Logistic Models Research Articles

Dynamic Response of Potato Growth Indicators to Effective Cumulative Temperature and Water and Nitrogen Regulation Based on a Logistic Model

Dynamic Response of Potato Growth Indicators to Effective Cumulative Temperature and Water and Nitrogen Regulation Based on a Logistic Model

Association between atherogenic index of plasma and post-stroke depression: a cross-sectional study

ABSTRACT Background: Few studies have established a link between the atherogenic index of plasma (AIP) and post-stroke depression (PSD). This study aims to further investigate the potential relationship between the AIP and PSD, and to provide references for the prevention and prognosis management of patients with PSD. Methods: A cross-sectional study was conducted using data from participants in the National Health and Nutrition Examination Survey from 2005 to 2018. Inclusion criteria required complete data on the AIP, stroke history, and depression status. Weighted logistic regression models and restricted cubic splines (RCS) were employed to examine the association between the AIP and PSD. By subgroup and interaction analyses, the stability associated with AIP and PSD was assessed between different subgroups. Results: Among the 32,364 participants ultimately enrolled in the study, 482 were diagnosed with PSD. In the weighted multivariate logistic regression adjustment model 3, AIP, as a continuous variable, was positively associated with the risk of PSD [odds ratio (OR) = 1.85, 95% confidence interval (CI): 1.18, 2.91; P = 0.007]. After the quartile classification of AIP, the adjusted model 3 showed that the risk of PSD in group Q4 was significantly higher than that in group Q1 (OR = 1.61, 95%CI:1.10, 2.34; P = 0.006). In the RCS linearity test, AIP was positively associated with the risk of PSD (P non-linear = 0.357). The interaction test demonstrated that AIP only had an interaction with gender (P interaction = 0.031) and not with other variables (P interaction > 0.05). Conclusion: AIP was positively associated with the prevalence of PSD, suggesting that AIP may be a promising predictor of the risk of developing PSD. In addition, the interaction of AIP and gender differences combined to influence the incidence of PSD.

Wrist Circumference as a Novel Predictor of Coronary Artery Disease and Metabolic Syndrome

Introduction: Wrist circumference is a good predictor of obesity and insulin resistance. Wrist circumference may be considered as an indirect determinant of hyperinsulinemia and insulin resistance. The present study aimed to assess wrist circumference as an alternative tool for differentiating patients with coronary artery disease and metabolic syndrome from those without coronary artery disease and metabolic syndrome. Materials and Methods: The study was conducted on patients ≥ 30 years old undergoing coronary angiography following acute coronary syndrome or for evaluation of coronary artery disease. Results: Diabetic, hypertensive, and obese patients had more wrist circumference. High TG, low HDL levels were associated with higher wrist circumference (p=0.005). Wrist circumference was positively correlated with waist-hip ratio (p<0.001). Patients with Metabolic Syndrome have a mean Wrist circumference of 16.54 whereas patients without Metabolic Syndrome have a mean wrist circumference of 15.89(p<0.001). Coronary artery disease patients had higher mean wrist circumference than non-coronary artery disease patients (16.59 vs 15.9) (p<0.001). Triple-vessel disease patients have higher wrist circumference than double-vessel-disease patients; Doublevessel- disease patients have higher wrist circumference than single-vessel disease (p<0.001). Multivariate logistic model shows the main predictors for coronary artery disease are male sex, smoking, high BMI, low HDL, and wrist circumference. Conclusion: Measurement of Wrist circumference can serve as an easy anthropometric marker to identify individuals at risk of cardio-metabolic disorder, and predict the severity of Coronary Artery Disease can be used in large epidemiological studies.

Research on Low-Carbon Site Selection Decision Model and Algorithm for Green Logistics

This work proposes a low-carbon site selection decision model and algorithm for green logistics. The focus is to minimize carbon emissions while optimizing the distribution network. With the development of smart shared logistics and increasing environmental awareness, there is an urgent need to tackle issues in urban logistics, including pollution, resource inefficiency, high carbon energy usage, and greenhouse gas emissions. By integrating geographic, environmental, and operational data, the proposed site selection model incorporates multi-objective optimization to balance carbon efficiency with cost-effectiveness in logistics site selection. We employ a hybrid algorithm combining Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) to solve the complex decision-making process. The model is tested using real-world logistics data, and the results demonstrate significant reductions in carbon emissions and transportation costs when compared to conventional logistics site selection methods. Further sensitivity analysis reveals that the model is robust under varying transportation demands and geographic constraints. Also, we highlight the role of green logistics in achieving corporate sustainability goals aligning with global carbon neutrality initiatives. We believe this model offers a practical approach to fostering environmentally responsible supply chains and will contribute to the advancement of sustainable logistics operations, helping organizations make informed, eco-friendly decisions in site selection.

