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.
In clinical studies, it is important to investigate the effectiveness of different therapeutic designs, especially, multiple treatment groups to one control group. The paper mainly studies homogeneity test of many-to-one risk differences from correlated binary data under optimal algorithms. Under Donner’s model, several algorithms are compared in order to obtain global and constrained MLEs in terms of accuracy and efficiency. Further, likelihood ratio, score, and Wald-type statistics are proposed to test whether many-to-one risk differences are equal based on optimal algorithms. Monte Carlo simulations show the performance of these algorithms through the total averaged estimation error, SD, MSE, and convergence rate. Score statistic is more robust and has satisfactory power. Two real examples are given to illustrate our proposed methods.
In medical clinical studies, we often encounter paired organs’ unilateral or bilateral data. For bilateral data, there exists an intraclass correlation between paired organs. Under an intraclass correlation model, this paper proposes asymptotic statistics for testing the equality of many-to-one relative risk ratios in combined unilateral and bilateral data. Furthermore, we calculate the explicit expressions of these statistics. Moreover, these procedures are adequate to solve the hypothesis problems of unilateral or bilateral data. Through comparison, the simulation results show that the score test has a robust empirical type-I error rate and sufficient power. We provide a clinical trial of acute otitis media to illustrate our proposed methods.
Gwet’s first-order agreement coefficient (AC1) is widely used to assess the agreement between raters. This paper proposes several asymptotic statistics for a homogeneity test of stratified AC1 in large sample sizes. These statistics may have unsatisfactory performance, especially for small samples and a high value of AC1. Furthermore, we propose three exact methods for small pieces. A likelihood ratio statistic is recommended in large sample sizes based on the numerical results. The exact E approaches under likelihood ratio and score statistics are more robust in the case of small sample scenarios. Moreover, the exact E method is effective to a high value of AC1. We apply two real examples to illustrate the proposed methods.
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