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Research Article
Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya
Paul Mwangi Kariuki
,
James Mwangi Kahiri*
Issue:
Volume 14, Issue 5, October 2025
Pages:
203-210
Received:
30 August 2025
Accepted:
10 September 2025
Published:
26 September 2025
Abstract: The study of causality in multivariate relationships in scientific studies involves the application of stochastic models in quantifying complex relationships. Stochastic models are becoming increasingly significant in health research due to their adaptability in practical situations and their ability to capture randomness, assess uncertainty, and inform decision-making. The models also provide reliable performance in capturing the complex determinants of malnutrition, demonstrating prediction precision and explanatory power. This study applies iterative parameter estimation methods for the multinomial regression model to investigate factors influencing childhood malnutrition in Kenya. Using data from the 2022 Kenya Demographic and Health Survey (KDHS), the research applies Newton-Raphson, Fisher’s Scoring, and Reweighted Least Squares methods to estimate parameters of the model and assess their classification performance. The study evaluates classification accuracy, goodness of fit, computational time, and predictive power of each method to identify the most reliable approach for modeling multinomial outcomes of childhood malnutrition, including stunting, wasting, underweight, and overweight. The methodological novelty of this study is the systematic comparison of iterative estimation methods, and the practical implications of selecting a method consistent with study objectives. By revealing causal relationships between malnutrition outcomes and significant demographic, socioeconomic, and environmental factors, the study aims to improve the analysis of multinomial datasets, provide accurate estimates, and support evidence-based decision-making for public health interventions in Kenya. The study results therefore, demonstrate practical policy implications for interventions toward high-risk children, prioritizing resource allocation and ensuring stronger credibility of evidence that supports nutritional policy decisions.
Abstract: The study of causality in multivariate relationships in scientific studies involves the application of stochastic models in quantifying complex relationships. Stochastic models are becoming increasingly significant in health research due to their adaptability in practical situations and their ability to capture randomness, assess uncertainty, and i...
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Research Article
Change Point Analysis of the Time to Recurrence in Colon Cancer Patients
Issue:
Volume 14, Issue 5, October 2025
Pages:
211-235
Received:
15 August 2025
Accepted:
30 August 2025
Published:
22 October 2025
DOI:
10.11648/j.ajtas.20251405.12
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Abstract: Change point analysis is essential in the identification of shifts in disease progression, particularly in assessing recurrence risk in cancer patients. This study evaluated whether the likelihood of colon cancer recurrence remains constant over time or changes across time. The Likelihood Ratio Test (LRT) was applied to detect significant changes in the hazard function, and maximum likelihood estimation was used to estimate the change points. A bootstrap resampling scheme generated the empirical distribution of the LRT statistic under the null hypothesis of no change. Simulation studies assessed the power of the LRT, showing improved accuracy with increased sample size, larger hazard differences, and centrally located change points. The proposed method was applied to a real colon cancer dataset comprising 888 patients, of whom 446 experienced recurrence. Four covariates—treatment type, number of positive nodes, extent of local spread, and time to registration—were found to be significant and were included in the change point detection analysis. Each covariate showed one significant change point based on the LRT exceeding the bootstrap critical value. In the Cox Proportional Hazards model, treatment was associated with a greater reduction in hazard after the change point, while the other covariates were associated with increased recurrence risk, with stronger effects post-change. In the Weibull Accelerated Failure Time (AFT) model, treatment was associated with a reduced hazard, while the covariates linked to increased hazard exhibited slightly weaker effects after the change. Model adequacy was evaluated using Cox–Snell and deviance residuals, Schoenfeld residuals, quantile–quantile plots, and the Grambsch–Therneau test. Models with change points performed better across all checks, except the Weibull AFT model, which failed the quantile– quantile plot test. Overall, the Cox Proportional Hazards model with covariate-specific change points provided the best fit, offering critical insight into dynamic recurrence risk patterns in colon cancer patients. These findings provide a basis for cancer surveillance agencies and public health organizations to refine screening programs and allocate resources efficiently by focusing on high-risk periods.
Abstract: Change point analysis is essential in the identification of shifts in disease progression, particularly in assessing recurrence risk in cancer patients. This study evaluated whether the likelihood of colon cancer recurrence remains constant over time or changes across time. The Likelihood Ratio Test (LRT) was applied to detect significant changes i...
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Research Article
Construction of D-Optimal Split-Plot Designs for the Second-Degree Kronecker Model Mixture Experiments in the Presence of Process Variables
Issue:
Volume 14, Issue 5, October 2025
Pages:
236-249
Received:
26 August 2025
Accepted:
5 September 2025
Published:
27 October 2025
DOI:
10.11648/j.ajtas.20251405.13
Downloads:
Views:
Abstract: Practical problems in mixture experiments are usually associated with the investigation of mixture of m ingredients, which are assumed to influence the response through the proportions in which they are blended together. Mixture experiments are modeled using Scheffe’ models or Kronecker models whichever that is applicable. In such problems, the response of mixture experiments may also be affected by the conditions under which the mixture in conducted. This creates a shift in the blending characteristics of the mixture ingredients hence affecting the end product hence the need for inclusion of these conditions during modeling of mixture experiments. The objective of this study is to construct D-optimal designs for mixture experiments in the presence of process variables. In order to achieve this, first, a combined model of the second-degree Kronecker model for mixture experiments and the second-degree polynomial in the process variables in developed. The D-optimal designs are constructed using a Monte Carlo algorithmic approach in the AlgDesign of the R-packages. The designs constructed in this study were augmented with two replications of a level of the process variable. The D-optimal designs are evaluated using their D-optimal values and their relative D-efficiencies. The results of this study illustrate the existence of two alternate designs; one replicating at (-1, -1) and (-1, 1) in Table 2 and the other replicating at (0, 0) in Table 1. In conclusion the results of this study indicate that a design replicating at different levels of the process variable performs better than the one replicating at the overall centroid.
Abstract: Practical problems in mixture experiments are usually associated with the investigation of mixture of m ingredients, which are assumed to influence the response through the proportions in which they are blended together. Mixture experiments are modeled using Scheffe’ models or Kronecker models whichever that is applicable. In such problems, the res...
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