Stochastic Learning Strategy with Varying Regularization Activation Layer-Based Diabetes Prediction Using Multilayer Perceptron

Diabetes makes people more susceptible to disorders like heart disease, kidney disease, Parkinson’s, cataracts, respiratory issues, and other illnesses. Numerous tests are employed to capture essential data for diagnosing diabetes, and the assessment is then used to decide the most appropriate course of action. Nevertheless, it is still challenging to identify the precise traits essential for the emergence of diabetes. Finding the critical factors that influence the target diabetes condition is the primary goal of this research. The Stochastic Learning Strategy with Varying Regularization Logistic Activation Multilayer Perceptron (MLP) model has been implemented with the Indian Diabetes patient dataset extracted from the UCI database repository. Data preprocessing was accomplished for the patients of the Indian diabetes dataset. This research tries to extract the correlation and distribution of all features from the Indian Diabetes Patient dataset. All classifiers demonstrate an accuracy of less than 80% when applied to the Indian Diabetes patient dataset with and without feature scaling, except the Random Forest classifier, which is found to have an accuracy of 78%, which is not the best. The Indian Diabetes patient dataset is fitted with MLP with various learning rates such as Constant learning, Constant momentum and Constant Nesterov momentum learning rate, Invasive Scaling, Invasive Scaling momentum and Invasive Scaling Nesterov momentum learning rate, Adaptive learning, Adaptive momentum and Adaptive Nesterov momentum learning rate for various activation layers like ReLU (Rectified Linear Unit), Identity, tanh and logistic activation layer and the performance is analyzed. The MLP with a logistic activation layer under the Adaptive momentum Learning rate strategy is examined with varying regularization parameter alpha to strengthen the prediction accuracy. The proposed Stochastic Learning Strategy with Varying Regularization Logistic Activation MLP model was further analyzed with the performance metrics precision, recall, FScore, runtime and accuracy and the experimental results exhibit 97% accuracy for MLP with logistic activation layer under Adaptive momentum Learning rate toward predicting the diabetes disease.

Potentially mineralizable nitrogen: Estimation of the labile and stabilized pools under woodland and cultivated soils in Mexico

Objective: The aim of this work was to evaluate nitrogen pool and its variation due to land uses in different soil orders. Design/methodology/approach: Alfisols, Entisols and Inceptisols under different uses (woodland and cultivated soils) were incubated for 20 weeks under controlled temperature and humidity. The mineralizable N (NO3--N and NH4+-N) was obtained and the potentially mineralizable nitrogen (N0) was estimated by the method of iterative adjustment. Nitrogen from 0 to 5 weeks was considered as labile nitrogen, and from 5 to 20 weeks was the stabilized nitrogen. The labile nitrogen was described by a potential model, while the stabilized nitrogen was described by a logistic model. The labile nitrogen and stabilized nitrogen pools were estimated after obtaining the first derivate and solving the integral of the potentially mineralizable nitrogen equation. Results: The greatest estimated amounts of labile and stabilized nitrogen were detected in an Alfisol under woodland use, and the minimum values were obtained in an Entisol under agricultural use. Similar results were obtained for the estimated amount of labile and stabilized nitrogen pool. Limitations on study/implications: It is important to measure the labile and stabilized fraction of nitrogen, which requires long-term incubations to obtain models of soil N pools, so other methods realiable and faster need to be considered. Findings/conclusions: The potentially mineralizable nitrogen was positively related to the different fractions of labile and stabilized nitrogen under the different land uses.

Comparison of Race-neutral Versus Race-specific Spirometry Equations for Evaluation of Child Asthma.

