Comparison of gatekeeping and other testing methods for identifying superior drug combinations in bifactorial designs with isotonic parameters

In this paper several multiple testing procedures are discussed with respect to the problem of detecting combination drug superiority for a bifactorial design with monotone gains. The testing methods include the generalized maximum test procedure (GMAXP) proposed by Soulakova (2009), and gatekeeping strategies: the general multistage gatekeeping method (GMGP) proposed by Dmitrienko et al. (2008a), and the serial Bonferroni gatekeeping method (TREE), proposed by Dmitrienko et al. (2007). The GMGP with the truncated Holm and Hochberg components is discussed. In addition, the truncated Sidak-Holm component is proposed, and shortcut alternatives to the GMGP are addressed. It is shown by simulations that the GMAXP achieves higher power if there are relatively many superior combinations, i.e., if the lower combinations are superior, while the gatekeeping methods perform better if there is a single or just a few superior combinations. While in some cases the GMGP with the truncated Sidak-Holm component outperforms the GMGP with the truncated Hochberg component, the observed power advantages are not substantial. Thus, the GMGP with the truncated Hochberg component is recommended as it can dominate the other methods when the Min test statistics are independent.