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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