1.1. Contribution

The contributions of this study are as follows:

• Proposes TRIDENT-Risk, a temporal risk-driven ensemble framework specifically designed for high-severity accident forecasting.
• Introduces multi-scale temporal risk descriptors including lag features, rolling statistics and risk acceleration indicators.
• Incorporates imbalance-aware gradient boosting together with adaptive threshold optimization for improving minority-class detection.
• Performs extensive evaluation on a large-scale US accident dataset and demonstrates superior ROC-AUC, PR-AUC and recall compared with four representative ML baselines.
• Provides interpretable accident-risk analysis through SHAP explanations and spatial hotspot validation.

1.2. Structure

The rest of this paper is organized as follows. Section 2 reviews the existing literature of traffic accident prediction and identifies the research needs that underlie the proposed methodology. Section 3 provides theoretical preliminaries, problem formulation, evaluation criteria and baseline models for comparison analysis. Section 4 presents the proposed TRIDENT-Risk framework encompassing spatial-temporal aggregation, multi-scale temporal feature engineering, imbalance-aware gradient boosting and risk-sensitive threshold optimization. Section 5 explains the experimental setup, dataset description, preprocessing steps, hyperparameter setting and evaluation protocol. In Section 6, the experimental results, the performance comparison, the interpretability analysis and the discussion of the results are presented. Section 7 presents limitations of the proposed framework and some avenues for future research. The paper concludes with Section 8, which summarizes the main findings and contributions.

2.1. Research gaps

Existing studies have greatly improved the prediction of traffic accidents with ML and DL methods. However, there are still some research gaps. First, many approaches only optimize the total accuracy while ignoring the identification of the minority class, which is more important in safety-critical contexts. Second, modeling temporal dependencies is usually done using either short-term lag features or sequential DL architectures, but relatively few research combine multi-scale temporal accumulation with imbalance-aware optimization. Third, threshold calibration is rarely implemented while it is important to trade off false alarms and missed detections. Also, many existing methodologies are limited in their interpretability which hinders their practical applicability for transportation authorities. These research gaps motivate the development of the proposed TRIDENT-Risk framework.

3.1. Problem formulation

Let the transportation region be partitioned into spatial grids indexed by and discretized in time into hourly intervals indexed by . For each grid–time pair (g,t), a feature vector is constructed, containing contextual and temporal variables such as accident counts, weather attributes, and lag-based risk indicators. The target variable denotes the occurrence of at least one high-severity accident within a predefined future horizon.

The objective is to learn a mapping given by Eq. 1:

(1)

that estimates the conditional probability shown by Eq. 2:

(2)

which represents the predicted high-severity accident risk for a given spatial–temporal unit. The prediction problem is characterized by class imbalance, where high-severity events occur less frequently than non-severe cases. Consequently, performance evaluation must consider discrimination capability and minority-class sensitivity rather than overall accuracy alone.

3.2. Evaluation metrics

To assess predictive performance comprehensively, multiple metrics are employed.

The Receiver Operating Characteristic Area Under Curve (ROC-AUC) measures the ability of the model to distinguish between positive and negative classes across all classification thresholds. Formally, it evaluates the tradeoff between true positive rate (TPR) and false positive rate (FPR).

Given a threshold , predictions are defined by Eq. 3:

(3)

Precision and recall for the high-risk class are defined by Eq. 4:

(4)

where TP, FP, and FN denote true positives, false positives, and false negatives, respectively.

The F1-score, which balances precision and recall, is given by Eq. 5:

(5)

The Precision–Recall Area Under Curve (PR-AUC) provides additional insight into performance under class imbalance and is particularly informative in safety-critical settings.

3.3. Baseline models

To ensure rigorous benchmarking, several widely adopted classification models are considered as baselines. These models represent linear, tree-based, ensemble-based, and neural network paradigms.

3.3.1. Logistic regression.

Logistic regression models the log-odds of the positive class as a linear function of input features. The probability estimate is defined by Eq. 6:

(6)

where is the weight vector, b is the bias term, and denotes the sigmoid function represented by Eq. 7:

(7)

Model parameters are learned by minimizing the binary cross-entropy loss given by 8:

(8)

Logistic regression provides a strong linear baseline and serves as a reference for evaluating nonlinear model improvements.

