• linear model;
  • unit-treatment additivity;
  • permuted-blocks randomization;
  • biased-coin randomization;
  • minimization;
  • randomization test

Randomization models are useful in supporting the validity of linear model analyses applied to data from a clinical trial that employed randomization via permuted blocks. Here, a randomization model for clinical trials data with arbitrary randomization methodology is developed, with treatment effect estimators and standard error estimators valid from a randomization perspective. A central limit theorem for the treatment effect estimator is also derived. As with permuted-blocks randomization, a typical linear model analysis provides results similar to the randomization model results when, roughly, unit effects display no pattern over time. A key requirement for the randomization inference is that the unconditional probability that any patient receives active treatment is constant across patients; when this probability condition is violated, the treatment effect estimator is biased from a randomization perspective. Most randomization methods for balanced, 1 to 1, treatment allocation satisfy this condition. However, many dynamic randomization methods for planned unbalanced treatment allocation, like 2 to 1, do not satisfy this constant probability condition, and these methods should be avoided. Copyright © 2012 John Wiley & Sons, Ltd.