JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1168 10.6339/25-JDS1168 Statistical Data Science Analysis of Bilateral and Unilateral Data: A Comparative Review of Model-Based and MLE-Based Methods for the Homogeneity Test of Proportions ZhangXueqing MaChang-Xingcxma@buffalo.edu1∗ The State University of New York at Buffalo, Buffalo, NY, US Corresponding author. Email: cxma@buffalo.edu. 20252812025234638647 Supplementary Material

This Supplementary Material contains SAS scripts for analyzing data from two groups ( g = 2) for bilateral and unilateral m = n = 20; true event proportion π 0 = 0.5; Correlation ρ = 0.4.

Files:

‘README.txt’: The explanation of the SAS scripts.

‘sim02_20_20_0.5_0.4.sas’: Prepares the dataset for analysis.

‘analysis.sas’: Performs statistical analysis.

2992024812025 2025 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2025 Open access article under the CC BY license.

In many medical comparative studies, subjects may provide either bilateral or unilateral data. While numerous testing procedures have been proposed for bilateral data that account for the intra-class correlation between paired organs of the same individual, few studies have thoroughly explored combined correlated bilateral and unilateral data. Ma and Wang (2021) introduced three test procedures based on the maximum likelihood estimation (MLE) algorithm for general g groups. In this article, we employ a model-based approach that treats the measurements from both eyes of each subject as repeated observations. We then compare this approach with Ma and Wang’s Score test procedure. Monte Carlo simulations demonstrate that the MLE-based Score test offers certain advantages under specific conditions. However, this model-based method lacks an explicit form for the test statistic, limiting its potential for further development of an exact test.

 correlated bilateral and unilateral data generalized estimating equations MLE-based test procedures Rosner’s model References Dallal GE (1988). Paired Bernoulli trials. Biometrics, 44(1): 253–257. https://doi.org/10.2307/2531913 Donner A (1989). Statistical methods in ophthalmology: An adjusted chi-square approach. Biometrics, 45(2): 605–611. https://doi.org/10.2307/2531501 Liang K, Zeger SL (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73(1): 13–22. https://doi.org/10.1093/biomet/73.1.13 Lu W, Ning R, Diao K, Ding Y, Chen R, Zhou L, et al. (2022). Comparison of two main orthokeratology lens designs in efficacy and safety for myopia control. Frontiers in Medicine, 9: 798314. https://doi.org/10.3389/fmed.2022.798314 Ma C, Shan G, Liu S (2015). Homogeneity test for correlated binary data. PLoS ONE, 10(4): e0124337. https://doi.org/10.1371/journal.pone.0124337 Ma C, Wang K (2021). Testing the homogeneity of proportions for combined unilateral and bilateral data. Journal of Biopharmaceutical Statistics, 31(5): 686–704. https://doi.org/10.1080/10543406.2021.1946693 Mandel EM, Bluestone CD, Rockette HE, Blatter MM, Reisinger KS, Wucher FP, et al. (1982). Duration of effusion after antibiotic treatment for acute otitis media: Comparison of cefaclor and amoxicillin. The Pediatric Infectious Disease Journal, 1(5): 310–316. https://doi.org/10.1097/00006454-198209000-00006 Pei Y, Tang M, Guo J (2008). Testing the equality of two proportions for combined unilateral and bilateral data. Communications in Statistics. Simulation and Computation, 37(8): 1515–1529. https://doi.org/10.1080/03610910802140232 Rosner B (1982). Statistical methods in ophthalmology: An adjustment for the intraclass correlation between eyes. Biometrics, 38(1): 105–114. https://doi.org/10.2307/2530293 Tang N, Tang M, Qiu S (2008). Testing the equality of proportions for correlated otolaryngologic data. Computational Statistics & Data Analysis, 52(7): 3719–3729. https://doi.org/10.1016/j.csda.2007.12.017