3.3.2. Random forest.

Random Forest is an ensemble of decision trees constructed using bootstrap aggregation. Each tree is trained on a random subset of data and features, thereby reducing variance and improving generalization.

Given M trees , the predicted probability is obtained by averaging represented by Eq. 9:

(9)

Each tree partitions the feature space into regions through recursive binary splits that minimize impurity measures such as the Gini index given by 10:

(10)

where represents the proportion of samples belonging to class k in a node.

Random Forest effectively captures nonlinear relationships and interactions without requiring extensive feature preprocessing.

3.3.3. Gradient boosting (XGBoost).

Gradient boosting constructs an additive model by sequentially fitting weak learners to the residual errors of previous iterations. The model at iteration m is expressed as Eq. 11:

(11)

where each is a regression tree.

The objective function consists of a differentiable loss component and a regularization term given by 12:

(12)

where penalizes model complexity.

XGBoost enhances classical gradient boosting by incorporating second-order optimization, regularization, and parallelized computation, leading to improved performance and stability in structured data environments.

3.3.4. Multilayer perceptron (MLP).

The multilayer perceptron is a feedforward neural network consisting of fully connected layers with nonlinear activation functions. For a network with L layers, the forward propagation is defined as Eq. 13:

(13)

where , denotes a nonlinear activation function such as ReLU, and and are learnable parameters.

The final output layer produces a probability estimate via a sigmoid activation. Parameters are optimized using backpropagation and stochastic gradient descent to minimize cross-entropy loss. MLP models can capture complex nonlinear feature interactions but may require careful regularization and hyperparameter tuning to prevent overfitting.

3.4. Discussion

The selected baseline models encompass diverse modeling philosophies, ranging from linear probabilistic classifiers to tree-based ensembles and neural architectures. This diversity ensures that the proposed framework is evaluated against strong and representative alternatives. By systematically comparing performance across these baselines, the effectiveness of the proposed temporal risk-driven ensemble approach can be rigorously validated in subsequent sections. The selected grid resolution is a compromise between local spatial representation and sufficient sample density, thus alleviating the effect of sparsity while retaining computational efficiency.

4.1. Dataset description

The proposed framework is developed and evaluated using the publicly available US-Accidents dataset((Accessed on: 14/02/2026) https://www.kaggle.com/datasets/sobhanmoosavi/us-accidents/data) [35,36]. This countrywide dataset covers 49 states of the United States and includes accident records collected from February 2016 to March 2023. The data were gathered in real time using multiple traffic APIs that broadcast incident information captured by state departments of transportation, law enforcement agencies, traffic cameras, and road-embedded sensors. The dataset contains approximately 7.7 million accident records and provides rich contextual information including spatial coordinates, timestamps, severity levels, and environmental attributes such as temperature, humidity, and visibility.

For computational feasibility and reproducibility, the dataset is spatially aggregated into regional grids and temporally discretized into hourly intervals. Each grid-time pair represents a spatial–temporal observation used for predictive modeling. High-severity events are defined based on severity levels exceeding a predefined threshold, thereby converting the problem into a binary classification task. The original dataset severity labels were used to define high-severity accidents, which were annotated using the same framework across all states and years in this study. The suggested approach uses standardized severity categories to assure model development and evaluation consistency. This uniform labeling technique reduces geographical or temporal inconsistencies and allows large-scale accident risk prediction. Although minor missing entries may exist due to network disruptions during data collection, appropriate preprocessing and imputation strategies are employed to ensure consistency. To balance spatial granularity, data density, and computational efficiency, the spatial grid resolution was chosen. A coarser grid can mask localized accident patterns due to excessive spatial aggregation, whereas a finer grid may increase spatial resolution but lead to sparse observations and unstable feature estimation. The grid resolution provides enough event density for reliable temporal feature extraction and enough spatial variability for large-scale accident risk prediction.

