2.1 Machine-learning life-expectancy prediction

The average life expectancy is the basic summary indicator of the health of a population [1,13]. Traditional actuarial methods based on Gompertz or Weibull distributions frequently fail when modelling heterogeneous multi-country panels due to too strong assumptions about proportional hazards and linearity of effects [13]. Contemporary studies prove that tree-based algorithms work better: Shakeelahamad et al. achieved adjusted R² = 0.9729 using XGBoost on WHO data [14], whereas Ozsahin et al. obtained RMSE = 1.8778 and R² = 0.9504 using LightGBM on a global benchmark [12]. Still, the existing research is mostly limited to single models with minor feature engineering and no uncertainty calibration.

2.2 Gradient-boosted ensembles and stacking

XGBoost and LightGBM are dominating approaches in tabular regression due to effective capturing of non-linear relations [4,5]. Stacked generalization decreases single-model variance via learning of a meta-model based on out-of-fold predictions of a variety of base learners [6,15,16]. Ideally, the ensemble error decreases proportionally to diversity increase, but this advantage becomes irrelevant with the correlation between base learners. In life-expectancy prediction, the existing ensemble frameworks increase accuracy, but none of them combines OOF diversity, meta-features of higher order, and residual correction.

2.3 Feature engineering and SHAP-based expansion

Feature engineering plays an important role in tabular health prediction [8]. Domain-specific features, LOO-encoding, PCA/K-means latent features, and polynomial interactions can enhance performance, but exhaustive polynomial expansion leads to multicollinearity problems. Stable SHAP provides feature importance in the case of correlated data [7], which makes it suitable for targeted interaction selection. The recent studies confirm that preprocessing impacts on SHAP magnitudes greatly [17,18]. However, there are no existing life-expectancy frameworks using SHAP-based selective polynomial expansion as an enrichment technique before stacking.

2.4 Interpretability in health prediction

Interpretability is recognized as an indispensable attribute of modern clinical AI [3]. TreeSHAP allows getting exact and efficient feature attributions for tree-based models, and PDPs help to discover marginal effects [7,8]. While prior life-expectancy studies usually stop at ranking of the most important features, they don’t aggregate explanations in terms of WHO-aligned policy domains (Demography, Nutrition, Infrastructure, etc.), which significantly limits the value of the model for the policy design [1,19].

2.5 Conformal prediction and uncertainty quantification

Uncertainty quantification is often ignored in health prediction [3]. Split-conformal prediction provides a way to construct distribution-free prediction intervals of finite sample size [9,10]. It is practically feasible and widely applicable approach, including for healthcare [20]. Nevertheless, the existing life-expectancy models only return the point estimate.

2.6 Residual correction and two-stage prediction

Gradient-boosted ensembles suffer from systematic tail bias in particular for imbalanced targets [4]. Residual correction in two-stage pipelines helps to deal with this problem by means of learning residuals with the second model. It frequently improves the RMSE in forecasting tasks [5]. LightGBM is especially appropriate as a residual corrector due to its leaf-wise growth and regularization. There is no life-expectancy framework containing the residual correction phase.

2.7 Consolidated research gaps

The six gaps that drive NEXUS-LE are summarized in Table 1. They are related to the lack of diversified stacking, SHAP-guided feature selection, meta-manifold structure, residual correction, explainability at the policy level, and conformal uncertainty intervals, respectively.

Collectively, these gaps define the methodological space occupied by NEXUS-LE. The proposed framework integrates SHAP-guided stacking, residual correction, conformal uncertainty quantification, and policy-level explainability into a single pipeline, extending prior life-expectancy prediction work beyond point estimation alone.

Algorithm 1 NEXUS-LE: Neuro-Symbolic Explainable Unified Stacking for Life Expectancy Prediction.

Require: Dataset ; target ; hyperparameters per Table 4.

Ensure: Trained NEXUS-LE pipeline ; conformal intervals at per Eq. (17).

  Phase 1 — Preprocessing & Feature Engineering

1: Detect via case-insensitive column matching.

2: Apply LOO encoding (1) to Country; ordinally encode remaining categoricals.

3: Engineer domain interactions per Eqs. (2)–(5).

4: for each with do

5:   [56 features]

6: end for

7: Drop near-constant columns; impute via KNN (k = 5).

8:  Append n=5 PCA + k=8 K-Means labels. [210 features total]

   Phase 2 — SHAP-Guided Polynomial Expansion

9:  Fit RF warm-up on ; rank by (7); select (top-N = 30).

10: Expand , d=2; form (8). [675 features]

    Phase 3 — Partitioning & Scaling

11: Split per Eq. (9); fit and apply RobustScaler on .

    Phase 4 — Multi-Level Stacking (NEXUS Core)

12: (10); .

13: for k = 1 to K₁ = 6 do

14:  for each do

15:   Train m on fold-k; store OOF in .

16:  end for

17: end for

18: Augment (11) via statistics, T-SVD, pairwise products.

19: (12); .

20: for k = 1 to K₂ = 5 do

21:  for each do

22:   Train m on fold-k of ; store OOF in .

23:  end for

24: end for

25: Form (13); train f_fusion .

26: Refit all , , f_fusion on complete .

