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Wang K, Ma CX. Interval estimation of relative risks for combined unilateral and bilateral correlated data. J Biopharm Stat 2024:1-24. [PMID: 38196244 DOI: 10.1080/10543406.2023.2297789] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 12/14/2023] [Indexed: 01/11/2024]
Abstract
Measurements are generally collected as unilateral or bilateral data in clinical trials, epidemiology, or observational studies. For example, in ophthalmology studies, the primary outcome is often obtained from one eye or both eyes of an individual. In medical studies, the relative risk is usually the parameter of interest and is commonly used. In this article, we develop three confidence intervals for the relative risk for combined unilateral and bilateral correlated data under the equal dependence assumption. The proposed confidence intervals are based on maximum likelihood estimates of parameters derived using the Fisher scoring method. Simulation studies are conducted to evaluate the performance of proposed confidence intervals with respect to the empirical coverage probability, the mean interval width, and the ratio of mesial non-coverage probability to the distal non-coverage probability. We also compare the proposed methods with the confidence interval based on the method of variance estimates recovery and the confidence interval obtained from the modified Poisson regression model with correlated binary data. We recommend the score confidence interval for general applications because it best controls converge probabilities at the 95% level with reasonable mean interval width. We illustrate the methods with a real-world example.
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Affiliation(s)
- Kejia Wang
- Bristol Myers Squibb, Princeton, New Jersey, USA
| | - Chang-Xing Ma
- Department of Biostatistics, University at Buffalo, New York, USA
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2
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Sun S, Li Z, Jiang H. Homogeneity test and sample size of risk difference for stratified unilateral and bilateral data. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2142240] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Shuman Sun
- College of Mathematics and System Science, Xinjiang University, Urumqi, China
| | - Zhiming Li
- College of Mathematics and System Science, Xinjiang University, Urumqi, China
| | - Haijun Jiang
- College of Mathematics and System Science, Xinjiang University, Urumqi, China
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3
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Ma CX, Wang H. Testing the Equality of Proportions for Combined Unilateral and Bilateral Data Under Equal Intraclass correlation model. Stat Biopharm Res 2022. [DOI: 10.1080/19466315.2022.2108133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- Chang-Xing Ma
- Department of Biostatistics, The State University of New York at Buffalo, Buffalo, NY 14214, USA
| | - Huipei Wang
- Department of Biostatistics, The State University of New York at Buffalo, Buffalo, NY 14214, USA
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4
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Mou KY, Ma CX, Li ZM. Homogeneity test of relative risk ratios for stratified bilateral data under different algorithms. J Appl Stat 2021; 50:1060-1077. [PMID: 37009591 PMCID: PMC10062238 DOI: 10.1080/02664763.2021.2017412] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
Medical clinical studies about paired body parts often involve stratified bilateral data. The correlation between responses from paired parts should be taken into account to avoid biased or misleading results. This paper aims to test if the relative risk ratios across strata are equal under the optimal algorithms. Based on different algorithms, we obtain the desired global and constrained maximum likelihood estimations (MLEs). Three asymptotic test statistics (i.e. T L , T S C and T W ) are proposed. Monte Carlo simulations are conducted to evaluate the performance of these algorithms with respect to mean square errors of MLEs and convergence rate. The empirical results show Fisher scoring algorithm is usually better than other methods since it has effective convergence rate for global MLEs, and makes mean-square error lower for constrained MLEs. Three test statistics are compared in terms of type I error rate (TIE) and power. Among these statistics, T S C is recommended according to its robust TIEs and satisfactory power.
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Affiliation(s)
- Ke-Yi Mou
- College of Mathematics and System Science, Xinjiang University, Urumqi, People's Republic of China
| | - Chang-Xing Ma
- Department of Biostatistics, University at Buffalo, Buffalo, NY, USA
| | - Zhi-Ming Li
- College of Mathematics and System Science, Xinjiang University, Urumqi, People's Republic of China
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Lin YQ, Zhang YS, Tian GL, Ma CX. Fast QLB algorithm and hypothesis tests in logistic model for ophthalmologic bilateral correlated data. J Biopharm Stat 2020; 31:91-107. [PMID: 33001745 DOI: 10.1080/10543406.2020.1814794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Abstract
In ophthalmologic or otolaryngologic studies, bilateral correlated data often arise when observations involving paired organs (e.g., eyes, ears) are measured from each subject. Based on Donner's model , in this paper, we focus on investigating the relationship between the disease probability and covariates (such as ages, weights, gender, and so on) via the logistic regression for the analysis of bilateral correlated data. We first propose a new minorization-maximization (MM) algorithm and a fast quadratic lower bound (QLB) algorithm to calculate the maximum likelihood estimates of the vector of regression coefficients, and then develop three large-sample tests (i.e., the likelihood ratio test, Wald test, and score test) to test if covariates have a significant impact on the disease probability. Simulation studies are conducted to evaluate the performance of the proposed fast QLB algorithm and three testing methods. A real ophthalmologic data set in Iran is used to illustrate the proposed methods.