4.2. Spatial-temporal aggregation

Let (Lat, Lon) denote the geographical coordinates of each accident record. The study region is partitioned into uniform spatial grids of size degrees. Each accident is mapped to a grid index g using Eq. 14:

(14)

Temporal discretizations is performed at hourly resolution. For each grid g and hour t, contextual variables are aggregated to form feature vectors . These include:

• High-severity accident count
• Total accident count
• Mean temperature
• Mean visibility
• Mean humidity
• Temporal indicators (hour-of-day, day-of-week)

The target variable is defined in Eq. 15:

(15)

This formulation enables proactive forecasting. Although uniform spatial grids allow computational scalability and reliable aggregation over millions of accident reports, grid-based partitioning may produce the Modifiable Areal Unit Problem (MAUP), where aggregation borders affect spatial patterns. The MAUP may affect prediction performance, but existing research have shown that intermediate grid resolutions often balance geographical detail with statistical stability. Therefore, a fixed grid resolution has been used throughout the study to ensure uniform feature representation and fair model comparison. Combining micro-level roadway factors including intersection layout, lane configuration, curvature, and signal control attributes may smooth them out. This analysis forecasts regional risk, not road-segment crashes. Choose an aggregation technique that balances computational robustness with spatial granularity. Adaptive zoning, graph-based road representations, and road-segment-level learning frameworks will be studied to reduce MAUP impacts.

4.3. Multi-scale temporal feature engineering

Temporal dynamics are explicitly modeled using multi-horizon lag and rolling statistics. For each grid g, lag features are defined in Eq. 16:

(16)

To avoid the leakage of temporal information, all lag features are generated based on the previous accident information seen and available before the prediction period. We define as the observed high-severity accident count in grid g at time interval t, which is different from the predicted objective.

Rolling mean risk over window w is defined in Eq. 17:

(17)

Risk volatility is captured using rolling standard deviation as defined in Eq. 18:

(18)

Risk acceleration is defined in Eq. 19:

(19)

Consider the lag and rolling properties has been calculated only from previous observations before the prediction instant. The variables , , , , rolling mean, rolling standard deviation, and risk acceleration has been derived using historical accident counts () instead of the future prediction target Independently, the aim variable was at least one high-severity mishap during the one-hour prediction horizon. Thus, the proposed feature engineering technique preserves temporal causality and precludes future observation information leakage into model training.

4.4. Imbalance-aware gradient boosting

In this study, class imbalance has been handled exclusively through class-weighted learning using XGBoost’s scale_pos_weight parameter, computed from the training data only. Validation and testing retained the original class distribution. The predictive backbone of proposed TRIDENT-Risk is a gradient boosting ensemble. The model constructs an additive function in Eq. 20:

(20)

where each is a regression tree trained to minimize a differentiable loss. The regularized objective function is defined as Eq. 21:

(21)

where denotes logistic loss and penalizes tree complexity. To address class imbalance, positive-class weighting is introduced as shown in Eq. 22:

(22)

where is the imbalance weight computed as shown in Eq. 23:

(23)

This weighting enhances sensitivity toward high-risk events.

4.5. Risk-sensitive threshold optimization

Instead of using a fixed threshold , TRIDENT-Risk selects by maximizing the F1-score as defined in Eq. 24:

(24)

This step ensures balanced detection of high-risk zones while controlling false alarms.

4.6. Algorithmic framework

This subsection formally summarizes the computational workflow of the proposed TRIDENT-Risk framework. Each algorithm is accompanied by explanatory context to clarify its role within the overall modeling pipeline.

4.7. Methodological summary

The TRIDENT-Risk framework integrates large-scale spatial aggregation, multi-scale temporal intelligence, imbalance-aware ensemble learning, and risk-sensitive threshold calibration into a coherent forecasting pipeline. The methodological design ensures robust discrimination, enhanced minority detection, and operational interpretability, making it suitable for proactive safety management within intelligent transportation systems.