   Phase 5 — Split-Conformal Calibration

27: Compute (14) on .

28: for each do

29:  Estimate (15); form (16).

30: end for

    Phase 6 — Residual Correction

31: Compute (18); train f_res on (19).

32: Return per Eq. (20) for .

    Phase 7 — Evaluation & XAI

33: Evaluate on : R², RMSE, MAE, MAPE, SMAPE; ablation A1–A4 (Table 9).

34: Compute global/local TreeSHAP, PDPs, policy-group importances.

3.1 Phase 1: Advanced preprocessing and feature engineering

The unified dataset [21] exhibits three structural challenges that motivate the preprocessing design: (i) 9.8% missingness across 150 heterogeneous features, (ii) 56 heavily right-skewed epidemiological indicators, and (iii) high-cardinality nominal variables (e.g., unique country codes) [22]. The following four steps address each challenge systematically.

3.1.1 Target auto-detection and leakage prevention.

The target column is identified via a case-insensitive regular-expression match on the column headers of , ensuring robustness to naming inconsistencies across the merged sub-datasets. High-cardinality nominal features (specifically Country) are encoded with Leave-One-Out (LOO) target encoding [23], which computes the conditional expectation of using only the observations outside the current row, preventing any form of target leakage:

(1)

All remaining categorical features are ordinally encoded; time-correlated and status identifiers (Year, Status) are dropped prior to model ingestion to prevent temporal leakage [24].

Data leakage was avoided through three safeguards: (i) Leave-One-Out encoding for the country variable was computed only within the training fold and never using the corresponding validation sample; (ii) all base-learner and meta-learner predictions were generated strictly using out-of-fold (OOF) procedures, ensuring that each sample’s meta-features were produced by models that had not seen that sample during training; and (iii) the calibration set used for split-conformal prediction was fully isolated from model fitting and used only for quantile estimation.

3.1.2 Domain-specific feature interactions.

As established in the global health literature [1,13], life expectancy is governed by ratios and multiplicative synergies among socioeconomic and clinical predictors rather than their individual magnitudes. Six mechanistic interaction features are therefore constructed deterministically from the raw columns:

(2)(3)(4)(5)

These features directly encode the epidemiological determinants catalogued in the WHO Global Health Observatory [1] and the GBD study [13].

3.1.3 Skewness mitigation.

For each numerical feature whose sample skewness exceeds the threshold , the variance-stabilising transformation

(6)

is applied. This transformation was triggered for 56 of 150 columns—including maternal mortality ratio, tuberculosis incidence, and infant mortality rate—and is consistent with standard practice for heavy-tailed public health indicators [5,8].

3.2 Phase 2: SHAP-guided polynomial feature expansion

Applying degree-2 polynomial expansion to all 210 features would yield terms, inducing severe multicollinearity and memory infeasibility. NEXUS-LE addresses this by using explainability scores to identify the N = 30 most predictively relevant features before expansion, a strategy directly motivated by the interpretability-first design principles discussed in Section 2.

3.2.1 Warm-up surrogate and TreeSHAP ranking.

A lightweight Random Forest regressor (T = 80, , ) is fitted on a stratified subsample of 6,000 rows. TreeSHAP attributions are computed over a 400-sample evaluation subset, and features are ranked by global mean absolute importance:

(7)

where is the SHAP value of feature j for sample i. The top-N = 30 features selected by Eq. (7) span a clinically interpretable spectrum including: country-level LOO encoding, PCA_Comp1, maternal and neonatal mortality rates, cardiovascular death burden, birth rate, universal health coverage, and environmental pollution indices. As reported in Section 4, these 30 features account for > 95% of cumulative SHAP importance, validating the selection threshold.

3.2.2 Degree-2 polynomial augmentation.

Degree-d = 2 polynomial and pairwise interaction terms are generated over using PolynomialFeatures, producing 465 additional non-linear terms. The augmented feature matrix is formed as:

(8)

3.3 Phase 3: Data partitioning and robust scaling

To ensure strict statistical independence between the stacking ensemble, the conformal calibrator, and the final evaluator, is partitioned into three non-overlapping subsets:

(9)

The calibration split is deliberately withheld from all training phases and is consumed solely by the conformal calibration procedure in Section 3.5, which is a requirement for the marginal coverage guarantee to hold. A RobustScaler is fitted exclusively on and subsequently applied to and ; its inter-quartile range normalisation renders the scaling insensitive to the extreme outliers documented for several low-income country indicators in the dataset.

3.4 Phase 4: Multi-level stacking ensemble

The predictive core of NEXUS-LE is a three-level stacking hierarchy that extends the classical stacked generalisation framework with an intermediate meta-manifold augmentation step.

3.4.1 Level 1: Base learner out-of-fold generation.

Three heterogeneous gradient-boosted base learners form :

(10)

XGBoost and LightGBM instances are diversified through differing random seeds, subsample rates (), and column-sample ratios (), which has been shown to maximise ensemble diversity without sacrificing individual model fidelity. Early stopping with a patience of 50 rounds is applied per fold to prevent overfitting. For each fold , model is trained on the in-fold complement and its out-of-fold predictions are written to , yielding structurally leak-free meta-features. The mean fold-level OOF ensemble R² was (range: 0.9865–0.9877), confirming stable convergence across folds.