Race-based estimates of pulmonary function in children could influence the evaluation of asthma in children from racial and ethnic minoritized backgrounds. To determine if race-neutral (GLI-Global) versus race-specific (GLI-Race-Specific) reference equations differentially impact spirometry evaluation of childhood asthma. The analysis included 8,719 children aged 5 to <12 years from 27 cohorts across the United States grouped by parent-reported race and ethnicity. We analyzed how the equations affected forced expiratory volume in 1 second (FEV1), forced vital capacity (FVC), and FEV1/FVC z-scores. We used multivariable logistic models to evaluate associations between z-scores calculated with different equations and asthma diagnosis, emergency department (ED) visits, and hospitalization. For Black children, the GLI-Global vs. Race-Specific equations estimated significantly lower z-scores for FEV1 and FVC but similar values for FEV1/FVC, thus increasing the proportion of children classified with low FEV1 by 14%. While both equations yielded strong inverse relationships between FEV1 and FEV1/FVC z-scores and asthma outcomes, these relationships varied across racial and ethnic groups (p<0.05). For any given FEV1 or FEV1/FVC z-score, asthma diagnosis and ED visits were higher among Black and Hispanic versus White children (p<0.05). For FEV1, GLI-Global equations estimated asthma outcomes that were more uniform across racial and ethnic groups. Parent-reported race and ethnicity influenced relationships between lung function and asthma outcomes. Our data show no advantage to race-specific equations for evaluating childhood asthma, and the potential for race-specific equations to obscure lung impairment in disadvantaged children strongly supports using race-neutral equations.

Prescribing patterns before the initiation of novel antidiabetic medicines in public, occupational, and private healthcare: a register study reflecting the guidelines of care in type 2 diabetes

BackgroundDisparities in access to healthcare has been implied before in Finland, a country with universal healthcare but de facto tiered primary care. Less is however known about the content of care provided in different settings. Previous studies indicate potential disparities in prescribing newer medicines between healthcare sectors. We compared the preceding prescribing patterns of patients who initiated a sodium-glucose co-transporter 2 (SGLT2) inhibitor or a glucagon-like peptide-1 (GLP-1) analogue in public, occupational, and private healthcare.MethodsWe used logistic models and patient-level register data from the city of Oulu, Finland, during 2014–2018. Among patients who initiated SGLT2 inhibitors or GLP-1 analogues, we studied whether it was a first-line treatment or if other antidiabetic medicines preceded the use. In addition, prior use of statins (a lipid-lowering medicine) and insulins were studied. Clinical guidelines for type 2 diabetes recommend in most cases metformin in first-line, and insulin only at later stages or in case of severe hyperglycaemia. Using a lipid-lowering medicine is typically recommended for all.ResultsThe examined novel antidiabetic medicines were seldom initiated in first-line, and no significant differences were observed for preceding statin use across sectors, net of patient characteristics. However, patients in the public sector were more likely to have used insulin previously compared to patients in occupational sector.ConclusionsBefore the initiation of the examined novel antidiabetic medicines, no marked differences across sectors in the use of other antidiabetic medicines or statins were observed. The higher likelihood of prior insulin use in the public sector might reflect initiation at a later stage and/or unobserved differences in clinical characteristics across patient populations.

Sex and gender disparities in health behaviors and adherence in patients recovering from percutaneous coronary intervention.

Sex-related disparities impact adherence to essential health behaviors like a cardiac-healthy diet, exercise, and smoking cessation. However, the influence of gender on these behaviors remains unexplored. The current study examined heterogeneity in adherence to health behavior over time by studying the effects of sex and gender differences among patients who have undergone percutaneous coronary intervention (PCI). A total of 512 participants (Mage = 64.37 ± 8.98; 84% male) responded to self-report questions concerning overall adherence, stress management, and dietary habits based on the Medical Outcomes Study. We added additional items to assess smoking status, medication adherence, and adequate physical activity. Assessments occurred following PCI (baseline) and 6- and 12-months post-PCI. A follow-up study also examined gender-related characteristics. Linear and logistic mixed models investigated the influence of sex, gender, their interaction, and various covariates on health behavior. Dietary behavior and medication adherence improved initially but stabilized after the first month. Physical activity improved but then decreased over time. Women and feminine individuals adhered more to stress reduction and dietary guidelines, while men and gender-conforming women (i.e., women with feminine norms) were more compliant with physical activity. The current study demonstrated that cardiac rehabilitation interventions focused on diet, physical activity, and stress reduction may benefit from taking a sex- and gender-sensitive approach. However, more evidence is needed on whether sex- and gender-sensitive interventions are beneficial in terms of improving health behavior among PCI patients. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Supplemental Material for Bayes Factors for Logistic (Mixed-Effect) Models

