Cluster randomization trials: A simulation study

A simulation study is conducted to compare several methods that test the common log odds ratio in multiple 2 × 2 tables when the data are correlated within clusters. Allowing cluster size to vary within each table, we evaluate the unadjusted Mantel-Haenszel chi-square statistic (χ_MH²), the adjusted Mantel-Haenszel chi-square statistics of Rao and Scott using both an unpooled design effect (χ_RSN²) and a pooled design effect (χ_RSP²), the adjusted Mantel-Haenszel chi-square statistic of Donald and Donner (χ_DD²), the chi-square statistic using the GEE approach (χ_GEE²), the adjusted Mantel-Haenszel chi-square statistic of Begg (χ_B²), the Wald (χ_W²), the robust Wald (χ_RW²), the score (χ_S²), the robust score (χ_RS²), and the adjusted Mantel-Haenszel chi-square statistics of Zhang and Boos (χ_ZBP² and χ_ZBN²). The test statistics above are compared in terms of empirical significance levels and empirical power levels. The robust score statistic χ_RS² and the adjusted Mantel-Haenszel chi-square statistics of Zhang and Boos (χ_ZBP² and χ_ZBN²) generally have empirical significance levels closer to the nominal value than the other statistics. These three statistics have similar empirical power levels when the intrachister correlation is zero or the cluster sizes are balanced. χ_RS² performs better in terms of empirical power levels when a positive intracluster correlation exists in the imbalance setting.