**Sankhya: The Indian Journal of Statistics**

1996, Volume 58, Series A, Pt. 2, pp. 311--327

**WEIGHTED COMBINATION OF WILCOXON TESTS WITH INTERLABORATORY LIFETIME DATA**

By

ZHIYI ZHANG, *University of North Carolina at Charlotte*

SUMMARY. Consider a study of evaluating a new treatment against an existing one when a number of individuals are allocated to several laboratories for treatements and observation. Suppose a rank based test, the generalized Wilcoxon test, for example, is used for the hypothesis that the new treatment is more effective than the other, then the comparison of the data for the two treatments is straightforward within a given laboratory. However problem remain for combining all data across laboratories when laboratory biases exist, particularly when the biases exist in location as well as in scale. In this paper, a weighted combination of Wilcoxon tests is proposed for interlaboratory lifetime data. The test is first motivated for the case of finite uncensored data. Then for the case of censored data, a weighted combination of the generalized Wilcoxon test is proposed. The main elements of focus in this paper are 1) the respective locally most powerful weighting schemes for combining the independent rank tests across the laboratories with and without censoring; and 2) the weight consistency random under random right censoring when the usual nonparametric consistent estimators of scale are nonexistent.

*AMS (1980) subject classification.* 62G10.

*Key words and phrases.* Combined Wilcoxon tests, interlaboratory study, meta-analysis, locally most powerful rank test(LMPR), life data, censorship, consistent estimation.