The detection of the configuration of parameters is one of the most important problems im statistical studies. It is well known that the Akaike's information criterion (AIC) is a key tool for this problem (see [1]). Usually, the AIC is defined as: AIC(μ^) := l(μ^) -p, where l(μ^) is the log-likelihood with the maximum likelihood estimator (MLE) μ for μ,
The primary goal of a phase I clinical trial is to find the maximum tolerable dose of a treatment. In this paper, we propose a new stepwise method based on confidence bound and information incorporation to determine the maximum tolerable dose among given dose levels. On the one hand, in order to avoid severe even fatal toxicity to occur and reduce the experimental subjects, the new method is executed from the lowest dose level, and then goes on in a stepwise fashion. On the other hand,in order to improve the accuracy of the recommendation, the final recommendation of the maximum tolerable dose is accomplished through the information incorporation of an additional experimental cohort at the same dose level. Furthermore, empirical simulation results show that the new method has some real advantages in comparison with the modified continual reassessment method.