3.4.2 Meta-manifold augmentation.

Passing directly to the next level discards information about the geometry of the base learner agreement space. NEXUS-LE introduces three complementary augmentations that enrich the 3-dimensional OOF space into a 17-dimensional meta-manifold:

1. (a) Row-wise summary statistics. Five statistics are computed per instance: , which serve as soft proxies for uncertainty by measuring the degree of inter-model agreement.
2. (b) Truncated SVD latents. Truncated SVD [27] with r = 2 components extracts the dominant low-rank structure from , capturing systematic co-variation patterns across the three base learners that are not directly visible in the raw predictions.
3. (c) Pairwise interaction products. The pairwise products , , are appended to encode multiplicative synergies between models.

The consolidated augmented meta-matrix is:

(11)

where , , and denote the statistics, SVD latents, and pairwise products respectively.

3.4.3 Level 2: Meta-learner out-of-fold generation.

Three structurally diverse meta-learners

(12)

are trained on using K₂ = 5-fold cross-validation, yielding with a mean OOF R² of 0.9867. The Huber regressor [28] ( by default) is included as a robustness backstop: its -insensitivity to outlying OOF values ensures that extreme fold-level prediction errors do not propagate into the Level-3 fusion input.

3.4.4 Level 3: Fusion meta-learner and full-data refit.

An XGBoost fusion model f_fusion (T = 800, , , ) is trained on the concatenated Level-2 representation:

(13)

with early stopping (patience = 50 rounds) yielding a best iteration of 206 and a training R² of 0.9879. This three-level design explicitly separates the roles of feature-space modelling (L1), meta-feature learning (L2), and final arbitration (L3), with each level systematically reducing residual variance. Following the OOF protocol, all , , and f_fusion are subsequently refitted on the complete to maximise the effective training signal for test-time inference.

3.5 Phase 5: Split-conformal prediction calibration

Reliable uncertainty quantification is indispensable for public health policy applications in which a point prediction without error bounds provides insufficient basis for decision-making. NEXUS-LE adopts the split-conformal inference framework, which provides distribution-free, marginal coverage guarantees without any Gaussian or parametric assumption on the residuals.

Non-conformity scores are computed on the withheld calibration split using the fitted ensemble:

(14)

For each significance level , the finite-sample–corrected empirical quantile is:

(15)

and the marginally valid prediction interval for a new sample is:

(16)

Formal Coverage Guarantee. Under the assumption of exchangeability of , the set satisfies:

(17)

Empirical validation on yielded years and years, with empirical coverages of 95.04% and 90.05% at the 95% and 90% nominal levels respectively—confirming that the theoretical guarantees of Eq. (17) hold in practice.

3.6 Phase 6: Residual correction layer

Even a well-calibrated ensemble retains structured systematic bias arising from the inductive limitations of gradient-boosted trees in specific sub-regions of the feature space—in particular, extreme low or high life-expectancy populations that are statistically under-represented in . NEXUS-LE introduces a dedicated residual correction layer, inspired by two-stage boosting residual fitting, as a safety net against these tail-region errors.

3.6.1 Residual isolation.

Training residuals of the fusion model are isolated as:

(18)

Empirical analysis of on revealed a near-zero mean (), standard deviation years, but maximum absolute error of 10.63 years, confirming the presence of non-random tail-region bias that a point ensemble cannot self-correct.

3.6.2 LightGBM corrector.

A LightGBM corrector f_res is trained on the extended stacked input:

(19)

with as the regression target. Appending both the Level-1 OOF predictions and the fusion output allows f_res to condition on the ensemble’s own residual uncertainty structure, facilitating targeted correction in high-error sub-populations.

3.6.3 Final inference equation.

For any unseen sample x^*, the final prediction is:

(20)

The residual correction reduced test-set RMSE from 1.0842 to 1.0665 years and improved R² from 0.9874 to 0.9878; the full ablation breakdown is reported in Table 9.

3.7 Phase 7: Evaluation protocol and explainability

4.1 Predictive performance: Benchmark against base learners

NEXUS-LE is benchmarked against its three constituent base learners—XGB-A, XGB-B, and LGBM-A—on the held-out test set (n = 3,308), which was never accessed during any training or calibration phase (Eq. (9)). Table 5 reports all metrics with absolute gains of NEXUS-LE over each baseline. Bold: best value per metric. rows report NEXUS-LE minus each baseline (negative = improvement for error metrics). SMAPE computed as . Fig 2 provides a four-panel diagnostic panel and (Top-left) R² bar chart; dashed green line marks the pre-specified target R² = 0.98. (Top-right) Actual vs. predicted scatter (R² = 0.9878); red dashed line = perfect fit. (Bottom-left) Residual histogram (, yr), confirming near-zero directional bias. (Bottom-right) 90% conformal prediction intervals on 80 sorted samples (empirical coverage = 89.9%; Table 12). Three principal findings emerge from the benchmark. Fig 3 visualises the metric-level comparison across all four systems.

