Testing ratio of marginal probabilities in clustered matched-pair binary data

In diagnostic methods evaluation, analysts commonly focus on the relative size of the treatment difference (ratio of marginal probabilities) between a new and an existing procedures. To assess non-inferiority (a new procedure is, to a pre-specified amount, no worse than an existing procedure) via a ratio of marginal probabilities between two procedures using clustered matched-pair binary data, four ICC-adjusted test statistics are investigated. The calculation of corresponding confidence intervals is also proposed. None of the tests considered require structural within-cluster correlation or distributional assumptions. Results of an extensive Monte Carlo simulation study illustrate that the new approaches effectively maintain the nominal Type I error even for small numbers of clusters. Thus, to design and evaluate non-inferiority via a ratio of marginal probabilities, researchers are suggested to utilize designs that have small cluster-size variability (e.g., nk≤5). Finally, to illustrate the practical application of the tests and recommendations, a real clustered matched-pair collection of data is used to illustrate testing non-inferiority.