The Potential for Increased Power by Combining Correlated Tests

• Activity Number: 447
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Guoguang Ma*+ and Jitendra Ganju
• Companies: Gilead Sciences and Gilead Sciences
• Keywords: robust inference ; small trials ; regression models

Abstract

For randomized trials, a common approach to hypothesis testing for formal inference is to identify a single test statistic thought to be optimal. Let T1, T2, . Tm denote m > 1 correlated test statistics for testing the same null hypothesis and the case where we do not know which Tj is best. Rather than relying on a single statistic, a function of the m Tjs can be used for inference. Suppose, for example, that the relationship between the response variable, the treatment X0, and the K covariates can be expressed as a linear model. The point of the paper is two-fold: (a) even when N - r(X) < =0, where N denotes the number of units and r(X) denote the rank of the full model matrix, inference can be made on X0 to reflect the influence of all covariates, and (b) when N - r(X) > 0, power can be increased, sometimes substantially, when compared with the power from a single test statistic. This is achieved by combining the positively correlated {Tj}, getting its critical value by reference to a permutation distribution. Functions of {Tj}considered are based on combined or ordered p-values. Simulation results and examples attest to the utility of the method.