Minimization--reducing predictability for multi-centre trials whilst retaining balance within centre

Minimization is often used to assign patients to treatment groups to ensure good balance in patient numbers within centre and other prognostic factors. Balance within centre is preferable since large imbalances between treatment arms may have logistical implications for centres, such as cost and resource implications. However, recent concern over high predictability of treatment allocation by centres when using minimization has caused this method to be questioned. We used data from current clinical trials to assess predictability and summarize subsequent within-centre imbalances with the aim of finding the most effective minimization method for reducing predictability whilst still retaining sufficient balance within centre, when randomization is to one of two treatments. We compared prediction rates and imbalances for deterministic minimization, and minimization incorporating various random elements, p (p=0.95,0.90,0.80,0.75,0.70). We also compared prediction rates and imbalance when centre was and was not included as a stratification factor. Incorporating a random element proved successful in reducing prediction rates whilst minimizing the inevitable increase in within-centre imbalance, whereas excluding centre as a stratification factor incurred major within-centre imbalance. We therefore suggest that minimization can still be used, and that centre can be included as a stratification factor, but a random element has to be incorporated into the minimization algorithm. Minimization incorporating a random element of 0.80 is the most efficient method to use based upon the simulations undertaken in this study of real clinical trial data using different probabilities of allocation.