1. (i) NEXUS-LE meets the pre-specified accuracy target. NEXUS-LE achieves and RMSE years, surpassing the R² > 0.98 threshold established. Against the weakest base learner (LGBM-A), the ensemble reduces RMSE by 0.0401 years (–3.6%), MAE by 0.0526 years (–7.8%), and MAPE by 0.0679 pp (–6.8%), confirming the variance-reduction benefit of hierarchical stacking over any individual learner.
2. (ii) XGB-B MAE/MAPE advantage is sub-threshold and metric-specific. XGB-B records marginally lower MAE (0.6151 vs. 0.6185, yr) and MAPE (0.9126% vs. 0.9239%, pp) than NEXUS-LE. Both differences lie within the Monte Carlo RMSE noise floor of years at n = 3,308, making them statistically indistinguishable. Mechanistically, XGB-B’s marginal median-error advantage reflects its single-model regularisation structure biasing predictions toward the central tendency, whereas NEXUS-LE optimises for squared-error reduction across the full range [24.83, 87.75] years—the more consequential objective for population-level life-expectancy projections used in health-policy planning.
3. (iii) Residual diagnostics confirm absence of systematic bias. The actual-versus-predicted scatter (Fig 2, top-right) exhibits tight alignment with the identity line across the complete target range, with marginal spread only at the distribution extremes—a known characteristic of gradient-boosted ensembles on class-imbalanced tails. The residual histogram (bottom-left) has near-zero mean ( yr) and standard deviation yr, providing no evidence of directional bias; the near-symmetric distribution satisfies the unbiasedness condition implicit in the conformal non-conformity score construction of Eq. (14). Conformal interval performance is reported separately in Section 4.5.

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Table 5. Test-set performance on (n = 3,308).

https://doi.org/10.1371/journal.pone.0353849.t005

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Fig 2. NEXUS-LE test-set diagnostic panel (, n = 3,308).

https://doi.org/10.1371/journal.pone.0353849.g002

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Fig 3. Per-metric bar comparison across NEXUS-LE, XGB-B, XGB-A, and LGBM-A on .

https://doi.org/10.1371/journal.pone.0353849.g003

4.2 Robustness analysis and overfitting investigation

To investigate the possibility of overfitting and to provide stronger evidence of generalisation, we conducted three complementary analyses, each addressing a distinct dimension of robustness.

4.2.2 Leave-region-out validation.

To assess geographic generalizability beyond standard random partitioning, we performed a leave-region-out (LRO) validation experiment in which NEXUS-LE was retrained six times, each time withholding one entire WHO region from the training set and evaluating on the withheld region. The results are summarised in Table 6. The framework generalises robustly across all six WHO regions, with R² values ranging from 0.961 to 0.976 and RMSE values ranging from 1.09 to 1.41 years. Specifically, for Africa, the model achieved R² = 0.961 and RMSE = 1.41 yr; for the Americas, R² = 0.974 and RMSE = 1.18 yr; for South-East Asia, R² = 0.969 and RMSE = 1.22 yr; for Europe, R² = 0.971 and RMSE = 1.14 yr; for the Eastern Mediterranean, R² = 0.963 and RMSE = 1.38 yr; and for the Western Pacific, R² = 0.976 and RMSE = 1.09 yr, yielding mean values of R² = 0.969 and RMSE = 1.24 yr across all six regions. These consistent results across geographically and epidemiologically distinct populations confirm that NEXUS-LE is not overfitted to any particular regional health profile and retains strong predictive capability when evaluated on entirely unseen geographic regions.

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Table 6. Leave-region-out (LRO) validation results. Bold values denote the best and mean performance across all regions.

https://doi.org/10.1371/journal.pone.0353849.t006

4.3 Generalization analysis

Random partitioning is not enough to justify the generalizability of the developed model based on longitudinal country-level health data due to possible high temporal and geographical correlation. This problem has been solved by conducting three additional validations including leave-region-out validation, temporal generalization testing, and external validation.

1. (a) Leave-Region-Out Validation. In order to test for geographical generalization of the developed model beyond random partitioning, NEXUS-LE was retrained six times, every time leaving out one complete WHO region and testing on the held-out region. As shown in Table 6, the framework generalizes successfully across geographically and epidemiologically heterogeneous population, resulting in and ,yr for all six WHO regions. On average, leave-region-out performance of R² = 0.969 and RMSE = 1.24,yr shows that NEXUS-LE is not overfitting to any specific regional health characteristics and can generalize effectively when tested on completely unseen geographical population.
2. (b) Temporal Generalization. In order to evaluate the robustness to the temporal distribution shift, the model was trained only on data ranging from 2000 to 2018 and tested on data from the subsequent 2019−2021 period. Such evaluation includes prediction of the effect of the significant global life expectancy perturbation caused by the COVID-19 pandemic—the drop by 1.8 years reported by the WHO in its 2024 World Health Statistics. The results of such challenging out-of-period testing show R² = 0.958 and RMSE = 1.39,yr, indicating that the framework is not relying on the temporal interpolation within the training period and is predictively stable despite the unprecedented global health shock. These results are reported in Table 7.
3. (c) Independent External Dataset Validation. For the purpose of obtaining truly external validation, the model NEXUS-LE was tested on the Health Nutrition and Population (HNP) Statistics dataset by the World Bank containing data for 189 countries in the period 2000–2021. The dataset had been prepared independently and had not been used in any phase of the models development. On that independent test dataset, NEXUS-LE gave R² = 0.952 and ,yr, reported in Table 8. These results confirm that the framework transfers to an independently collected dataset without retraining and supports its potential for broader deployment in international health analytics.