Supplemental Material for Bayes Factors for Logistic (Mixed-Effect) Models

Features of building a successful logistics business in the USA

The very intensive development of e-commerce and changing consumer behavior in the United States have provoked an unprecedented increase in freight traffic. This trend is increasing every year. Existing logistics models sometimes demonstrate the inability to effectively cope with the increased workload, which necessitates a rethink of traditional approaches to business organization in the area under consideration.There is no common position in the scientific community regarding optimal scaling strategies for logistics companies in the context of digital transformations. A number of researchers advocate the priority of technological modernization, while others focus on strengthening regional partner networks. The indicated contradiction is aggravated by the lack of knowledge of synergetic effects when integrating various options for action.The purpose of the study is to identify key success factors in building and scaling a logistics business in the United States through the prism of technological transformation of the industry and changes in market conditions.It is noted that companies integrating elements of classical logistics with digital platform solutions demonstrate an increase in the profitability of operations. At the same time, the critical success factor is not the volume of investments in technological modernization, but the ability to create effective synergy between various parts of the entrepreneurial model. The author’s view on the options for the development and scaling of logistics entrepreneurship in the United States is proposed.The article is of value to the heads of logistics companies, investors considering the possibility of entering this sector in the United States, as well as researchers dealing with the digital transformation of the analyzed industry.

Impact of Age of Sexual Debut on HIV Care Engagement among Sexual and Gender Minorities in Nigeria.

Sexual and gender minorities (SGM) bear a high burden of HIV. The age of anal sexual debut may influence HIV care engagement. Our objective was to evaluate this relationship to help healthcare providers promote and anticipate future HIV care engagement among at-risk SGM. The TRUST/RV368 study provided HIV testing and treatment at SGM-friendly clinics in Abuja and Lagos, Nigeria. Self-reported age of sexual debut was dichotomized as <16 or ≥16 years. Multivariable logistic models estimated adjusted odds ratios (aOR) and 95% confidence intervals (CI) for the association of sexual debut with 1) prior HIV testing history, 2) HIV testing at the clinics, 3) initiation of antiretroviral therapy (ART) within 6 months of a clinic diagnosis, 4) viral suppression within 12 months of ART initiation. Of the 2,680 participants, 30% (n=805) reported a sexual debut <16 years. Those with an <16-year debut had significantly more receptive sex partners, condomless sex, and transactional sex (all p<0.01) and were 24% less likely to have tested for HIV before enrollment (aOR: 0.76; CI: 0.62-0.93). However, <16-year debut was not associated with HIV testing, receiving ART or achieving viral suppression once engaged with TRUST/RV368 (all p>0.05). SGM with <16-year debut engaged in behaviors that could increase HIV risk and were less likely to have a history of HIV testing. However, once enrolled in SGM-friendly clinics, uptake of HIV care was not associated with <16-year debut, suggesting that SGM-friendly care models may promote HIV care engagement.

Exploring disparities in post-cancer treatment instructions: an analysis of rural vs. urban breast cancer survivors in Missouri using BRFSS data

BackgroundThere are more than 4 million breast cancer survivors in the United States. With continuing improvements in early detection and treatment, the number of breast cancer survivors will only continue to increase. Breast cancer survivors face a lifetime risk of long-term or late-effects from cancer treatments, thus post-cancer treatment care, referred to as survivorship care, is critical. Social determinants of health, including where a breast cancer survivor lives, may impact cancer survivorship care. Our purpose was to evaluate the relationship between rural/urban status and receipt of cancer survivorship care and instructions for Missouri breast cancer survivors using state-level data from a nationwide telephone survey—the Behavioral Risk Factor Surveillance System (BRFSS).MethodsMissouri included the BRFSS Cancer Survivorship Module in 2014, 2016, 2018, and 2020. Module items ask cancer survivors about receipt of a “post-cancer-treatment summary” and “follow-up instructions.” We hypothesized chances of receipt of both components would differ among four level Rural–Urban Commuting Area (RUCA) Code groups (Rural, Small-Town, Micropolitan, Metropolitan). Data from 430 breast cancer survivors over four survey years were combined and grouped according to RUCA status. Using a logistic model with a multilevel approach (after sampling weights calibration), the relationship between receipt of survivorship instructions and RUCA group was examined.Results46% of Missouri breast cancer survivors reported receipt of complete survivorship instructions. Compared to rural breast cancer survivors, micropolitan breast cancer survivors had 5.9 times higher odds of receiving survivorship instructions (p < 0.0001).ConclusionsLess than half of respondents reported receiving complete post-cancer treatment instructions. More urban respondents were more likely to receive instructions than their rural counterparts which raises questions about the quality of post-treatment care between rural and urban survivors. A sophisticated and purposeful approach to mitigating potential disparities is warranted. Receipt of cancer survivorship care plans may be impacted by rurality/urbanicity. Clinicians caring for cancer survivors living in rural or urban settings must continue to be diligent with providing personalized survivorship care.

