A general class of correlation coefficients for the 2 x 2 crossover design.
The Pearson correlation coefficient and the Kendall correlation coefficient are two popular statistics for assessing the correlation between two variables in a bivariate sample. We indicate how both of these statistics are special cases of a general class of correlation statistics that is parameterized by gamma element of [0, 1]. The Pearson correlation coefficient is characterized by gamma = 1 and the Kendall correlation coefficient by gamma = 0, so they yield the upper and lower extremes of the class, respectively. The correlation coefficient characterized by gamma = 0.5 is of special interest because it only requires that first-order moments exist for the underlying bivariate distribution, whereas the Pearson correlation coefficient requires that second-order moments exist. We derive the asymptotic theory for the general class of sample correlation coefficients and then describe the use of this class of correlation statistics within the 2 x 2 crossover design. We illustrate the methodology using data from the CLIC trial of the Childhood Asthma Research and Education (CARE) Network.
Chinchilli
Vernon M
VM
Department of Health Evaluation Sciences, Penn State College of Medicine, Hershey, PA, USA. vchinchi@psu.edu
Phillips
Brenda R
BR
Mauger
David T
DT
Szefler
Stanley J
SJ
D000293:Adolescent; D001249:Asthma / Q000188:drug therapy; D002648:Child; D017326:Clinical Trials, Phase III as Topic / Q000379:methods / Q000706:statistics & numerical data; D018592:Cross-Over Studies; D006801:Humans; D015233:Models, Statistical; D016032:Randomized Controlled Trials as Topic / Q000145:classification / Q000379:methods / Q000706:statistics & numerical data*; D012107:Research Design / Q000706:statistics & numerical data*; D018709:Statistics, Nonparametric