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Affiliation(s)
- Yi-Qi Lin
- Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T, Hong Kong, P. R. China
| | - Yu-Shun Zhang
- Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, Guangdong Province, P. R. China
| | - Guo-Liang Tian
- Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, Guangdong Province, P. R. China
| | - Chang-Xing Ma
- Department of Biostatistics, The State University of New York at Buffalo, Buffalo, New York, USA
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Yang Z, Tian GL, Liu X, Ma CX. Simultaneous confidence interval construction for many-to-one comparisons of proportion differences based on correlated paired data. J Appl Stat 2020; 48:1442-1456. [DOI: 10.1080/02664763.2020.1795815] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Zhengyu Yang
- Department of Biostatistics, School of Public Health and Health Professions, University at Buffalo, Buffalo, NY, USA
| | - Guo-Liang Tian
- Department of Biostatistics, School of Public Health and Health Professions, University at Buffalo, Buffalo, NY, USA
| | - Xiaobin Liu
- Department of Biostatistics, School of Public Health and Health Professions, University at Buffalo, Buffalo, NY, USA
| | - Chang-Xing Ma
- Department of Biostatistics, School of Public Health and Health Professions, University at Buffalo, Buffalo, NY, USA
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Xue Y, Ma CX. Interval estimation of proportion ratios for stratified bilateral correlated binary data. Stat Methods Med Res 2019; 29:1987-2014. [DOI: 10.1177/0962280219882043] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Confidence interval (CI) methods for the ratio of two proportions in the presence of correlated bilateral binary data are constructed for comparative clinical trials with stratified design. Simulations are conducted to evaluate the performance of the presented CIs with respect to mean coverage probability (MCP), mean interval width (MIW), and the ratio of mesial non-coverage probability to the distal non-coverage probability (RMNCP). Based on the empirical results, we suggest the use of the proposed CI method based on the complete score statistics (CS) for general applications. An example from a rheumatology study is used to demonstrate the proposed methodologies.
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Affiliation(s)
- Yuqing Xue
- Department of Biostatistics, University at Buffalo, Buffalo, NY, USA
| | - Chang-Xing Ma
- Department of Biostatistics, University at Buffalo, Buffalo, NY, USA
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Shen X, Ma CX, Yuen KC, Tian GL. Common risk difference test and interval estimation of risk difference for stratified bilateral correlated data. Stat Methods Med Res 2018; 28:2418-2438. [PMID: 29916335 DOI: 10.1177/0962280218781988] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Bilateral correlated data are often encountered in medical researches such as ophthalmologic (or otolaryngologic) studies, in which each unit contributes information from paired organs to the data analysis, and the measurements from such paired organs are generally highly correlated. Various statistical methods have been developed to tackle intra-class correlation on bilateral correlated data analysis. In practice, it is very important to adjust the effect of confounder on statistical inferences, since either ignoring the intra-class correlation or confounding effect may lead to biased results. In this article, we propose three approaches for testing common risk difference for stratified bilateral correlated data under the assumption of equal correlation. Five confidence intervals of common difference of two proportions are derived. The performance of the proposed test methods and confidence interval estimations is evaluated by Monte Carlo simulations. The simulation results show that the score test statistic outperforms other statistics in the sense that the former has robust type I error rates with high powers. The score confidence interval induced from the score test statistic performs satisfactorily in terms of coverage probabilities with reasonable interval widths. A real data set from an otolaryngologic study is used to illustrate the proposed methodologies.
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Affiliation(s)
- Xi Shen
- 1 Department of Biostatistics, The State University of New York at Buffalo, Buffalo, NY, USA
| | - Chang-Xing Ma
- 1 Department of Biostatistics, The State University of New York at Buffalo, Buffalo, NY, USA
| | - Kam C Yuen
- 2 Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, P. R. China
| | - Guo-Liang Tian
- 3 Department of Mathematics, Southern University of Science and Technology, Shenzhen, Guangdong Province, P. R. China
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Liu X, Yang Z, Liu S, Ma CX. Exact methods of testing the homogeneity of prevalences for correlated binary data. J STAT COMPUT SIM 2017. [DOI: 10.1080/00949655.2017.1351971] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
| | - Zhengyu Yang
- Department of Biostatistics, University at Buffalo – The State University of New York, Buffalo, NY, USA
| | - Song Liu
- Department of Biostatistics and Bioinformatics, Roswell Park Cancer Institute, Buffalo, NY, USA
| | - Chang-Xing Ma
- Department of Biostatistics, University at Buffalo – The State University of New York, Buffalo, NY, USA
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10
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Shen X, Ma CX. Testing homogeneity of difference of two proportions for stratified correlated paired binary data. J Appl Stat 2017. [DOI: 10.1080/02664763.2017.1371679] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Xi Shen
- Department of Biostatistics, School of Public Health and Health Professions, University at Buffalo, Buffalo, NY, USA
| | - Chang-Xing Ma
- Department of Biostatistics, School of Public Health and Health Professions, University at Buffalo, Buffalo, NY, USA
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