Minimization method for balancing continuous prognostic variables between treatment and control groups using Kullback-Leibler divergence

This paper proposes a method for balancing prognostic variables between treatment and control groups in design of clinical trials. It assumes that some of prognostic variables are continuous and others are categorical and that they are independently distributed. The proposed method uses the Kullback-Leibler divergence (KLD) as the index of difference in distribution between two groups. It sequentially allocates each subject to a group using a biased coin method so as to reduce the estimate of KLD. That is, when first i subjects have been allocated to two groups and the (i + 1)th subject is enrolled, the KLD is estimated if the (i + 1)th subject was to be allocated to either of the groups, and the subject is then allocated with a certain probability, e.g. 0.80, so as to make the KLD small. Simulation studies based on the hypothetical prognostic variables and on the actual data of hyperlipidemia patients were carried out in order to compare the proposed method with the Pocock–Simon method, which transforms the continuous prognostic variables into categorical variables by dividing the whole scale into several categories. The p values of homogeneity test of means and variances were used to evaluate the achieved balance. The observed p values in the proposed method were better than those in the Pocock–Simon method. In addition to the balance, the precision of parameter estimates assuming analysis of covariance model was examined. The results showed the precision of estimators tended to be more stable in the proposed method than the Pocock–Simon method.