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Research Article
Bivariate Radialsymmetric Kernel Density Estimation of Well-being Distribution and Poverty Index
Youssou Ciss
,
Mamadou Djitan Sinclair,
Mohamed Dinah Bangoura,
Aboubakary Diakhaby
Issue:
Volume 15, Issue 5, October 2026
Pages:
177-201
Received:
9 June 2026
Accepted:
24 July 2026
Published:
5 September 2026
DOI:
10.11648/j.ajtas.20261505.11
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Abstract: In two previous papers, we proposed two bivariate product kernel estimators for the bi-dimensional extension of the Foster, Greer and Thorbecke (FGT) index based respectively on classical and adaptive kernel. The Foster, Greer and Thorbecke (FGT) index was introduced in the literature for the purpose of a dominance approach to multidimensional poverty. The poverty measure utilized in this dominance method is fundamentally a generalization, from one to two dimensions, of this Foster, Greer and Thorbecke index with separate poverty aversion parameters for each dimension. This statistical method (the product kernel estimator) has the following main disadvantes: the curse of dimensionality, the complex selection of the bandwidth, and high computational costs. In this study, we focus on a bivariate radialsymmetric kernel estimator for the bi-dimensional extension of the Foster, Greer and Thorbecke index. Our new bivariate kernel estimator is developed with a classical bivariate kernel of Parzen-Rosenblatt of a probability density function (pdf) utilizing Riemann sums. We next provide complete asymptotic behaviour by establishing both almost-sure uniform and uniform mean square consistencies for the bivariate radialsymmetric kernel estimator. A simulation study indicates that the proposed bivariate kernel estimator performs favorably for small samples comparatively to the bivariate multiplicative kernel estimator.
Abstract: In two previous papers, we proposed two bivariate product kernel estimators for the bi-dimensional extension of the Foster, Greer and Thorbecke (FGT) index based respectively on classical and adaptive kernel. The Foster, Greer and Thorbecke (FGT) index was introduced in the literature for the purpose of a dominance approach to multidimensional pov...
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Research Article
The Accelerated Failure Time Regresssion Model Under the Generalised Gull Alpha Power Log Logistic Distribution for Handling Survival Data in Presence of Covariates
Teresa Wambui*,
Mutua Kilai,
Peter Gachoki
Issue:
Volume 15, Issue 5, October 2026
Pages:
202-212
Received:
3 August 2026
Accepted:
18 August 2026
Published:
11 September 2026
Abstract: This study develops a Generalised Gull Alpha Power Log-Logistic Accelerated Failure Time (GGAPLL-AFT) regression model for analysing censored survival data in the presence of covariates. The model was developed by integrating the Generalised Gull Alpha Power Log-Logistic (GGAPLL) distribution into the Accelerated Failure Time framework, thereby combining the flexibility of the GGAPLL distribution with the interpretability of AFT regression. The proposed model is intended to provide a flexible approach for survival data characterised by different hazard rate structures, including increasing, decreasing, and unimodal hazards. The mathematical formulation of the proposed model was established by deriving its cumulative distribution function, probability density function, survival function, hazard function, and conditional survival function. The AFT formulation relates the logarithm of survival time to a linear function of covariates and a GGAPLL-distributed error term, allowing covariate effects to be interpreted in terms of acceleration or deceleration of survival time. The unknown model parameters were estimated using the Maximum Likelihood Estimation (MLE) method. Since the resulting likelihood equations are nonlinear and do not have closed-form solutions, numerical optimisation was performed using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The performance of the proposed estimators was evaluated through a Monte Carlo simulation study under increasing, decreasing, and unimodal hazard scenarios. Simulations were conducted for different sample sizes and censoring levels, with estimator performance assessed using Absolute Bias (AB), Root Mean Square Error (RMSE), coverage probability, and Akaike Information Criterion (AIC). The simulation results showed that estimator performance improved as sample size increased, with reductions in bias and RMSE and coverage probabilities approaching the nominal 95% level. These findings demonstrate that the proposed GGAPLL-AFT model provides a flexible and reliable framework for parameter estimation and survival regression under diverse hazard structures.
Abstract: This study develops a Generalised Gull Alpha Power Log-Logistic Accelerated Failure Time (GGAPLL-AFT) regression model for analysing censored survival data in the presence of covariates. The model was developed by integrating the Generalised Gull Alpha Power Log-Logistic (GGAPLL) distribution into the Accelerated Failure Time framework, thereby com...
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Research Article
Modelling Mortality Risk in Malaria Patients Using Logistic Regression Model: A Case Study of Nakuru Level 6 Hospital
Issue:
Volume 15, Issue 5, October 2026
Pages:
213-230
Received:
7 August 2026
Accepted:
19 August 2026
Published:
11 September 2026
Abstract: Malaria remains a major cause of preventable illness and death in sub-Saharan Africa, yet routinely collected hospital data are not consistently integrated into objective tools for identifying patients at greatest risk of death. This study developed and internally evaluated a five-predictor logistic regression model for in-hospital mortality among malaria patients admitted to Nakuru Level 6 Hospital, Kenya. A retrospective observational design was used, drawing on electronic medical records from 1,500 patients admitted between 2020 and 2026. In-hospital death was the binary outcome, with age, sex, parasite density, haemoglobin level, and platelet count included as predictors. Fifty-four patients died, corresponding to a mortality rate of 3.6%. The original prespecified linear model showed strong discrimination (AUC = 0.922), but diagnostic testing identified significant nonlinearity for age, haemoglobin level, and platelet count. These three predictors were therefore refitted using restricted cubic splines while retaining the same five clinical predictors. The corrected nonlinear model significantly improved fit and discrimination, with an apparent AUC of 0.962. Bootstrap validation produced an optimism-corrected AUC of 0.955 and a Brier score of 0.0275, while repeated stratified cross-validation produced an AUC of 0.954 and a Brier score of 0.0273. Calibration intercepts were close to zero, although slopes below one indicated some residual optimism. Parasite density remained positively associated with mortality, sex remained non-significant, and nonlinear relationships were observed for age, haemoglobin, and platelet count. The conventional 0.5 threshold showed poor sensitivity, while lower thresholds improved detection but were not considered clinically established cut-offs. The findings support use of routine hospital data for mortality risk stratification, but external validation, possible recalibration, and prospective evaluation of clinical thresholds and utility are required before implementation in practice.
