Homogeneity Test of Difference Between Two Correlated Proportions in Stratified Matched-Pair Studies

Abstract

Stratified matched-pair studies are often designed for adjusting stratification factors in modern medical researches. This article investigates a homogeneity test of differences between two correlated proportions in stratified matched-pair studies. We propose three test procedures, including an asymptotic test, bootstrap test, and multiple comparison procedures, and determine sample size requirements for such tests in a stratified matched-pair study. Simulation studies are conducted to evaluate the performance of the three test procedures and the accuracy of our derived sample size formulas. Empirical results show that (1) the likelihood ratio statistic is robust, while the score statistic and the modified score statistic are conservative in some cases of our considered settings; (2) the likelihood ratio statistic and the score statistic with the bootstrap method and the MaxT procedure behave satisfactorily in the sense that their type I error rates are close to the pre-given significance level; and (3) the derived sample size formulas are rather accurate. A real example from a clinical laboratory study is used to illustrate the proposed methodologies.

Testing the common risk difference of proportions for stratified uni‐ and bilateral correlated data

“…Consider two special cases of global MLEs. If m lij ≡ 0, then the global MLEs πij = n 1ij ∕n +ij in stratified binary data, see Tang et al (2013). For stratified bilateral correlated data, that is n lij ≡ 0, Xue and Ma (2019) obtained global MLEs πij and Rj by a three-order polynomial…”

“…Remark 3. Tang et al (2013) applied the Fisher scoring algorithm to obtain unconstrained MLEs δ and π1j in stratified binary data (m lij ≡ 0). In this work, the unconstrained MLEs are given by a third-order polynomial…”

“…Remark Pei et al (2008); Tang et al (2013) provided a binary structure in a stratified matched‐pair study. Tang and Qiu (2012) and Xue and Ma (2019) showed the structure of stratified bilateral data.…”

“…Tang, Li, and Tang (2010) constructed a confidence interval (CI) of relative risks. Li and Tang (2011) investigated the homogeneity test of rate ratios, and Tang, Zhang, and Li (2013) proposed several methods for testing the homogeneity of risk differences.…”

Testing Homogeneity of Proportion Ratios for Stratified Bilateral Correlated Data

“…Intraclass correlation in bilateral data has been investigated in the recent decades with various statistical methods [1][2][3][5][6][7][8][9]. Rosner proposes that a conditional probability of response at one side of paired body parts or organs gives a response at the other body parts or organs is a positive constant R time the response rate [1].…”