5.1. Data preprocessing and aggregation

The raw US-Accidents dataset was first filtered to retain relevant attributes including spatial coordinates, timestamp information, severity level, and selected weather variables such as temperature, visibility, and humidity. Records with missing essential spatial or temporal information were removed to maintain structural consistency. Minor missing environmental values were imputed using median-based strategies within spatial–temporal neighborhoods to preserve statistical robustness. Spatial aggregation was performed by partitioning the study region into uniform geographic grids of fixed resolution. Each accident record was mapped to its corresponding grid cell based on latitude and longitude coordinates. Temporal discretizations was performed at hourly resolution, producing grid-hour observations. For each grid and hour, accident counts and contextual averages were computed. This transformation reduced sparsity and enabled structured supervised learning. To preserve the temporal causality, the dataset was ordered chronologically before model construction. The first 80% of observations were used as training data for the models, while the next validation subset was used just for hyperparameter modification and threshold optimization. The last 20% of the observations in chronological order remained back as an unseen test set. No random shuffling was undertaken to avoid predicting past data using future measurements at any time. This approach prevents temporal leakage and better reflects deployment scenarios where future risk must be predicted using historical data. All temporal features were constructed before the prediction horizon using just historical observations, ensuring no future accident information was used. The geographical aggregation resolution was fixed at providing a compromise between spatial coverage and data sparsity. The prediction horizon was set to H = 1 hour, i.e., in the next hourly interval the framework predicts if at least one high-severity accident will occur or not.

The total dataset had 356,883 grid-hour observations. A chronological train-test split has been used with 285,506 training samples and 71,377 testing samples. Under the adopted evaluation technique, high-severity accident prediction maintained its inherently imbalanced characteristics with a positive-class prevalence of 41.29% in the training set and 25.44% in the testing set as shown in Table 2s Because grid-hour observations may have identical manufactured feature values, repeated feature vectors were found after aggregate during data verification. These distinct spatial and temporal observations were kept for model development and evaluation rather than duplicated accident records.

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Table 2. Summary of the processed dataset and train-test split.

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5.2. Feature configuration

The final feature space included contextual, temporal, and engineered variables. Contextual variables consisted of accident counts and environmental attributes. Temporal encoding included hour-of-day and day-of-week indicators to capture cyclical mobility patterns. Multi-scale temporal intelligence was incorporated through lag variables at 1, 3, 6, and 12-hour intervals, rolling mean statistics over 6-hour and 12-hour windows, rolling standard deviation to capture volatility, and a risk acceleration term defined as the difference between short-term and medium-term lag values. These engineered features expanded the input dimensionality while preserving interpretability. All numerical features were retained in their natural scale for tree-based models. For neural network baselines, features were standardized using training-set statistics to ensure stable convergence.

5.3. Model configuration

All baseline models were implemented using widely adopted ML libraries to ensure comparability. Logistic regression employed regularization with default solver settings. Random Forest models were configured with 200 trees and balanced class weighting. To ensure fair comparison, hyperparameter optimization was also performed for the primary baseline models using controlled search spaces. The reported results correspond to the best-performing configurations identified on the validation set. The proposed TRIDENT-Risk model utilized an optimized gradient boosting configuration obtained via randomized search with three-fold cross-validation on the training set. The architectural design of proposed model was motivated by the characteristics of large-scale traffic accident data, which exhibit strong class imbalance, heterogeneous feature distributions, nonlinear interactions, and temporal persistence. Conventional deep learning models such as MLPs are highly dependent on balanced training data and often require extensive architectural tuning to effectively learn minority-class patterns. In contrast, gradient boosting ensembles inherently focus on difficult-to-classify samples through iterative residual learning and are particularly effective for structured tabular datasets. The integration of multi-scale temporal features allows the model to capture short-term fluctuations, medium-term accumulation effects, and longer-term risk persistence, while class-weighted optimization increases sensitivity toward rare high-severity events. Finally, threshold calibration aligns the decision boundary with safety-oriented objectives, resulting in improved minority-class recall and PR-AUC performance. The final hyperparameter configuration included a shallow tree depth, moderate subsampling, and controlled learning rate to balance bias and variance. Class imbalance was addressed using a positive class weight computed as the ratio of negative to positive samples in the training set. Validation probabilities were threshold optimized over candidate thresholds from 0.10 to 0.90 in increments of 0.01. The threshold that gave the best validation F1-score was chosen and then applied to the held-out test set. This decreases the possibility of overfitting to the test set, while ensuring that decision boundaries are consistent with operational safety goals. This strategy ensures that the final decision boundary aligns with safety-sensitive detection priorities rather than relying on a fixed probability cutoff.

