FOR CLINICAL TRIALS BASED ON MARKOV CHAINS

SUMMARY A new type of closed sequential design for clinical trials is constructed using a fundamental equation of Markov chains. The designs are easily constructed and are applicable to a wide range of sequential clinical trials. These designs should be useful in cases where a smaller variance for the sample size is desired than that given by Armitage's plan. advantages of closed sequential designs for clinical trials and each has developed a design. Bross's and Spicer's designs were constructed empirically, based on some arbitrary boundaries. Their computational processes are somewhat complicated and only a few results are published. Armitage's design was based on approximation by a diffusion process and the adequacy of the approximation has not yet been fully investigated. Applications of these designs are restricted because they require relatively large maximum sample sizes. For example, many clinical trials based on Bross's scheme were not conclusive since the sequence of preferences did not cross any boundary when the trials were ternminated. In addition, the properties of these designs are difficult to investigate theoretically. For example, the average sample number (ASN) and variance of sample number are not well investigated. In this paper, we construct a new closed sequential design based on a simple equation of Markov chains. We are concerned solely with sequential designs comparing two binomial parameters. The computational scheme is similar to one proposed by Stockman and Armitage