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Table 7. Temporal generalization results.

https://doi.org/10.1371/journal.pone.0353849.t007

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Table 8. Independent external dataset validation results (Table 13).

https://doi.org/10.1371/journal.pone.0353849.t008

4.4 Ablation study

To isolate the contribution of each architectural component, we evaluated four progressively enriched configurations on under identical preprocessing (Algorithm 1, Phases 1 and 3), data partition (Eq. (9)), and random seed (). The first configuration, A1, is a single XGBoost model (T = 1000, ) trained on the 210 domain-engineered features and serves as the feature-only baseline. The second, A2, applies the same single XGBoost learner to the SHAP-guided degree-2 augmented matrix (Eq. (8)), thereby isolating the effect of explicit polynomial expansion in a single-model setting. The third, A3, replaces the single learner with the three-model Level-1 out-of-fold ensemble (Eq. (10)) and uses simple mean aggregation, but excludes the meta-manifold, Level-2 learners, and residual corrector. Finally, A4 is the complete NEXUS-LE pipeline (Algorithm 1), including the meta-manifold (Eq. (11)), the Level-2 ensemble (Eq. (12)), the fusion model f_fusion (Eq. (13)), and the residual corrector f_res (Eq. (20)).

In addition to these four configurations, we introduced two targeted ablations regarding the country-level encoding and the modest incremental gain over the baseline. Specifically, we evaluated an ordinal-encoding variant, denoted , in which the Leave-One-Out encoding for country identifiers was replaced with ordinal encoding to test whether the reported improvement could be attributed to leakage-like effects. We also report a lightweight practical variant, A3, because it captures most of the performance gain at substantially lower computational cost than the full pipeline. These additions allow us to disentangle genuine heterogeneity-driven gains from possible inflation due to encoding choices, while also clarifying the trade-off between accuracy and deployment cost. A1–A4 progressively add architectural components; replaces Leave-One-Out encoding with ordinal encoding. rows report differences relative to A4 (negative values indicate improvement for error metrics). Bold denotes the best value per metric.

Finding 1 — Polynomial expansion is a penalty on single-model learners (A1 vs. A2).

Adding 465 degree-2 polynomial terms (Phase 2) to the single XGBoost model leads to degradation in the prediction quality in the sense of increased RMSE and lower R². It shows that in the single-model scenario, extra interactions bring additional collinear features that cannot be effectively regularized by the axis-aligned tree splits. Hence, the utility of the enrichment is revealed only after stacking, where the high-level learners can utilize the enriched features space without inheriting the full burden of collinearity.

Finding 2 — Diverse ensembles achieve the greatest error reduction (A2 vs. A3).

Switching from the single learner to the three models Level-1 out-of-fold ensemble brings the biggest reduction in error metrics, especially in MAE and MAPE. It demonstrates that diversity of base learners is the key ingredient responsible for the boost in performance of NEXUS-LE. The heterogeneous setup of due to various depths, learning rates and sampling schemes diminishes the correlation between the models and enhances generalization ability.

Finding 3 — Meta-manifold and residual correction stage bring additional gains (A3 vs. A4).

The NEXUS-LE procedure provides an extra increase in RMSE, MAE and MAPE when applied to the Level-1 ensemble. Though these improvements are not large in magnitude, but still significant and consistent across all metrics. Hence, each component of NEXUS-LE: meta-manifold, fusion stage and residual correction stage contributes complementary improvement to the model. The latter is particularly justified by the presence of the structured tail bias in the Level-1 ensemble residuals.

Finding 4 — Contextualizing the A1 RMSE anomaly.

A1 exhibits the lowest RMSE value, which should be carefully interpreted. The difference from A4 is negligible and lies below the noise level predicted based on the number of observations in the test set. Also, the MAE and MAPE values of A1 are clearly worse than those of A4. Moreover, A1 provides no OOF stacking, no calibrated uncertainty estimates and no post-processing step for interpretability layer. Therefore, NEXUS-LE should be considered better in view of the combination of accuracy, uncertainty and interpretability.

Finding 5 — LOO encoding indeed brings heterogeneity signal.

The ordinal encoding variant demonstrates a slightly higher RMSE, MAE and MAPE compared to the full model. This proves the hypothesis that Leave-One-Out encoding brings heterogeneity signal instead of inflating the accuracy using the target leakage. The results on the temporal generalization provided in Section 4.3 support the same conclusion.

Finding 6 — Practical cost–benefit trade-off.

Despite being more computationally intensive compared to the baseline, the extra cost is well worth the additional uncertainty quantification, explainability of the policy-domain and tail bias adjustment capabilities. On the other hand, the Level-1 ensemble alone already provides the majority of the increase in accuracy, but at a significantly reduced computational price point compared to the complete interpretability stack.

In particular, we have performed an expanded ablation study by adding two additional setups that help disentangle the influence of PCA and K-Means based manifold learning. The first setup is an XGBoost model (T = 1000, ), which has been trained solely on raw feature set, without including PCA, K-Means clustering and polynomial expansion and therefore represents the most fundamental baseline. The second setup adds the manifold features extracted using PCA and K-Means to the original XGBoost model, but does not include SHAP guided polynomial expansion and hence allows us to assess the impact of the manifold representation on the predictive performance.

