Abstract
Multivariate one-sided hypothesis-testing problems are very common in clinical trials with multiple endpoints. The likelihood ratio test (LRT) and union-intersection test (UIT) are widely used for testing such problems. It is argued that, for many important multivariate one-sided testing problems, the LRT and UIT fail to adapt to the presence of subregions of varying dimensionalities on the boundary of the null parameter space and thus give undesirable results. Several improved tests are proposed that do adapt to the varying dimensionalities and hence reflect the evidence provided by the data more accurately than the LRT and UIT. Moreover, the proposed tests are often less biased and more powerful than the LRT and UIT.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bloch DA, Lai TL, Tubert-Bitter P (2001) One-sided tests in clinical trials with multiple endpoints. Biometrics 57:1039–1047
Hsu JC (1996) Multiple comparisions – theory and methods. Chapman and Hall, London
Murphy SA, Johnson LC, Wu L, Fan JJ, Lohan J (2003) Bereaved parents’ outcomes 4 to 60 months after their children’s deaths by accident, suicide, or homicide: a comparative study demonstrating differences. Death Stud 27:39–61
O’Brien PC (1984) Procedures for comparing samples with multiple endpoints. Biometrics 40:1079–1087
Perlman MD (1969) One-sided testing problems in multivariate analysis. Ann Stat 40:549–567
Perlman MD, Wu L (1999) The Emperor’s new tests (with discussion). Stat Sci 14:355–381
Perlman MD, Wu L (2003) On the validity of the likelihood ratio and maximum likelihood methods. J Stat Plan Inf 117:59–81
Perlman MD, Wu L (2004) A note on one-sided tests with multiple endpoints. Biometrics 60:276–280
Robertson T, Wright FT, Dykstra RL (1988) Order-restricted statistical inference. Wiley, New York
Shimodaira H (2000) Approximately unbiased one-sided tests of the maximum of normal means using iterated bootstrap corrections. Technical report no. 2000–07, Department of Statistics, Stanford University, Stanford
Shimodaira, Hasegawa (1999) Multiple comparisons of log-likelihoods with applications to phylogenetic inference. Mol Biol Evol 16:1114–1116
Tamhane AC, Logan BR (2004) A superiority-equivalence approach to one-sided tests on multiple endpoints in clinical trials. Biometrika 91:715–727
Tang D-I (1994) Uniformly more powerful tests in a one-sided multivariate problem. J Am Stat Assoc 89:1006–1011
Wollan PC, Dykstra RL (1987) Algorithm AS 225. Appl Stat 36: 234–240
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Perlman, M.D., Wu, L. Some Improved Tests for Multivariate One-Sided Hypotheses. Metrika 64, 23–39 (2006). https://doi.org/10.1007/s00184-006-0028-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-006-0028-0