Conditional Markov Chain Design for Accrual Clinical Trials

Abstract

Randomization in a comparative experiment has, as one aim, the control of bias in the initial selection of experimental units. When the experiment is a clinical trial employing the accrual of patients, two additional aims are the control of admission bias and control of chronologic bias. This can be accomplished by using a method of randomization, such as the “biased coin design” of Efron, which sequentially forces balance.As an extension of Efron's design, this paper develops a class of conditional Markov chain designs. The detailed randomization employed utilizes the sequential imbalances in the treatment allocation as states in a Markov process. Through the use of appropriate transition probabilities, a range of possible designs can be attained.An additional objective of physical randomization is to provide a model for data analysis. Such a randomization theoretic analysis is presented for the current designs. In addition, Monte Carlo sampling results are given to support the proposed normal theory approximation to the exact randomization distribution.