A Local Limit Theorem for a Biased Coin Design for Sequential Tests

Abstract

In a clinical comparison of responses to two treatments, patients are admitted sequentially and given one of the two treatments. The allocation is determined randomly, to decrease the possibility of personal bias in the selection of subjects for the test. To balance the assignments, the probability of receiving one treatment is a function of the proportion of patients previously assigned to that treatment. A local limit theorem for the distribution of the number of patients assigned to the first treatment is developed.