COMPARING TRIALS WITH MULTIPLE OUTCOMES - THE MULTIVARIATE ONE-SIDED HYPOTHESIS WITH UNKNOWN COVARIANCES

被引:10
作者
FRICK, H [1 ]
机构
[1] INST DATENANAL & VERSUCHSPLANUNG,GAUTING,GERMANY
关键词
EXTENDED OLS AND GLS TEST; WEI-LACHIN TEST;
D O I
10.1002/bimj.4710370803
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
The paper deals with a problem arising for tests in clinical trials. The outcomes of a standard and a new treatment to be compared are multivariate normally distributed with common but unknown covariance matrix. Under the null hypothesis the means of the outcomes are equal, under the alternative the new treatment is assumed to be superior, i.e. the means are larger without further quantification. For known covariance matrix there is a variety of tests for this problem. Some of these procedures can be extended to the case of unknown covariances if one is willing to accept a bias. There is, however, also an efficient unbiased test. The paper contains some numerical comparisons of these different procedures and takes a look on the minimax properties of the unbiased test.
引用
收藏
页码:909 / 917
页数:9
相关论文
共 12 条
[1]  
Frick H., A maxmin linear test and its application to Lachin's data, Communications in Statistics - Theory and Methods, 23, pp. 1021-1029, (1994)
[2]  
Kieser M., Wassmer G., Reitmeir P., (1994)
[3]  
Kudo A., A multivariate analogue of the one‐sided test, Biometrika, 50, pp. 403-418, (1963)
[4]  
Lachin J.M., Some large‐sample distribution‐free estimators and tests for multivariate partially incomplete data from two populations, Statist. Med., 11, pp. 1151-1170, (1992)
[5]  
Lehmann E.L., Testing statistical hypotheses, (1986)
[6]  
O'brien P.C., Procedures for comparing samples with multiple endpoints, Biometrics, 40, pp. 1079-1087, (1984)
[7]  
Perlman M.D., One‐sided testing problems in multivariate analysis, The Annals of Mathematical Statistics, 40, pp. 549-567, (1969)
[8]  
Schafsma W., Smid L.J., Most stringent somewhere most powerful tests against alternatives restricted by a number of linear inequalities, The Annals of Mathematical Statistics, 37, pp. 1161-1172, (1966)
[9]  
Tang D.-I., Gnecco C., Geller N.L., An approximate likelihood ratio test for a normal mean vector with nonnegative components with application to clinical trials, Biometrika, 76, pp. 577-583, (1989)
[10]  
Tang D.-I., Gnecco C., Geller N.L., Design of group sequential clinical trials with multiple end points, Journal of the American Statistical Association, 84, pp. 776-779, (1989)