In conclusion, the results of our ablation study shown in Table 9 establish the following evidence chain: polynomial expansion only works inside the stacking hierarchy; ensemble diversity leads to the maximum decrease in error; meta-manifold and residual corrector give consistent gains; and, finally, LOO encoding gives real heterogeneity information rather than overestimated performance.

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Table 9. Ablation study on (n = 3,308).

https://doi.org/10.1371/journal.pone.0353849.t009

4.4.1 Computational cost.

To illustrate the aforementioned trade-off of the predictive power versus efficiency, the computational cost of each setup was analyzed with regard to the training time and memory consumption during the process. From Table 10 it follows that the baseline XGBoost predictor (A1) is the most efficient algorithm, taking 42 s and consuming 1.8 GB of RAM. With the addition of polynomial features, the costs rise up slightly to 51 s and 2.4 GB, while the Level-1 ensemble alone (A3) consumes 138 s and 3.1 GB of RAM because of the need for an out-of-fold training of additional predictors. The most computationally expensive method is the entire NEXUS-LE pipeline (A4), taking 559 s and consuming 6.2 GB of RAM because of the combination of stacking, meta-manifold construction, residual correction, and conformal calibration.

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Table 10. Computational cost of the evaluated configurations.

https://doi.org/10.1371/journal.pone.0353849.t010

4.4.2 Conformal prediction discussion.

The conformal prediction results are discussed in greater detail to clarify their relevance for public health decision-making. In particular, the 90% and 95% prediction interval widths are interpreted in relation to the overall target range, with explicit discussion of the sharpness–coverage trade-off. The results indicate that the 90% interval provides the most practical balance for policy use, whereas the 95% interval offers stronger protection against undercoverage at the expense of wider bounds.

A subgroup calibration analysis was also added to assess whether the prediction intervals remain well calibrated across WHO income groups. As shown in Table 11, empirical coverage remains close to the nominal 95% level across low-income, lower-middle-income, upper-middle-income, and high-income countries, with no systematic over- or under-coverage across strata. Lastly, the above discussion is extended to compare split-conformal prediction methods with Bayesian methods among others. Even though there are Bayesian methods that can be used to obtain posterior predictive intervals, most Bayesian methods need a prior and computational resources, unlike the distribution-free and computationally efficient method adopted in this case.

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Table 11. Conformal prediction performance and subgroup calibration.

https://doi.org/10.1371/journal.pone.0353849.t011

4.5 Uncertainty quantification via conformal calibration

Reliable uncertainty communication is a prerequisite for evidence-based health-policy deployment. NEXUS-LE provides distribution-free prediction intervals (PIs) via the split-conformal procedure of Section 3.5 (Eqs. (14)–(17)), calibrated exclusively on the withheld partition (3,308 samples) and validated on . Table 12 reports the quantile estimates, nominal guarantees, and empirical coverages at . Finite-sample tolerance computed as at the 95% confidence level. All widths are symmetric around per Eq. (16).

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Table 12. Split-conformal prediction interval results on (n = 3,308).

https://doi.org/10.1371/journal.pone.0353849.t012

Both intervals satisfy the marginal coverage guarantee of Eq. (17): the 95% PI exceeds nominal by +0.04 pp and the 90% PI falls short by only –0.10 pp, well within the finite-sample tolerance band ( pp and pp respectively), confirming that the exchangeability assumption holds on this panel dataset. The interval visualisation in Fig 2 (bottom-right) shows symmetric 90% bands that tightly bracket actual values across the full sorted test range, with no systematic under- or over-coverage in any life-expectancy sub-region—a direct visual validation of the theoretical guarantee. The average 90% PI width of years is clinically actionable: it is narrower than the inter-decile range of ( years) while remaining wide enough to accommodate genuine between-population heterogeneity, a balance that meets the precision-vs-conservatism criterion advocated for WHO-facing health projection tools. Critically, this calibrated uncertainty is unavailable in any ablation variant A1–A3 (Table 9), underscoring the indispensability of the dedicated calibration partition in the NEXUS-LE design.

4.6 Global explainability: TreeSHAP feature importances

Global model transparency is operationalised via TreeSHAP importance scores (Eq. (7)) computed over the full test set (n = 3,308). Fig 4 ranks the top-20 features by mean , Bar length encodes (Eq. (7)). indicates degree-2 polynomial terms introduced in Phase 2. Table 13 consolidates the top-10 with their importance scores and policy-domain assignments. Feature type: O = original, P = SHAP-guided polynomial interaction.

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Table 13. Top-10 globally important features ranked by TreeSHAP mean on .

https://doi.org/10.1371/journal.pone.0353849.t013

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Fig 4. Global SHAP importance ranking for NEXUS-LE (, n = 3,308).

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Four epidemiologically interpretable patterns emerge.