5.4. Hyperparameter configuration

To ensure fair comparison and reproducibility, all baseline models and the proposed TRIDENT-Risk framework were configured using controlled and well-documented hyperparameter settings. For baseline models, standard configurations were adopted to reflect commonly used practical setups, while the proposed model employed hyperparameters selected through randomized search with cross-validation on the training set. The final configuration reflects a balance between generalization capability, computational stability, and minority-class sensitivity. Table 3 summarizes the hyperparameter settings for each model.

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Table 3. Validated Hyperparameter Configurations of Baseline Models and the Proposed TRIDENT-Risk Framework.

https://doi.org/10.1371/journal.pone.0357089.t003

5.5. Evaluation protocol

Performance was evaluated using multiple complementary metrics. ROC-AUC was used to assess overall discriminative capability independent of threshold selection. PR-AUC was emphasized due to class imbalance and the importance of minority-class performance. Precision, recall, and F1-score for the high-severity class were reported to quantify operational effectiveness. Accuracy was included for completeness but was not treated as the primary optimization objective. All comparisons were conducted on the identical test set to ensure fairness. Probability-based metrics were computed directly from predicted scores, while classification metrics were derived using the optimized decision threshold.

5.6. Implementation environment

The experiments were conducted in a Python-based environment using Scikit-learn for baseline models and XGBoost for gradient boosting implementations. Data manipulation and aggregation were performed using Pandas and NumPy. Spatial visualizations were generated using Matplotlib with high-resolution configuration for publication-quality figures. The experimental pipeline was executed in a cloud-based notebook environment with sufficient memory resources to handle large-scale aggregated datasets efficiently.

The complete workflow—from spatial aggregation and temporal feature engineering to model training and evaluation—was implemented in a modular manner to ensure reproducibility and extensibility. This structured experimental setup enables rigorous comparison between baseline approaches and the proposed TRIDENT-Risk framework, thereby providing a reliable foundation for the subsequent performance analysis.

6.1. Quantitative performance comparison

Table 4 summarizes the predictive performance of all evaluated models on the held-out test set.

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Table 4. Performance Comparison of Baseline Models and Proposed TRIDENT-Risk Framework.

https://doi.org/10.1371/journal.pone.0357089.t004

As shown in Table 4, the proposed TRIDENT-Risk framework achieves the highest ROC-AUC of 0.8917, indicating superior discriminative capability across all thresholds. The PR-AUC of 0.7266 further demonstrates improved minority-class precision–recall tradeoff under imbalanced conditions. Most notably, recall for high-severity accidents increases to 0.81, representing a substantial improvement over the strongest baseline (MLP: 0.70). This improvement directly enhances early-warning sensitivity in safety-critical applications. Although overall accuracy remains comparable across models, accuracy is not the primary optimization objective due to class imbalance. The observed increase in minority recall without drastic degradation in precision confirms the effectiveness of imbalance-aware optimization and threshold calibration.

6.2. ROC and precision–recall analysis

The ROC curve comparison illustrates consistent dominance of the proposed model across false-positive rates as shown in Fig 2 and The precision–recall curves shown in Fig 3 provide further insight under class imbalance.

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Fig 2. ROC curve comparison of baseline models and the proposed framework.

https://doi.org/10.1371/journal.pone.0357089.g002

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Fig 3. Precision–Recall curve comparison across models.

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The proposed framework maintains higher precision across a wide recall range, demonstrating robustness in minority-class detection. The improvement is particularly evident in medium-to-high recall regions, where safety systems typically operate.