Abstract: Malaria remains a major cause of preventable illness and death in sub-Saharan Africa, yet routinely collected hospital data are not consistently integrated into objective tools for identifying patients at greatest risk of death. This study developed and internally evaluated a five-predictor logistic regression model for in-hospital mortality among ...
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Research Article
Bayesian Latent Class Models for Multiple Imputation of Multivariate Categorical Data Under Ignorable Missingness Mechanism
Daniel Fundi Murithi,
Josephine Njeri Ngure,
Victor Muthama Musau
Issue:
Volume 15, Issue 5, October 2026
Pages:
231-242
Received:
10 August 2026
Accepted:
20 August 2026
Published:
20 September 2026
DOI:
10.11648/j.ajtas.20261505.14
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Abstract: Missing data are a pervasive challenge in the analysis of multivariate categorical data and can lead to biased estimation and reduced statistical efficiency when handled inappropriately. Bayesian latent class multiple imputation provides a flexible framework for addressing this problem by exploiting the underlying latent structure of the data. However, conventional Bayesian latent class imputation models generally assume that latent class membership is independent of observed covariates, potentially limiting estimation accuracy when covariates are informative of the latent class structure. This study proposes a covariate-dependent Bayesian latent class model for multiple imputation under the MAR mechanism. The proposed approach models latent class membership using multinomial logistic regression, allowing observed covariates to influence class allocation while preserving the latent class formulation for the response variables. Bayesian inference is performed using Gibbs sampling, with Pólya--Gamma data augmentation facilitating efficient posterior estimation of the regression coefficients. The performance of the proposed model was evaluated through a comprehensive simulation study under varying strengths of covariate effects and sample sizes, and compared with the conventional Bayesian latent class model. Performance was assessed using multiple imputation inference, latent class proportion recovery, regression coefficient recovery, posterior stability, and empirical coverage probabilities. The proposed model produced unbiased inference and demonstrated improved estimation accuracy when covariates were associated with latent class membership, while maintaining performance comparable to the conventional model when covariate effects were absent. Furthermore, RMSE decreased consistently as the sample size increased, providing empirical evidence of posterior concentration and improved estimation precision. These findings demonstrate that incorporating covariates into Bayesian latent class multiple imputation provides a practical and effective extension of the conventional latent class framework for multivariate categorical data with missing values under the MAR mechanism.
Abstract: Missing data are a pervasive challenge in the analysis of multivariate categorical data and can lead to biased estimation and reduced statistical efficiency when handled inappropriately. Bayesian latent class multiple imputation provides a flexible framework for addressing this problem by exploiting the underlying latent structure of the data. Howe...
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Research Article
Machine Learning Modelling of Mental Disorders in the People of South Sudan
Atem Bul Malang*,
Timothy Kevin Kuria Kamanu,
David Musyimi Ndetei,
Zakariya Mohammed Salih Mohammed,
Stephen Wanyonyi Luketero
Issue:
Volume 15, Issue 5, October 2026
Pages:
243-256
Received:
11 August 2026
Accepted:
28 August 2026
Published:
20 September 2026
DOI:
10.11648/j.ajtas.20261505.15
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Abstract: The increase in mental health challenges among the population has raised serious concerns among educators, healthcare professionals, and lawmakers. Because of the substantial impact of mental diseases on emotions, cognition, and social relationships, creative preventative and intervention measures are required, particularly for those living in conflict-prone locations. Early detection is critical, and medical predictive analytics could change healthcare, especially given the severe impact of mental disorders on individuals. However, the conventional methods of mental illness prediction often suffer from the issue of either over-detection or under-detection and the time-consuming manual review process of patients' data during screening sessions. Therefore, the main objective of the study was to utilize machine learning approaches in the prediction of mental health problems that can complement the traditional clinical screening and diagnosis process. It developed five machine learning models namely logistic regression, Support Vector Machine, Random Forest, Decision Tree, and K-Nearest Neighbors that can be used to predict mental disorders outcomes among the people of South Sudan. They were trained and evaluated on the cross-sectional dataset collected from the South Sudan Demobilization, Disarmament and Re-integration Commission’s community surveys (DDRC, 2021). The study results show that the random forest model performs better than the other four models and the most important predictors of the target variable (mental health disorders) were, in order of influence, state, income and number of children. The study demonstrates that the use of machine learning models can help with mental health assessment, giving a patient-friendly and a solution that is scalable option for early detection. It is conceivable to integrate machine learning models into digital health platforms to help mental health providers make decisions that are informed and provide timely interventions. The research suggests that in order to enhance generalizability across diverse populations, it is necessary to incorporate multimodal information, enhance models, and utilize a variety of datasets in future investigations. AI-powered mental healthcare solutions have the potential to revolutionize the processes of diagnosing and arranging treatment for individuals with mental health issues in countries with limited resources.
Abstract: The increase in mental health challenges among the population has raised serious concerns among educators, healthcare professionals, and lawmakers. Because of the substantial impact of mental diseases on emotions, cognition, and social relationships, creative preventative and intervention measures are required, particularly for those living in conf...
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