Group sequential large sample T2-like chi2 tests for multivariate observations.
In many studies, a K degree of freedom large sample chi2 test is used to assess the effect of treatment on a multivariate response, such as an omnibus T2-like test of a difference between two treatment groups in any of K repeated measures. Alternately, a K df chi2 test may be used to test the equality of K+1 groups in a single outcome measure. Jennison and Turnbull (Biometrika 1991; 78: 133-141) describe group sequential chi2 and F-tests for normal errors linear models, and Proschan, Follmann and Geller (Statist. Med. 1994; 13: 1441-1452) describe group sequential tests for K+1 group comparisons. These methods apply to sequences of statistics that can be characterized as having an independent increments variance-covariance structure, thus simplifying the computation of the sequential variance-covariance matrix and the resulting sequential test boundaries. However, many commonly used statistics do not share this structure, including a Liang-Zeger (Biometrika 1986; 73: 13-22) GEE longitudinal analysis with an independence working correlation structure and a Wei-Lachin (J. Amer. Statist. Assoc. 1984; 79: 653-661) multivariate Wilcoxon rank test, among others. For such analyses, this paper describes the computation of group sequential boundaries for the interim analysis of emerging results using K df tests that are expressed as quadratic forms in a statistics vector that is distributed as multivariate normal, at least asymptotically. We derive the elements of the covariance matrix of multiple successive K df chi2 statistics based on established theorems on the distribution of quadratic forms. This covariance matrix is estimated by augmenting the data from the successive interim analyses into a single analysis from which the component sequential tests and their variance-covariance matrix can then be extracted. Boundary values for the sequential statistics can then be computed using the method of Slud and Wei (J. Amer. Statist. Assoc. 1982; 77: 862-868) or using the alpha-spending function of Lan and DeMets (Biometrika 1983; 70: 659-663) with a surrogate measure of information. An example is presented using the analysis of repeated cholesterol measurements in a clinical trial.
Lachin
John M
JM
The Biostatistics Center, The George Washington University, 6110 Executive Boulevard, Suite 750, Rockville, MD 20852, USA. jml@biostat.bsc.gwu.edu
Greenhouse
Samuel W
SW
Bautista
Oliver M
OM
D001699:Biometry / Q000379:methods*; D016009:Chi-Square Distribution; D002784:Cholesterol / Q000097:blood; D006801:Humans; D008137:Longitudinal Studies; D015233:Models, Statistical; D015999:Multivariate Analysis; D018709:Statistics, Nonparametric
D002784:Cholesterol