# Test non-inferiority and sample size determination based on the odds ratio under a cluster randomized trial with noncompliance

##### Lui, K-Jong.; Chang, K-Chao.

#### Journal of Biopharmaceutical Statistics 21(1): 94-110

#### 2011

**ISSN/ISBN: 1054-3406**

PMID: 21191857

DOI: 10.1080/10543401003602623

Accession: 056149265

Because the odds ratio (OR) possesses certain desirable statistical properties, the OR has been recommended elsewhere to measure the relative treatment effect in establishing non-inferiority. For cost efficiency, we may often employ a cluster randomized trial (CRT), in which randomized units are clusters of patients. Furthermore, it is not uncommon to encounter data in which there are patients not complying with their assigned treatment. Under the Dirichlet multinomial model, we have developed a test statistic for assessing non-inferiority based on the OR between two treatments under a CRT with noncompliance. We have further derived a sample size formula accounting for both noncompliance and the intraclass correlation for a desired power 1 - β of detecting non-inferiority with respect to the OR at a nominal α level. Using Monte Carlo simulation, we have evaluated the performance of the proposed test statistic and sample size formula. Finally, we use the CRT studying the effect of vitamin A supplementation on mortality among preschool children to illustrate the use of the sample size formula given here.