6.3. High-risk detection performance

Fig 4 compares recall and F1-score for the high-risk class. The substantial increase in recall achieved by TRIDENT-Risk confirms its enhanced capability to detect severe accident conditions. The balanced F1-score further validates that recall gains are not achieved at the expense of severe precision degradation. The multi-metric radar comparison in Fig 5 highlights overall dominance across evaluation criteria.

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Fig 4. High-risk recall and F1-score comparison across models.

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Fig 5. Multi-metric radar comparison of baseline models and the proposed framework.

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6.4. Spatial risk validation

Spatial validation is illustrated in Fig 6, which overlays predicted risk intensity with actual high-severity accident density.

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Fig 6. Predicted risk versus actual high-severity accident density.

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High-risk zones identified by the model correspond closely with regions exhibiting elevated actual accident density, confirming spatial consistency and practical applicability. This alignment demonstrates that the model captures meaningful geographic patterns rather than overfitting random noise.

6.5. Interpretability analysis

To further validate model reliability, SHAP analysis was performed, as illustrated in Fig 7.

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Fig 7. SHAP summary plot illustrating feature importance and impact direction.

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The SHAP summary plot indicates that rolling temporal features and lag-based variables contribute most significantly to risk prediction. Environmental attributes such as temperature and visibility exert secondary influence, while static accident count alone provides limited predictive power. This confirms the importance of multi-scale temporal modeling in high-severity accident forecasting. SHAP analysis shows lag and rolling temporal elements as dominant predictors, although the framework is not auto-regressive. The feature space includes environmental parameters, accident density indicators and hour-of-day and day-of-week temporal context descriptors. Timeline train-test separation prevents time leaking and ensures label memorization does not affect expected performance. Accident persistence, not auto regressive bias makes temporal accumulation attributes significant. SHAP values were generated using the TreeExplainer technique, designed for tree-based ensemble models, to increase explainability analysis reliability and consistency. Explanations were based on the independent test dataset, whereas a background sample of 1,000 observations estimated model output. This arrangement ensures consistent and computationally efficient feature attributions, ensuring SHAP values appropriately reflect each feature’s contribution to model predictions.

6.6. Statistical validation

To assess the statistical dependability of the proposed TRIDENT-Risk framework, the uncertainty in the model’s predictive performance has been estimated using bootstrap resampling. Specifically, 500 bootstrap iterations were performed by repeatedly sampling the test set with replacement, and the Area Under the Receiver Operating Characteristic Curve (AUROC) was calculated for each iteration. The bootstrap distribution so obtained was used to estimate the mean AUROC and the related 95% confidence interval, which gives a robust assessment of the stability of the model. Furthermore, Receiver Operating Characteristic (ROC) confidence bands were created to test the variability of the classifier at different choice thresholds. Decision Curve Analysis (DCA) was also undertaken to examine the possible clinical and practical usefulness of the proposed framework at different threshold probabilities. The tight confidence intervals and consistent model performance on bootstrap samples show the model is stable and reliable in terms of predictive capabilities, which supports the application of the model for the real-world accident risk prediction.

6.7. Calibration analysis

In addition to discrimination performance, the calibration of the proposed TRIDENT-Risk framework was assessed to evaluate the agreement between anticipated probability and the observed occurrence of high-severity incidents. The calibration performance measured using the Brier score, calibration intercept and calibration slope, all measures of the dependability and accuracy of probabilistic predictions. The proposed methodology achieved a Brier score of 0.1594 suggesting an overall strong probabilistic accuracy with reasonably low prediction error. The calibration intercept is −0.2725 with the calibration slope of 1.3470, indicating that the projected probabilities were well aligned with the observed outcomes with small calibration variance. The calibration curve is shown in Fig 8,where the predicted probabilities are close to the ideal calibration line, indicating that the estimated risk is consistent with the actual occurrence of accidents.

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Fig 8. Calibration analysis of the proposed TRIDENT-Risk framework.

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The threshold for operational decision-making was 0.5. The precision was 60.66%, and the recall was 57.11%. With this threshold, the proposed architecture generated 17,095 alerts, with an average of 6.69 alerts per day. Of these, 10,370 were real alarms and 6,725 were false alarms with a false alarm rate of 39.34%.

6.8. Discussion