Operating characteristics of the standard phase I clinical trial design

In this communication we study the statistical properties of a widely used method for Phase I clinical trials. The designs typically applied in this context are derived from fixed sample versions of the Up and Down scheme defined by Dixon and Mood (1948). Earlier investigations such as those by Wetherill (1963) and Storer (1989, 1993) concentrate mainly on the asymptotic and fixed sample properties of these procedures without dealing with the issue of early stopping. Our main focus is the standard scheme which includes a stopping rule as described by Korn et al. (1994). Since it is felt that the advantage of the stopping rule is to use less subjects and to quickly proceed to phase II trials, we study the relationship between the total number of included patients and accuracy of the final recommendation. The error probabilities can all be worked out explicitly in any given situation and are studied over a large class of possible realities. We conclude that for trials that terminate after the inclusion of relatively few subjects the risk of choosing an incorrect level is large; much larger, we suspect, than is generally believed to be the case. Furthermore, it seems that any trial using such a stopping rule and concluding after having included less than 15 subjects is too unreliable to be of any use at all.