On O’Brien’s OLS and GLS tests for multiple endpoints

Brent R. Logan, Ajit C. Tamhane

Source: Y. Benjamini, F. Bretz and S. Sarkar, eds., Recent Developments in Multiple Comparison Procedures (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004), 76-88.

Abstract

In this article we obtain some new results and extensions of the OLS and GLS tests proposed by O’Brien (1984), Procedures for comparing samples with multiple endpoints, for the one-sided multivariate testing problem. In particular, we empirically obtain an accurate small sample approximation to the critical point of the OLS test. Next we give a power comparison between the OLS test and a competing test proposed by Läuter (1996). Exact t and F tests for analyzing studies with multiple endpoints. Lastly, we extend the OLS and GLS tests to the heteroscedastic setup where the control and treatment populations have different covariance matrices.