Homogeneity Test of Many‐to‐One Risk Differences for Correlated Binary Data under Optimal Algorithms

Abstract

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.

Comparative Analysis of Exact Methods for Testing Equivalence of Prevalences in Bilateral and Unilateral Combined Data with and without Assumptions of Correlation

“…Let L(M * ; π, ρ) represent L(M * ; π 1 = π 2 = ... = π g = π, ρ) for ease of notation. With H 0 , the maximum likelihood estimates (MLEs) can be obtained by setting the partial derivatives with respect to π i and ρ to zero and solving Equations ( 6) and (7).…”

“…In the context of bilateral data, Ma and Liu [6] derived three asymptotic methods, the likelihood ratio test, the score test, and the Wald-type test, to assess the homogeneity of prevalences of multiple groups. Mou and Li [7] compared multiple algorithms for estimating parameters and investigated asymptotic statistics for the homogeneity test of many-to-one risk differences. Liu et al [8] considered four exact approaches, the E approach, the M approach, the E + M approach, and the C approach, as alternatives to the methods proposed by Ma and Liu [6] when the sample size cannot ensure a good asymptotic approximation.…”