Minimization: A Dynamic Randomization Technique for Randomizing Patients

Randomization and stratification are necessary components for recruitment patient for most multi-armed clinical trials. The purpose of randomization methods is to eliminate selection bias and to insure a balance of measured and unobserved covariates between the treatment groups. Block and permuted block randomization with stratification are typically used to avoid selection bias and insure balance between observed and unobserved confounding variables.  However, randomization may introduce significant imbalances in patient prognostic factors, particularly in trial with smaller sample sizes, and these imbalances can reduce the validity of data analysis.

Minimization is an adaptive randomization technique designed to reduce imbalances of prognostic factors between treatment arms. Minimization is a dynamic approach, first proposed simultaneously by Taves (1974) and by Pocock & Simon (1975) which attempts to balance the treatment arms balance with respect to the stratification variables while also maintaining an overall treatment balance. An imbalance scores is computed for the possible patient allocations which represent the imbalance that would be generated in each of the treatment arms while taking into account the prognostic factors (stratifying variables).  In general, the allocation that results in the lowest imbalance score is given preference.

Implementing minimization algorithms involves more difficult computational work which is beyond the expertise of many clinical researchers.  To simplify the process of implementing minimization, Dacima has incorporated minimization algorithms in its web randomization module of its EDC software (Dacima Clinical Suite).


Taves DR, Minimization: a new method of assigning patient to treatment and control groups. Clinical Pharmacology and Therapeutics 1974; 15:443-453.

Pocock SL, Simon R.  Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics 1975; 31: 103-115.

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