Variational Bayesian Estimation of Quantile Nonlinear Dynamic Latent Variable Models with Possible Nonignorable Missingness

Our study presents an innovative variational Bayesian parameter estimation method for the Quantile Nonlinear Dynamic Latent Variable Model (QNDLVM), particularly when dealing with missing data and nonparametric priors. This method addresses the computational inefficiencies associated with the traditional Markov chain Monte Carlo (MCMC) approach, which struggles with large datasets and high-dimensional parameters due to its prolonged computation times, slow convergence, and substantial memory consumption. By harnessing the deterministic variational Bayesian framework, we convert the complex parameter estimation into a more manageable deterministic optimization problem. This is achieved by leveraging the hierarchical structure of the QNDLVM and the principle of efficiently optimizing approximate posterior distributions within the variational Bayesian framework. We further optimize the evidence lower bound using the coordinate ascent algorithm. To specify propensity scores for missing data manifestations and covariates, we adopt logistic and probit models, respectively, with conditionally conjugate mean field variational Bayes for logistic models. Additionally, we utilize Bayesian local influence to analyze the Ecological Momentary Assessment (EMA) dataset. Our results highlight the variational Bayesian approach’s notable accuracy and its ability to significantly alleviate computational demands, as demonstrated through simulation studies and practical applications.

Study on the effect of water on the shear behavior and microstructure of red mudstone

Red mudstone has significant hydrophilicity, that is hard at low water contents and soft and unstable at high water contents, and understanding the whole range of water content on the shear behavior of red mudstone is critical for evaluating red beds landslide stability. However, the deterioration mechanism of red mudstone in the process of gradual humidification is not clear in the whole range of water content. In this study, a series of mechanical and microscopic tests were carried out in the whole range of water content. A mechanical behavior prediction model for the entire process under the coupling of initial damage and load damage was constructed. The results show that the deterioration of shear strength, elastic modulus and strength parameters conforms to the “logistic model” curve with the increase of water content in the whole range of water content. In addition, the water sensitivity of cohesion was higher than the internal friction angle, and it gradually stabilized as water content increased. The weakening mechanism of the mechanical strength in the accelerated decline stage is the initiation and propagation of microcracks caused by mineral expansion, which leads to the corresponding shear behavior. Finally, the constructed damage model can be transformed into different yield conditions through parameter changes. The introduction of coupling damage enables the model to more accurately describe and predict the accelerated attenuation stage of red mudstone in the process of gradual humidification in the whole range of water content.

Service Quality of Express Terminal Logistics in Dongguan China Basis for Developing a New Model for Service Quality

In this study, the questionnaire was used to analyze the three groups of respondents (home delivery, self-service pick up container and post office) in Dongguan China terminal logistics from five dimensions (Tangibility, Reliability, Responsiveness, Assurance, and Empathy) in terms of their customer expectations of service quality and perceived service quality by quantitative analysis such as mean, ANOVA, and Pearson's correlation coefficient. Through the analysis, it was found that the three groups of respondents in Dongguan terminal logistics expected service quality and perceived service quality have no relationship, but there was a significant difference, among them, the gap in the Empathy dimension was the largest, followed by the Assurance dimension, the Reliability dimension, the Responsiveness dimension, and finally the Tangibility dimension has the smallest gap. The analysis of the results led to the proposal of the Dongguan terminal logistic service quality model, the larger the gap, the lower the customer satisfaction, and the greater the room for improvement. Finally, the conclusion dictated relevant suggestions, in order to achieve the purpose of improving service quality and enhance the core competitiveness of Dongguan terminal logistic enterprises.

