Email updates

Keep up to date with the latest news and content from BMC Medical Research Methodology and BioMed Central.

Open Access Open Badges Research article

Comparison of three tests of homogeneity of odds ratios in multicenter trials with unequal sample sizes within and among centers

Zahra Bagheri, Seyyed Mohammad Taghi Ayatollahi* and Peyman Jafari

Author Affiliations

Department of Biostatistics, Shiraz University of Medical Sciences, Shiraz, Iran

For all author emails, please log on.

BMC Medical Research Methodology 2011, 11:58  doi:10.1186/1471-2288-11-58

Published: 26 April 2011



Mixed effects logistic models have become a popular method for analyzing multicenter clinical trials with binomial data. However, the statistical properties of these models for testing homogeneity of odds ratios under various conditions, such as within-center and among-centers inequality, are still unknown and not yet compared with those of commonly used tests of homogeneity.


We evaluated the effect of within-center and among-centers inequality on the empirical power and type I error rate of the three homogeneity tests of odds ratios including likelihood ratio (LR) test of a mixed logistic model, DerSimonian-Laird (DL) statistic and Breslow-Day (BD) test by simulation study. Moreover, the impacts of number of centers (K), number of observations in each center and amount of heterogeneity were investigated by simulation.


As compared with the equal sample size design, the power of the three tests of homogeneity will decrease if the same total sample size, which can be allocated equally within one center or among centers, is allocated unequally. The average reduction in the power of these tests was up to 11% and 16% for within-center and among-centers inequality, respectively. Moreover, in this situation, the ranking of the power of the homogeneity tests was BD≥DL≥LR and the power of these tests increased with increasing K.


This study shows that the adverse effect of among-centers inequality on the power of the homogeneity tests was stronger than that of within-center inequality. However, the financial limitations make the use of unequal sample size designs inevitable in multicenter trials. Moreover, although the power of the BD is higher than that of the LR when K≤6, the proposed mixed logistic model is recommended when K≥8 due to its practical advantages.