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st: Stratified Wilcoxon Test
I need to carry out a stratified Wilcoxon test to compare the results in two groups. Each unit receives one of the two treatments; they are stratified by one other factor, which has three levels. The outcome measure is a continuous variable.
Specifically, I have two treatment groups in a clinical trial, with three investigator sites, and I have a duration as one of my outcome measures. I plan to do other analyses as well, but this one is absolutely required by previous commitments made by the client. Also, the stratified Wilcoxon test needed here does not appear to be the stratified Wilcoxon test used in a Cox regression analysis, but rather a stratified version of the usual Wilcoxon rank-sum test.
My initial literature search turned up no discussion in the SAS documentation (I first looked to do this in SAS), nothing on sas.com, and no detailed description of this test. A further check in the STATA 6 manuals (no, I haven't upgraded yet :-) didn't turn up what I was looking for either, so I'm turning to the list for help.
I can see several possible approaches to the problem. One is to normalize the Wilcoxon statistic for each stratum, then combine the normalized values to get another normal incorporating results from all three strata; however, one of the strata is relatively small, so I have some concern about the validity of the normal approximation there. An alternative is to treat this as an exact inference problem, and find the overall significance level either by enumeration or by simulation.
Any suggestions of references to the literature or code (in Stata, SAS, or S-Plus) would be appreciated. All I've found so far is a reference in the Stata manual to an article by Breslow in Biometrika, 1970, v. 57 pp. 579-594: "A Generalized Kruskal-Wallis Test for Comparing k Samples Subject to Unequal Patterns of Censorship." Alan Cantor's BBU book, "Extending SAS Survival Analysis Techniques for Medical Research" cites the same article, and the earlier related article by Gehan (Biometrika 1965 v. 52 pp. 203-223, "A Generalized Wilcoxon Test for Comparing Arbitrarily Singly Censored Samples"). However, both seem to function strictly in a survival analysis context (at least from the examples I've seen), not in a rank-based statistics context. I will pursue that if I don't get anything else, in case they can be applied more generally, but I'm hoping for both some other references and suggestions about implementation. (Anyone happen to know whether StatXact handles this?)
Incidentally, I'm rather surprised that I didn't find more on doing Wilxocon rank-sum type tests in a stratified fashion. Any thoughts on why this doesn't seem to be commonly discussed? It's a common technique, and stratification is a common situation.
Thanks for any advice.
Director of Biostatistics
Spectrum Pharmaceutical Research Corp.
San Antonio, TX
SAlbert at SpectrumCRO dot com
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