An Allocation Method for Balancing Prognostic Variables Including Continuous Ones among Treatment Groups Using the Kullback-Leibler Information

Abstract

We propose an allocation method for balancing prognostic variables among treatment groups in clinical trials under the condition that some prognostic variables are continuous and others are categorical. In principle, the proposed method utilizes the sum Sr, with respect to groups, of the Kullback-Leibler information (KLI) from the group-pooled distribution of prognostic variables to the group-specific distribution as the criterion for overall balancing, assuming normal and multinomial distributions, respectively. In the realized procedure, the proposed method allocates sequentially enrolled new subjects to a group with probability Pa so as to achieve the minimum of Sr under the condition that the maximum difference of the number of subjects among groups is in the prespecified allowable range DN . Monte-Carlo simulation studies were conducted in order to compare the performance of the proposed method with the Pocock-Simon method which was the most popular method. The homogeneity test of mean and variance among groups for evaluating the achieved balance showed greater P values in the proposed method than those in the Pocock-Simon method. The parameter estimates of treatment effect adjusted for prognostic variables were also likely to be more stable in the proposed method than in the Pocock-Simon method.