Methods and Applications of Statistics in Clinical Trials, Volume 1: Concepts, Principles, Trials, and Designs

Chapter 30

Up-and-Down and Escalation Designs

Anastasia Ivanova and Assaf P. Oron

30.1 Introduction

Up-and-down (U&D) designs are widely used in both preclinical (animal) and clinical dose-finding trials. These designs operate on pre-specified set of doses of the investigational product, d₁ < ··· < d_M. The decision rules used in U&D designs are very simple and intuitive: the dose for the next subject (or cohort of subjects) is repeated, increased or decreased according to a limited number of immediately prior outcomes. The goal is to find the maximally tolerated dose (MTD). The MTD is usually defined as the dose whose probability of toxicity is closest to a prespecified rate Γ, or as the highest dose whose toxicity rate is less than Γ. This article restricts the discussion to the case Γ ≤ 0.5, typical of clinical trials. However, the methods are generic, and have been used for higher quantiles. The only underlying assumption is that the probability of toxicity is a non-decreasing function of dose in the population studied by the experiment. Hence, U&D is a nonparametric design family. The hallmark of U&D designs is that the sequence of assigned doses forms a Markov chain.

Escalation designs are often conflated with U&D designs. They also operate on a fixed dose set d₁ < ··· < d_M, and their transition rules also depend upon the number of toxicities observed on recent cohorts. However, escalation designs have strict stopping rules which also include the recipe for choosing the MTD. ...