Pearson's chi-square test and rank correlation inferences for clustered data.
Pearson's chi-square test has been widely used in testing for association between two categorical responses. Spearman rank correlation and Kendall's tau are often used for measuring and testing association between two continuous or ordered categorical responses. However, the established statistical properties of these tests are only valid when each pair of responses are independent, where each sampling unit has only one pair of responses. When each sampling unit consists of a cluster of paired responses, the assumption of independent pairs is violated. In this article, we apply the within-cluster resampling technique to U-statistics to form new tests and rank-based correlation estimators for possibly tied clustered data. We develop large sample properties of the new proposed tests and estimators and evaluate their performance by simulations. The proposed methods are applied to a data set collected from a PET/CT imaging study for illustration.
Biometric Research Program, National Cancer Institute, 9609 Medical Center Drive, Rm 5W124, Bethesda, Maryland 20892, U.S.A.
Joanna H
JH
Shih
Biostatistics Research Branch National Institute of Allergy and Infectious Diseases, Bethesda, Maryland 20852, U.S.A.
Michael P
MP
Fay
D001699:Biometry; D016009:Chi-Square Distribution; D016000:Cluster Analysis; D006801:Humans; D000072078:Positron Emission Tomography Computed Tomography; D018709:Statistics, Nonparametric
Association; Chi-square test; Clustered data; Kendall's tau; Spearman rank correlation; U-statistics; Within-cluster resampling; midrank