A New Approach to Dose Finding For Phase I Clinical Trials

In a phase I clinical trial, we are interested in finding a dose J-L that will produce toxicity at an acceptable probability level r in the target population. In this paper, we investigate different estimators of the target dose 1-l to be used with the up-and-down Biased Coin Design (BCD) introduced by Durham and Flournoy (1994). These estimators of 1-l are derived using isotonic regression, maximum likelihood, weighted lea.c:;t squares and the simple empirical mean. Given a vector of probability of toxicity at the different doses,we show how to derive the exact distribution of these (and many other) estimators in the BCD setting. However, due to computational limitations, for modest samples (n > 15) the exact method becomes infeasible and bootstrap methods are used. A modified isotonic regression estimate is shown to perform very well, in terms of mean square error (MSE) and average time to converge, in all the scenarios we have studied. Key Words: Up-and-down design, isotonic regression, sequential estimation, quantal estimation, logistic regression, experimental design.