Measuring Spatial Ability: Analysis of Spatial Ability Test for Gulf State Students Using Item Response Theory

This study evaluates the psychometric properties of the spatial ability test using the three-parameter logistic model within item response theory. The final version of the scale comprised 29 dichotomous items, administered to a sample of 2,694 male and female students from grades 5 and 6 across schools in the Arab Gulf region. The test adhered to the three-parameter model, satisfying the assumptions of unidimensionality and local independence. The item difficulty parameters ranged from -1.541 to 1.735, discrimination parameters spanned from 0.419 to 5.252, and guessing parameters varied between 0.00 and 0.346. With a marginal reliability coefficient of 0.86, the scale demonstrated strong stability. These findings indicate that the test items align with established measurement principles, supporting the spatial ability test as a valid and reliable assessment tool for measuring spatial abilities in the Gulf region. The results have important implications for educational assessment in the Arab Gulf and could guide the development of similar assessments in other educational contexts. Further research is recommended to improve the test’s precision and explore its application in diverse educational settings.

Archetypal crop trait dynamics for enhanced retrieval of biophysical parameters from Sentinel-2 MSI

We present a new method for estimating biophysical parameters from Earth Observation (EO) data using a crop-specific empirical model based on the PROSAIL Radiative Transfer (RT) model, called an ‘archetype’ model. The first-order model presented uses maximum biophysical parameter magnitude, phenological and soil parameters to describe the spectral reflectance (400–2500 nm) of vegetation over time. The approach assumes smooth variation and archetypical coordination of crop biophysical parameters over time for a given crop. The form of coordination is learned from a large sample of observations. Using Sentinel-2 observations of maize from Northeast China in 2019, we map reflectance to biophysical parameters using an inverse model operator, synchronise the parameters to a consistent time frame using a double logistic model of LAI, then derive the model archetypes as the median value of the synchronised samples. We apply the model to estimate time series of biophysical parameters for different cereal crops using an ensemble framework with a weighted K-nearest neighbour solution, and validate the results with ground measurements of different crops collected near Munich, Germany in 2017 and 2018. The results show R values greater than 0.8 for leaf area index (LAI) and leaf brown pigment content (Cbrown), with an RMSE of 0.94 m2/m2 for LAI and 0.15 for Cbrown. The chlorophyll content (Cab) and canopy water content (CCw) were retrieved at a higher level of accuracy, with R values around 0.9 and an RMSE of 6.59μg/cm2 for Cab and 0.03 g/cm2 for CCw. Comparison of forward-modelled hyperspectral reflectance with independent ground measures shows that the retrieved parameters account for 90% of the variation in canopy reflectance, with an overall RMSE of around 0.05 in reflectance units. The retrievals for all terms are mostly within 1σ when measurement and prediction uncertainty are taken into account, except for some early and late season issues in leaf and canopy water due to the complexity of canopy structure and understory during these periods. The approach provides a new form of constraint for the simultaneous estimation of biophysical parameters from EO and greatly reduces the rank of the problem. It is suitable for monitoring crop conditions where biophysical parameters vary smoothly over time consistently with each archetype form. The approach can be refined for other canopy types and canopy representations and could provide strong constraints on expected smoothly-varying canopy features to aid in the interpretation of EO signals across different regions of the electromagnetic spectrum.

Access to and utilisation of COVID-19 antigen rapid diagnostic tests (Ag-RDTs) among the general population in Phnom Penh: a cross-sectional study

ObjectivesGlobally, there is a lack of evidence regarding access to and utilisation of antigen rapid diagnostic tests (Ag-RDTs). This might hinder public health interventions to increase testing. We conducted a...

A new branch-and-Benders-cut algorithm for the time-dependent vehicle routing problem

Daily traffic congestion poses significant challenges for companies operating in urban areas. By considering predicted travel times throughout the day, route planning systems can improve delivery schedules, thereby reducing costs associated with delays and congestion. Although the time-dependent vehicle routing problem presents a more realistic model for city logistics, it also introduces significant computational challenges due to the size of the network of the associated models. This paper presents the first exact method using logic-based Benders decomposition for the time-dependent vehicle routing problem. Two problem formulations based on two, and three-index vehicle routing models are proposed and solved using a branch-and-cut procedure. Moreover, a logic-based branch-and-Benders-cut algorithm is developed. Computational experiments on real-world instances demonstrate that the proposed algorithm achieves better solutions, especially when applied to the three-index formulation. Typical optimality gaps are lower than 5% even in the bigger instances. Moreover, the paper evaluates various design choices for the algorithm and their impact on the solutions of the problem. Finally, managerial insights highlight the importance of solving time-dependent vehicle routing problem by demonstrating that congestion adds significant delays and costs to transportation systems.