Sample size determination for assessing equivalence based on proportion ratio under a randomized trial with non-compliance and missing outcomes

Sample size determination for testing equality in a cluster randomized trial with noncompliance

For administrative convenience or cost efficiency, we may often employ a cluster randomized trial (CRT), in which randomized units are clusters of patients rather than individual patients. Furthermore, because of ethical reasons or patient's decision, it is not uncommon to encounter data in which there are patients not complying with their assigned treatments. Thus, the development of a sample size calculation procedure for a CRT with noncompliance is important and useful in practice. Under the exclusion restriction model, we have developed an asymptotic test procedure using a tanh(-1)(x) transformation for testing equality between two treatments among compliers for 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 at a nominal α level. We have employed Monte Carlo simulation to evaluate the finite-sample performance of the proposed test procedure with respect to type I error and the accuracy of the derived sample size calculation formula with respect to power in a variety of situations. Finally, we use the data taken from a CRT studying vitamin A supplementation to reduce mortality among preschool children to illustrate the use of sample size calculation proposed here.

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

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.

Using the instrumental variables estimator to analyze noninferiority trials with noncompliance

The standard intent-to-treat (ITT) approach can lead to erroneous conclusions about treatment efficacy in noninferiority trials with noncompliance. Per-protocol and as-treated analyses are also known to result in biased comparisons of treatment effects. Alternative statistical methods are therefore needed to better address the effects of noncompliance in noninferiority trials. In this paper, we consider the use of the instrumental variables (IV) estimator in a noninferiority trial with a binary outcome and evaluate the performance of this approach in comparison to other conventional analytic methods. Unlike the ITT, per-protocol, and as-treated approaches, the IV method provides an unbiased estimate of the average causal effect of treatment among the subgroup of compliers and maintains the nominal type I error rate, but does increase the sample size requirements of the study as the expected proportion of noncompliers increases. Further development of the IV estimator for more general patterns of noncompliance would be useful and would encourage broader application of this method in noninferiority trials.