impurity-based scores, such as bias toward high-cardinality splits, or permutation effects under correlated features. This descriptive cross-check contextualizes the global patterns while reinforcing the need for local metrics such as fidelity and robustness.

Clinical relevance and scope of global explanations.

The global explanation summaries discussed above (e.g., aggregated SHAP importances, EBM main-effect functions, and TabNet attention profiles) are intended as descriptive, numerical context rather than as statistically grounded feature selection, causal analysis, or clinical validation. Their role is to summarize model behavior and to support a qualitative alignment check against well-established risk factors reported in the clinical literature. No clinician-led qualitative review was conducted, and we do not claim clinical significance or medical decision validity based on these results alone. Clinician-in-the-loop validation is outside the scope of this methodological study and is identified as a direction for future work. These summaries should therefore be interpreted as interpretability-oriented diagnostics that complement, rather than replace, domain-expert evaluation.

Human-centred evaluation.

We assess explanation quality via quantitative, reproducible proxies, including fidelity, simplicity, inter-explainer consistency, robustness, and precision–coverage evaluated across datasets. Direct human-centred evaluation (e.g., clinician task accuracy, completion time, error rate, SUS/NASA–TLX, perceived trust or appropriateness) is beyond the scope of this study and planned as future work with domain experts. Direct clinician involvement in reviewing explanation outputs and assessing medical plausibility was not part of this study and is identified as a necessary direction for future work.

Scope of coverage.

Our emphasis is on a principled evaluation framework and transparent operationalization of quantitative XAI metrics, not exhaustiveness over explainer families. Metrics are reported only where theoretically appropriate to each explainer’s output type (e.g., rank-based consistency for per-instance attribution vectors; precision/coverage for rule sets). This policy avoids cross-paradigm conflation and supports reuse; future extensions can broaden method families under the same protocol.

Design choices.

Our post-hoc comparison is performed on a single focal predictor selected after benchmarking via a pre-specified average-rank rule (F1 primary; accuracy tie-breaker). This design controls model-induced variance so that differences among LIME, SHAP, and Anchors are attributable to the explainer rather than to changes in the underlying decision function. The selected RF model is not the best-performing classifier on every dataset, including Diabetes retinopathy; therefore, the post-hoc findings should be interpreted as conditional on this focal explainee rather than as model-invariant explainer behavior. Replicating the protocol across alternative top-ranked predictors such as XGB or GBC would be valuable for studying explainer–model interactions, but introduces an additional experimental axis beyond the present study boundary. EBM and TabNet are assessed via their inherent interpretability and should therefore be understood as native interpretable model configurations, not as explanations of the RF decision function. We also avoid extensive per-dataset hyperparameter tuning (fixed seeds; library defaults) to reduce confounding variability in explanation metrics. While this may affect absolute predictive scores, it improves comparability and reproducibility of explainer results.

Global tree importances.

PFI and Gini/MDI are global summaries: they aid triangulation but neither guarantee local agreement with the model nor immunity to known biases (e.g., impurity-based bias toward high-cardinality features; permutation underestimation/instability with collinear predictors or leakage). Their sensitivity to data distribution and feature correlation further motivates our use of local, instance-level metrics (fidelity, robustness) for post-hoc explainers.

Perturbation model (robustness).

Robustness was quantified using small, zero-mean, element-wise Gaussian perturbations as a method-agnostic numerical sensitivity probe. This design supports controlled comparison across explainers and datasets, but it does not model clinically plausible or physiologically meaningful patient variation. Because the perturbation is applied to numerically encoded inputs, it does not preserve categorical levels, ordinal constraints, feature codebooks, or valid biomarker ranges. The robustness scores should therefore be interpreted as explanation sensitivity under a fixed computational stress test. Future work should complement this generic perturbation scheme with domain-calibrated perturbations that preserve categorical levels, respect feature ranges, and use biomarker- or codebook-aware variation.

Method breadth.

We study widely used representatives, post-hoc feature-attribution methods (SHAP, LIME), a rule-based local explainer (Anchors), and inherently interpretable models (EBM, TabNet), rather than an exhaustive catalog. Other rule-list/decision-set learners and glass-box variants could be included; our open code is structured to accommodate such extensions.

Metric scope.

The reported metrics are computed deterministically on a fixed test set, and the study is designed for descriptive, instance-level comparison rather than population inference. Accordingly, we report dispersion via standard deviation to characterize variability and potential failure modes across patients.

We consolidate and operationalize commonly cited quantitative metrics (fidelity, simplicity, consistency, robustness, and precision/coverage for rule-based explanations). These do not exhaust all meaningful criteria (e.g., human-centered measures such as usefulness or actionability), and some metrics are family-specific by design (e.g., precision/coverage for rules; rank-based consistency for single-feature attribution lists). Where relevant, partial sensitivity is reported directly in the results (e.g., multiple simplicity thresholds and Anchor precision levels), while broader sensitivity analyses are deferred to future work.

Future work.

Future research should: (i) extend the benchmark to temporal and multimodal clinical datasets; (ii) run clinician-in-the-loop studies to assess perceived usefulness and cognitive effort; (iii) integrate additional explainer families, especially counterfactual and example-based methods, with appropriate, family-specific metrics (e.g., plausibility, feasibility, actionability); (iv) replicate the post-hoc analysis on alternative top-ranked predictors (e.g., boosted trees or a neural tabular model) to probe explainer–model interactions and assess cross-model generalizability; (v) harmonize evaluation between inherent and post-hoc explanations (e.g., restricting EBM consistency to main-effect functions or developing interaction-aware consistency measures); (vi) systematically characterize RF–SHAP divergence under controlled feature correlation and cardinality settings to identify regimes where traditional tree importances deviate most from TreeSHAP-based local additive attributions; and (vii) develop domain-calibrated perturbation schemes for robustness (biomarker- and codebook-aware ranges) and compare them to generic Gaussian jitter to assess clinical impact.