1. (i) Country-level structural dominance. The LOO-encoded Country feature ranks first with years— the second-ranked feature—confirming that persistent structural determinants (health-system capacity, institutional quality, geographic disease burden) encoded in country identity explain the dominant share of between-country life-expectancy variance. This is corroborated at the instance level by the local attribution years for a representative high-income test sample.
2. (ii) Demographic and mortality predictors. Death Rate % Population Aged 0--14 (I = 0.93) and Gender (I = 0.75) rank 2nd and 3rd, consistent with established evidence that age-stratified mortality rates and sex-specific survival differentials are robust proxies for systemic health investment levels.
3. (iii) Polynomial interaction terms validate Phase-2 expansion. Four of the top-10 features are SHAP-guided degree-2 terms, directly validating the SHAP-guided polynomial strategy of Phase 2. Their presence confirms that a purely linear feature space would miss multiplicative synergies between country context and clinical indicators that are epidemiologically meaningful.
4. (iv) Health-system interaction for policy targeting. Country UHC Coverage ranks 9th (I = 0.27), quantifying the marginal life-expectancy gain attributable to expanding universal health coverage conditional on existing country-level infrastructure—a finding directly actionable for WHO SDG 3.8 intervention prioritization. Full policy-domain aggregations are reported in Table 14.

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Table 14. Policy-domain aggregated SHAP importance on (n = 3,308).

https://doi.org/10.1371/journal.pone.0353849.t014

4.7 Policy-factor XAI grouping

To bridge the gap between feature-level SHAP attributions and actionable health-policy inference, all 675 features were aggregated into seven thematic domains following the WHO determinants-of-health taxonomy. Aggregated importance is defined as the sum of per-feature mean within each group. Fig 5 visualises the distribution and Bar length encodes summed mean per domain (Table 14). Other and Demography jointly account for 96.3% of total attribution, with Nutrition contributing the only other substantive share (4.5%). Table 14 provides the quantitative breakdown with cumulative shares.

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Fig 5. Policy-factor aggregated SHAP importance for NEXUS-LE ().

https://doi.org/10.1371/journal.pone.0353849.g005

Three policy-relevant findings emerge from the domain grouping.

1. (i) Structural and demographic co-dominance. The Other and Demography groups collectively account for of total SHAP attribution. Demography (46.03%) subsumes age-sex stratified mortality rates, birth rates, and population age-structure features, whose dominance is consistent with the demographic transition framework: age-structure shifts and under-5 mortality reduction are the primary drivers of population-level life-expectancy gains in low- and middle-income countries. The Other group (50.27%) is anchored by the LOO-encoded Country fixed effect () and its polynomial interactions, confirming that persistent systemic determinants—health-system quality, institutional capacity, and geographic disease burden—are the single largest source of explainable variance in this dataset.
2. (ii) Nutrition as the sole clinically modifiable contributor. Nutrition contributes 4.51% (0.614 SHAP units), representing the only domain with a substantive share beyond structural and demographic effects. BMI-related interaction terms and the AlcoholBMI feature (Eq. (2)–(5)) retain measurable marginal predictive power after controlling for country fixed effects, confirming that dietary risk factors act on life expectancy through pathways partially independent of socioeconomic development level. This finding is directly actionable: targeted nutritional interventions may yield life-expectancy gains even within countries whose structural profile is already favourable.
3. (iii) Conditionally attenuated contributions of immunisation, lifestyle, and socioeconomic domains. Immunisation, Lifestyle, and Socioeconomic each contribute < 0.35% of total attribution. This does not imply causal irrelevance; rather, after conditioning on country-level fixed effects—which absorb systemic variation in vaccination infrastructure, GDP, and public health investment—their marginal explanatory contribution to population-mean life expectancy is suppressed, a finding consistent with the GBD 2019 comparative risk attribution analysis. The implication for policy design is that interventions in these domains are more likely to yield measurable life-expectancy gains when deployed in contexts where the country-level structural baseline is weak (low Country LOO score), as captured by the interaction terms identified in Table 13.

4.8 Partial dependence analysis

Partial Dependence Plots (PDPs) decompose the marginal dose–response relationship between each top-ranked feature and the predicted life expectancy, averaging over the joint distribution of all remaining features in . Fig 6 presents PDPs for the four highest-ranked features in (Table 13): Country, Death Rate^2, Country^2, and Gender. The y-axis is the marginal predicted life expectancy (years) after averaging over all other features. (Top-left) Country (LOO): sigmoid-like monotone increase spanning years, encoding the non-linear HDI gradient. (Top-right) Death Rate^2: monotone decrease ( yr), capturing the accelerating mortality penalty that a linear term would underestimate. (Bottom-left) Country^2: shallow positive gradient ( yr), encoding quadratic amplification of country-level structural advantages. (Bottom-right) Gender: near-flat decline ( yr), consistent with the global female longevity advantage. Table 15 summarises the direction, range, and epidemiological interpretation of each curve. Range = marginal span across the observed feature domain; Direction: increasing, decreasing. All values are marginal life-expectancy years.

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Table 15. PDP curve characteristics for the top-4 SHAP-ranked features (Fig 6).

https://doi.org/10.1371/journal.pone.0353849.t015

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Fig 6. Partial Dependence Plots for the top-4 SHAP-ranked features (, , n = 3,308).

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Four mechanistic findings are evident.

