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Table 1 Theoretical comparison of allocation methods

From: Simulation and minimization: technical advances for factorial experiments designed to optimize clinical interventions

  Unpredictability Balanced sample sizes across conditions Equivalent baseline characteristics across conditions Cost & complexity
Simple randomization Best; random assignment prevents predictability Poor; likely to result in differences across cells Poor; likely to result in differences across cells Best; simple to implement
Stratification with permuted blocks OK; Random order of assignments within blocks within strata reduces predictability but known block sizes increase predictability Very good; blocking improves balance, but this is mitigated by stratification Good; stratification improves equivalence on specific variables Very good; more complex, but solutions are widely available
Maximum tolerated imbalance Very good; random assignment protects against selection bias until big stick is needed. Very good; results at or below maximum tolerated imbalance of samples Poor; No better than simple randomization OK; can be implemented in a range of available software, but requires coding
Minimal sufficient balance Very good; random assignment protects against selection bias until biased coin is needed Poor; No better than simple randomization Very good; results at or below maximum tolerated inequivalence of covariates OK; can be implemented in a range of available software, but requires coding
Minimization Poor when purely deterministic; improved with incorporation of random element Very good; should promote balance, depending on algorithm Best; promotes equivalence on a large number of variables OK; can be implemented in a range of available software, but requires coding