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Biometrika 1988 75(2):295-302; doi:10.1093/biomet/75.2.295
© 1988 by Biometrika Trust
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Constructing exact significance tests with restricted randomization rules

CYRUS R. MEHTA, NITIN R. PATEL and L. J. WEI

Harvard University, Dana-Farber Cancer Institute 44 Binney Street, Boston, Massachusetts 02115, U.S.A.
Indian Institute of Management Ahmedabad, 380015 India
Department of Biostatistics, University of Michigan Ann Arbor, Michigan 48109, U.S.A.

In a clinical trial comparing two treatments, suppose that subjects are assigned sequentially to the treatment groups by a restricted randomization rule. Under the randomization model, an efficient recursive algorithm is provided to generate the exact permutational distribution for linear rank statistics, given the final imbalance between the number of patients in the two groups. If only the significance level of the test is required, the efficiency of the algorithm can be improved significantly. In general, by the time the size of the trial reaches 30, the large-sample approximation to the permutation distribution (Wei, Smythe & Smith, 1986) is satisfactory. The new procedure is illustrated by censored survival data from a prostatic cancer clinical trial. We show that, if the study subjects are not a random sample from a well-defined population, then the treatment allocation rule used at the design stage should not be ignored in the analysis.

Key Words: Biased coin design • Exact permutational test • Linear rank statistic • Network algorithm • Randomization model • Urn design


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