Predictability of designs which adjust for imbalances in prognostic factors

Minimisation is a method often used in clinical trials to balance the treatment groups with respect to some prognostic factors. In the case of two treatments, the predictability of this method is calculated for different numbers of factors, different numbers of levels of each factor and for different proportions of the population at each level. It is shown that if we know nothing about the previous patients except the last treatment allocation, the next treatment can be correctly guessed more than 60% of the time if no biased coin is used. If the two previous assignments are known to have been the same, the next treatment can be guessed correctly around 80% of the time. Therefore, it is suggested that a biased coin should always be used with minimisation. Different choices of biased coin are investigated in terms of the reduction in predictability and the increase in imbalance that they produce. An alternative design to minimisation which makes use of optimum design theory is also investigated, by means of simulation, and does not appear to have any clear advantages over minimisation with a biased coin.