Resampling-based methods in single and multiple testing for equality of covariance/correlation matrices.

TitleResampling-based methods in single and multiple testing for equality of covariance/correlation matrices.
Publication TypeJournal Article
Year of Publication2012
AuthorsYang Y, Degruttola V
JournalInt J Biostat
Volume8
Issue1
PaginationArticle 13
Date Published2012
ISSN1557-4679
KeywordsAIDS Vaccines, Analysis of Variance, Biostatistics, CD4 Lymphocyte Count, Clinical Trials, Phase III as Topic, Computer Simulation, Data Interpretation, Statistical, HIV Infections, HIV-1, Humans, Models, Statistical, Multivariate Analysis, Sample Size, Viral Load
Abstract

Traditional resampling-based tests for homogeneity in covariance matrices across multiple groups resample residuals, that is, data centered by group means. These residuals do not share the same second moments when the null hypothesis is false, which makes them difficult to use in the setting of multiple testing. An alternative approach is to resample standardized residuals, data centered by group sample means and standardized by group sample covariance matrices. This approach, however, has been observed to inflate type I error when sample size is small or data are generated from heavy-tailed distributions. We propose to improve this approach by using robust estimation for the first and second moments. We discuss two statistics: the Bartlett statistic and a statistic based on eigen-decomposition of sample covariance matrices. Both statistics can be expressed in terms of standardized errors under the null hypothesis. These methods are extended to test homogeneity in correlation matrices. Using simulation studies, we demonstrate that the robust resampling approach provides comparable or superior performance, relative to traditional approaches, for single testing and reasonable performance for multiple testing. The proposed methods are applied to data collected in an HIV vaccine trial to investigate possible determinants, including vaccine status, vaccine-induced immune response level and viral genotype, of unusual correlation pattern between HIV viral load and CD4 count in newly infected patients.

DOI10.1515/1557-4679.1388
Alternate JournalInt J Biostat
PubMed ID22740584
Grant ListR01-AI51164 / AI / NIAID NIH HHS / United States
R37 AI051164 / AI / NIAID NIH HHS / United States