1. (i) Non-linear HDI gradient (Country, Fig 6 top-left). The PDP spans years across the LOO-encoded country range, exhibiting a sigmoid dose–response curve consistent with the non-linear HDI–life-expectancy relationship documented in UNDP reports. Below a LOO threshold of (corresponding to HDI ), marginal gains in country-level health determinants yield accelerating life-expectancy improvements; above this threshold, returns diminish—a saturation pattern directly informing the targeting of SDG 3 investments toward lower-HDI nations.
2. (ii) Polynomial mortality penalty (Death Rate^2, top-right). The monotone decreasing PDP ( years) confirms that the quadratic death-rate term introduced in Phase 2 captures a non-linear, accelerating mortality burden that a linear predictor would systematically underestimate at high-burden values. This validates the SHAP-guided expansion strategy: the polynomial term provides incremental explanatory power beyond the raw death rate already present in .
3. (iii) Quadratic country amplification (Country^2, bottom-left). The shallow positive gradient ( years) of Country^2 encodes the accelerating structural advantage conferred on high-income countries: small increments in an already-favourable country index yield disproportionately larger marginal life-expectancy gains, a pattern consistent with compounding returns to health-system maturity.
4. (iv) Female longevity advantage (Gender, bottom-right). The near-flat PDP declines by years between Gender (female-majority strata) and Gender = 0.5 (male-majority strata), consistent with the universally documented biological female longevity advantage. The attenuation of this effect at extreme positive values reflects the compression of the sex-gap in contexts of persistently high male–female mortality differentials in low-income settings, a nuance invisible to linear predictors but captured by NEXUS-LE’s non-linear ensemble. Together, the four PDPs provide falsifiable, epidemiologically coherent dose–response curves that strengthen the trustworthiness audit of NEXUS-LE as a deployable health-prediction system.

4.9 Computational profile and deployment considerations

To support practical deployment, we report the Table 16 on computational profile of the proposed pipeline in terms of wall-clock time, memory usage, and hardware requirements across all seven phases.The above decomposition explains the cost associated with processing each block, revealing that the most computationally intensive operation is the L1 OOF stacking layer while all other layers have minimal computation requirements and can be easily processed using a CPU-only approach. For even better assistance with the design of resource-limited implementations, the following CPU versus GPU comparisons and a lighter A3 version are included.

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Table 16. Per-phase computational requirements of the NEXUS-LE pipeline.

https://doi.org/10.1371/journal.pone.0353849.t016

4.10 Comparative analysis

To contextualise the performance of NEXUS-LE within the broader life-expectancy prediction literature, we benchmark it against two representative prior systems and the three constituent base learners evaluated on the same held-out test set (, n = 3,308). Shakeel Ahmad et al. [14] demonstrated that XGBoost achieves an adjusted R² = 0.9729 on the standard WHO life-expectancy dataset, substantially outperforming ordinary least squares regression and establishing gradient-boosted trees as the dominant paradigm for this task. Ozsahin et al. [12] compared Random Forest (RF), LightGBM (LGBM), AdaBoost, and XGBoost on a global life-expectancy benchmark, finding LGBM superior with RMSE = 1.8778 years and R² = 0.9504—the strongest single-model result reported prior to this work. Despite this progress, both studies rely on single-model architectures applied to raw WHO indicators, without hierarchical stacking, SHAP-guided polynomial enrichment, meta-manifold augmentation, or statistically guaranteed prediction intervals [14,12]. Table 17 reports five-metric test-set performance for NEXUS-LE against its three base learners (XGB-A, XGB-B, LGBM-A). Bold: best value per metric. rows report NEXUS-LE minus each baseline; negative values on error metrics denote improvement. Prior-art results [14,12] are evaluated on their respective datasets and are included for directional reference. NEXUS-LE achieves R² = 0.9878 and RMSE = 1.0665 years, surpassing the pre-specified accuracy target and improving upon the Ozsahin et al. baseline [12] by 0.7113 years in RMSE (37.9% reduction) and 0.0374 in R². Relative to the weakest base learner (LGBM-A), NEXUS-LE reduces RMSE by 0.0401 yr (3.6%), MAE by 0.0526 yr (7.8%), and MAPE by 0.0679 pp (6.8%), directly quantifying the variance-reduction benefit of three-level OOF stacking over any individual learner.

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Table 17. Test-set benchmark on (n = 3,308).

https://doi.org/10.1371/journal.pone.0353849.t017

Although XGB-B records marginally lower MAE (0.6151 yr) and MAPE (0.9126%) than NEXUS-LE, both differences fall within the Monte Carlo RMSE noise floor of yr at n = 3,308 and are therefore statistically indistinguishable. Mechanistically, XGB-B’s marginal median-error advantage reflects its single-model regularisation structure, which biases predictions toward the central tendency; by contrast, NEXUS-LE optimises for squared-error reduction across the full life-expectancy range [24.83, 87.75] years—the more consequential objective for population-level health-policy projections. Critically, none of the prior-art or base-learner systems provide statistically guaranteed prediction intervals, SHAP-guided polynomial enrichment, or WHO-taxonomy policy-domain attributions; NEXUS-LE uniquely satisfies all three FUTURE-AI deployment requirements (interpretability, uncertainty quantification, and bias auditing) within a single unified pipeline.