Testing homogeneity of difference of two proportions for stratified correlated paired binary data

Common risk difference test and interval estimation of risk difference for stratified bilateral correlated data

“…Therefore, these MLEs can be computed by repeating the following steps derived by Ma and Liu 11 and Shen and Ma. 20 We can simplify the first equation into a cubic equation and obtain the MLE of π ij by solving the real root of it. Then ρ j can be updated by the Fisher scoring algorithm.…”

“…Closed-form solutions of (ρ^j,π^1j,d^) are not available. Similarly, we can employ the two-step approach of Shen and Ma 20 by updating the common d via the Newton–Raphson algorithm. Then, we apply the Fisher scoring algorithm to estimate π1j and ρ j with a given d from each stratum.…”

“…First, we consider testing homogeneity proposed by Shen and Ma. 20 For the homogeneity test, the null hypothesis is H 0 : d1=d2=d3Δ=d versus H a : some of d j s are not equal for j∈{1,2,3}, values of the three test statistics are T L = 2.83, T W = 2.93, T SC = 2.76 and the corresponding p -values are 0.24, 0.23, 0.25, respectively. We note that all p -values are greater than the nominal level α=0.05, indicating that the differences of cured ears between two groups are not correlated to the age effect.…”

Statistical methods for the bilateral correlated data

“…然 而, 有约束的最大似然估计基于所有分层的差异均为零的特殊情形, 而不是所有分层的差异都相等. 在 组内相关的假定下, 对分层配对相关数据的两个比例差异的同质性检验, Shen 和 Ma [32] 根据检验方 法 (似然比检验、 Wald 检验和得分检验) 提出 3 个可替代的最大似然估计. 更一般地, 有约束的最大似 然估计可利用分层之间相等的共同差异导出.…”

“…Shen 等 [35] 提出了 3 种检验方法 (似然比检验、对数变换的 Wald 检验和得分检验), 在相关系 数相等假设下检验分层配对相关数据的比值比同质性, 利用 Monte Carlo 模拟评估该检验方法的性 能. 结果表明, 对数变换的 Wald 检验和得分检验表现良好, 高功率且能稳健控制 I 类错误, 因此建 议使用.…”