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The asymptotic log rank and generalized Wilcoxon tests are the standard procedures for comparing samples of possibly censored survival times. For comparison of samples of very different sizes, StatXact-5 offers an exact test that is based on a complete permutation of log rank or Wilcoxon scores (Mehta and Patel, 2002). While the asymptotic tests do not keep their nominal sizes if sample sizes differ substantially, StatXact's complete permutation test requires equal follow-up of the samples. Therefore we have developed and present two new exact tests also suitable for unequal follow-up (Heinze, Gnant and Schemper, 2003; Heinze, 2002). The first of these is an exact analogue of the asymptotic log rank test and conditions on observed risk sets, whereas the second approach permutes survival times while conditioning on the realized follow-up in each group. In an empirical study we compared the new procedures with the asymptotic log rank test, the exact complete permutation test, and an earlier proposed approach which equalizes the follow-up distributions by artificial censoring (Jennrich, 1984). Results confirmed highly satisfactory performance of the exact procedure conditioning on realized follow-up (ECF), particularly in the case of unequal follow-up. A SAS macro program performing all tests compared are available for download below. 

Heinze, G., Gnant, M., Schemper, M. (2003): "Exact logrank tests for unequal follow-up", Biometrics 59, pp.1151-1157
Heinze, G. (2002): "Exact linear rank tests for possibly heterogeneous follow-up", Technical Report 08/2002, Section for Clinical Biometrics, CeMSIIS, Medical University of Vienna
Mehta, C. and Patel, N. (2002): StatXact 5 User Manual, Cytel Software Corporation, Cambridge (MA), USA
Jennrich, R. (1984): "Some exact tests comparing survival curves in the presence of unequal right censoring", Biometrika 71, 57 - 64


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