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Search Results (3)

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Keywords = Donner’s model

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23 pages, 2188 KB  
Article
Statistical Analysis of a Generalized Linear Model for Bilateral Correlated Data Under Donner’s Model
by Jinlong Cheng, Zhiming Li and Keyi Mou
Axioms 2025, 14(7), 500; https://doi.org/10.3390/axioms14070500 - 26 Jun 2025
Viewed by 315
Abstract
Paired data often arise in medical studies, with a correlation between responses of paired organs or parts. Under an intra-correlated model, this paper proposes a generalized linear model to investigate probable confounding factors of the individual response rates in paired data. The main [...] Read more.
Paired data often arise in medical studies, with a correlation between responses of paired organs or parts. Under an intra-correlated model, this paper proposes a generalized linear model to investigate probable confounding factors of the individual response rates in paired data. The main link functions include logistic, log–log, complementary log–log, probit, and double exponential. The estimators of model parameters are calculated through the Newton–Raphson, quadratic lower bound, and Fisher bounded algorithms. Then, three tests (i.e., likelihood ratio test, Wald-type test, and score test) are constructed to analyze whether covariates significantly affect the response rate. Finally, the proposed methods are illustrated by numerical simulation and visual impairment data from Iran. Full article
(This article belongs to the Special Issue Recent Stochastic and Statistical Approaches for Modeling Complex Systems and Dependent Variables)
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16 pages, 362 KB  
Article
Homogeneity Test of Ratios of Two Proportions in Stratified Bilateral and Unilateral Data
by Huipei Wang and Chang-Xing Ma
Mathematics 2024, 12(17), 2719; https://doi.org/10.3390/math12172719 - 30 Aug 2024
Viewed by 1084
Abstract
In paired-organ studies such as ophthalmology, otolaryngology, and rheumatology, etc., various approaches take highly correlated bilateral data into account for homogeneity tests but are less likely to focus on combined bilateral and unilateral data structures. Also, it is necessary and important to adjust [...] Read more.
In paired-organ studies such as ophthalmology, otolaryngology, and rheumatology, etc., various approaches take highly correlated bilateral data into account for homogeneity tests but are less likely to focus on combined bilateral and unilateral data structures. Also, it is necessary and important to adjust the effect of confounders on stratified combined bilateral and unilateral data since, in these data structures, ignoring intra-class correlation and confounding effects can cause biased statistical inference. This article derived three homogeneity tests (the likelihood ratio test, the Wald test, and the score test) concerning these cooperative structure data to detect if ratios of proportions retain consistency across strata. Simulation shows that the score test provides a robust Type I error rate and satisfactory power performance. Finally, a real example is applied to demonstrate the application of these three proposed tests. Full article
(This article belongs to the Special Issue Current Research in Biostatistics)
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17 pages, 349 KB  
Article
Testing the Homogeneity of Differences between Two Proportions for Stratified Bilateral and Unilateral Data across Strata
by Xueqing Zhang and Changxing Ma
Mathematics 2023, 11(19), 4156; https://doi.org/10.3390/math11194156 - 3 Oct 2023
Cited by 2 | Viewed by 1965
Abstract
Medical comparative studies often involve collecting data from paired organs, which can produce either bilateral or unilateral data. While many testing procedures are available that account for the intra-class correlation between paired organs for bilateral data, more research needs to be conducted to [...] Read more.
Medical comparative studies often involve collecting data from paired organs, which can produce either bilateral or unilateral data. While many testing procedures are available that account for the intra-class correlation between paired organs for bilateral data, more research needs to be conducted to determine how to analyze combined correlated bilateral and unilateral data. In practice, stratification is often used in analysis to ensure participants are allocated equally to each experimental condition. In this paper, we propose three Maximum Likelihood Estimation (MLE)-based methods for testing the homogeneity of differences between two proportions for stratified bilateral and unilateral data across strata using Donner’s model. We compare the performance of these methods with a model-based method based on Generalized Estimating Equations using Monte Carlo simulations. We also provide a real example to illustrate the proposed methodologies. Our findings suggest that the Score test performs well and offers a valuable alternative to the exact tests in future studies. Full article
(This article belongs to the Section D1: Probability and Statistics)
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