Small-sample confidence sets for the MTD in a phase I clinical trial

Properties of procedures for interval estimation of the maximum tolerable dose (MTD) in a Phase I clinical trial are examined, using a two-stage stochastic sampling scheme (Storer, 1989) as a paradigm for development. Although the likelihood function for the data arising from such a scheme is identical to one arising under a conditional binomial sampling assumption, intervals based on the exact distribution of the usual large-sample statistics under this assumption do not offer improvement over unadjusted intervals. However, consideration of the distribution of these statistics based on the true stochastic sampling scheme can lead to the construction of intervals with correct coverage probabilities that do not depend on the true values of the model parameters. Membership in the confidence set can be evaluated by Monte Carlo simulation at a restricted maximum likelihood estimate of the nuisance slope parameter, despite upward bias in its estimation from the up-and-down sampling scheme. The lack of information in the small-sample setting is reflected in a large proportion of confidence intervals that include infinite values for the MTD, especially when the dose-response curve is shallow. Intervals based on a likelihood ratio criterion perform best in this regard.