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In clinical studies focusing on paired body parts, diseases can manifest on either both sides (bilateral) or just one side (unilateral) of the organs. Consequently, the data in these studies may consist of records from both bilateral and unilateral cases. There are two different methods of analyzing the data. One of the methods is assuming that the pair of measurements from the same subject are independent, while the other considers the correlation between paired organs. In terms of the homogeneity test of proportions, asymptotic methods have been proposed given the moderate size of data. This article extends the existing work by proposing exact methods to deal with the scenarios when the sample size is small and asymptotic methods perform poorly. The impact of the correlation assumption is also explored. Among the proposed methods, calculating p-values by replacing unknown parameters with estimated values while accounting for the correlation is recommended based on its satisfactory type I error controls and statistical powers. The proposed methods are applied to three real examples for illustration. [ABSTRACT FROM AUTHOR]

Intraclass correlation in bilateral data has been investigated in recent decades with various statistical methods. In practice, stratifying bilateral data by some control variables will provide more sophisticated statistical results to satisfy different research proposed in randomized clinical trials. In this article, we propose three test statistics (the likelihood ratio test, score test, and Wald-type test statistics) to evaluate the homogeneity of proportion ratios for stratified bilateral correlated data under an equal correlation assumption. Monte Carlo simulations of Type I error and power are performed, and the score test yields a robust outcome based on empirical Type I error and power. Lastly, two real data examples are conducted to illustrate the proposed three tests. [ABSTRACT FROM AUTHOR]

In medical clinical studies, uni‐ and bilateral data naturally occurs if each patient contributes either one or both of paired organ measurements in a stratified design. This paper mainly proposes a common test of risk differences between proportions for stratified uni‐ and bilateral correlated data. Likelihood ratio, score, and Wald‐type test statistics are constructed using global, unconstrained, and constrained maximum likelihood estimations of parameters. Simulation studies are conducted to evaluate the performance of these test procedures in terms of type I error rates and powers. Empirical results show that the likelihood ratio test is more robust and powerful than other statistics. A real example is used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

In clinical research, data are commonly collected bilaterally from paired organs or bodily parts within individual subjects. However, unilateral data arise when constraints or limiting factors impede the collection of complete bilateral data. In this article, we propose three large-sample tests and five confidence interval methods for making inferences on the common treatment effect, measured by the odds ratio, in a stratified design under integrated bilateral and unilateral data. Our simulation results show that the likelihood ratio-based and score-based tests, along with their associated confidence interval methods, demonstrate robust control of type I error and close-to-nominal coverage probabilities. We apply the proposed methods to real-world datasets of acute otitis media and myopic eyes to showcase their validity and applicability in clinical practice. [ABSTRACT FROM AUTHOR]

Bilateral correlated data frequently arise in medical clinical studies such as otolaryngology and ophthalmology. Based on an equal correlation coefficient model, this paper mainly aimed to investigate the statistical inference for the odds ratio of two proportions in bilateral correlated data, including not only three test procedures but also four confidence interval (CI) constructions. Through iterative algorithms, all unknown parameters are estimated in order to construct the likelihood ratio, score and Wald-type tests. Furthermore, the profile likelihood CI, score CI, and Wald-type CI are obtained by the bisection root-finding algorithm. We provided another Wald-type CI based on an asymptotic normality property. The performance of the proposed tests were investigated with regard to empirical type I error rate and power, and CI methods were compared in terms of mean coverage probability and mean interval width. Numerical simulations show that the score test is more robust, and has higher power than other tests. The score CI also has a shorter interval width, and its coverage probability is closer to 0.95. A real example is used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

This paper proposes asymptotic and exact methods for testing the equality of correlations for multiple bilateral data under Dallal's model. Three asymptotic test statistics are derived for large samples. Since they are not applicable to small data, several conditional and unconditional exact methods are proposed based on these three statistics. Numerical studies are conducted to compare all these methods with regard to type I error rates (TIEs) and powers. The results show that the asymptotic score test is the most robust, and two exact tests have satisfactory TIEs and powers. Some real examples are provided to illustrate the effectiveness of these tests. [ABSTRACT FROM AUTHOR]

In a parallel group study comparing a new treatment with a standard of care, missing data often occur for various reasons. When the outcome is binary, the data from such studies can be summarized into a 2 × 3 contingency table, with the missing observations in the last column. When the missingness is neither related to the outcome of interest nor related to other outcomes from the study but it is covariate dependent with the sole covariate being treatment, this type of missing data mechanism is considered as missing at random. In 2016, Tian et al. proposed three statistics to test the hypothesis that the response rate is equivalent for a parallel group study with missing data. The asymptotic limiting distributions of these test statistics were used for statistical inference. However, asymptotic approaches for testing proportions generally do not have satisfactory performance with regard to type I error rate control for a clinical trial with the sample size from small to medium. For this reason, we consider an exact approach based on maximization to provide valid and efficient statistical inference for a parallel group study with missing data. Exact approaches can guarantee the type I error rate and they are computationally feasible in this setting. We conduct extensive numerical studies to compare the performance of the exact approach based on the three statistics for a one-sided hypothesis testing problem. We conclude that the exact approach based on the likelihood ratio statistic is more powerful than the exact approach based on the other two statistics. Two real clinical trial data sets are used to illustrate the application of the proposed exact approach. [ABSTRACT FROM AUTHOR]