Novel dose-finding designs, using estimation to assign the best estimated
maximum- tolerated-dose (MTD) at each point in the experiment, most commonly
via Bayesian techniques, have recently entered large-scale implementation in
Phase I cancer clinical trials. We examine the small-sample behavior of these
"Bayesian Phase I" (BP1) designs, and also of non-Bayesian designs sharing the
same main "long-memory" traits (hereafter: LMP1s).
We examine Phase I cancer clinical trial designs that use toxicity estimates
based on all available data at each dose-allocation decision, but refrain from
employing parametric models or Bayesian decision rules. We show that one such
design family, called here "interval designs", converges almost surely to the
maximum tolerated dose under fairly general conditions. Another family called
"point designs" does not converge.