Abstract:
We provide a novel approach to approximate conditional randomization tests fol-
lowing Efron's randomization procedure by sampling from the conditional reference
set. We use combinatorial algebra to derive the conditional distribution of the num-
ber of subjects randomized to a treatment. The result is a simple and e±cient Monte
Carlo technique that is invariant to the total sample size, the degree of imbalance
between treatments, the choice of test statistic, or the biased coin parameter. More-
over, it provides an unbiased and strongly consistent estimator for the conditional
randomization test p{value. Additionally, the technique is easily extended to the
approximation of conditional strati¯ed randomization tests. Finally, sampling from
the conditional reference set enables the approximation of conditional randomization
tests when sequential monitoring is performed in the course of the experiment.
