Resumen
We introduce a new design for dose-finding in the context of toxicity studies for which it is assumed that toxicity increases with dose. The goal is to identify the maximum tolerated dose, which is taken to be the dose associated with a prespecified “target” toxicity rate. The decision to decrease, increase or repeat a dose for the next subject depends on how far an estimated toxicity rate at the current dose is from the target. The size of the window within which the current dose will be repeated is obtained based on the theory of Markov chains as applied to group up-and-down designs. But whereas the treatment allocation rule in Markovian group up-and-down designs is only based on information from the current cohort of subjects, the treatment allocation rule for the proposed design is based on the cumulative information at the current dose. We then consider an extension of this new design for clinical trials in which the subject's outcome is not known immediately. The new design is compared to the continual reassessment method.

Resumen
Let toxicity to treatment be a Bernoulli random variable for which the probability of failure increases with dose. Consider the problem of identifying a dose ? having pre-specified probability of failure using data from groups of subjects who arrive sequentially for treatment. There is considerable theory available in this setting for fully sequential up-and-down procedures. This paper presents asymptotic and finite theoretical results for Markovian up-and-down procedures when subjects are treated in groups. Practical instructions are given on how to select the design parameters so as to cause the treatments to cluster around the unknown dose ?. Examples are given to illustrate how this group procedure behaves for small sample sizes.