Author's Rejoinder to Commentaries on 'Designs for dose-escalation trials with quantitative responses'

In a dose-escalation trial for a new drug, each successive dose is tested on a new cohort of volunteer subjects, so that if any dose produces severe adverse reactions then higher doses are not tested. However, if there are other differences between the cohorts, such as differences in environmental health factors, type of person or experimental procedure, then these differences may obscure the differences between doses. Therefore, cohorts should be fitted in the analysis, as either fixed or random effects. I suggest that, if this is done, then there are three simple principles that reduce variance (i) allocating no more than half the subjects in any cohort to any single dose; (ii) subject to safety constraints, using as many different doses as possible in each cohort; (iii) using one more cohort than the number of doses, without increasing the total number of subjects. Using these principles, I propose some new designs that conform to the safety rules of traditional dose-escalation trials while reducing the variance of the estimators of differences between the doses by a factor of two or more, for the same number of subjects. Copyright (C) 2009 John Wiley & Sons, Ltd.