Bayesian Optimal Designs for Phase I Clinical Trials

Abstract

A broad approach to the design of Phase I clinical trials for the efficient estimation of the maximum tolerated dose is presented. The method is rooted in formal optimal design theory and involves the construction of constrained Bayesian c- and D-optimal designs. The imposed constraint incorporates the optimal design points and their weights and ensures that the probability that an administered dose exceeds the maximum acceptable dose is low. Results relating to these constrained designs for log doses on the real line are described and the associated equivalence theorem is given. The ideas are extended to more practical situations, specifically to those involving discrete doses. In particular, a Bayesian sequential optimal design scheme comprising a pilot study on a small number of patients followed by the allocation of patients to doses one at a time is developed and its properties explored by simulation.

Adaptive Bayesian compound designs for dose finding studies

“…Specifically in regard to binary response data, Dixon and Mood (1948) and Robbins and Monro (1951) presented the early work in this area. More recent developments have come from Haines et al (2003) and Dror and Steinberg (2008).…”

“…Similar to the CRM, this methodology was developed with phase I cancer trials in mind. Haines et al (2003) presented formal (Bayesian) optimal design theory based on -and -optimality to estimate an MTD. They too imposed constraints to keep a low probability of an administered dose exceeding some maximum acceptable dose level and also extended their approach to adaptive trials.…”

“…In both papers, toxicity was controlled by bounding exposure to the drug, that is, not administering a dose if the estimated exposure is larger than a pre-defined tolerance level. Other approaches deal with the issue of safety by restricting the doses available for administration (as mentioned above, see Babb et al (1998) and Haines et al (2003)). Further examples include Dragalin et al (2008), who developed a twostage design approach accounting for both efficacy and safety by only selecting doses within a therapeutic range.…”

Penalized optimal designs for dose-finding

“…This is used by Haines et al (2003), with φ(x, θ) = I I [Q R (θ),∞) (x), where I I A (x) is the indicator function of the set A (1 if x ∈ A, 0 otherwise) and Q R (θ) is a quantile of the probability of toxicity, parameterized by θ, defining the maximum acceptable probability of toxicity (note that IE θ {φ(x, θ)} = ν{Q R (θ) ≤ x}, the prior probability that x exceeds Q R ).…”

Compound optimal designs for percentile estimation in dose–response models with restricted design intervals

“…In spite of an extensive amount of literature on optimal design for the binary response model on an unrestricted design space, so far there are relatively few articles concerning the topic of optimal design on restricted design spaces in this model. Extensive literature search yielded three related papers, one by Mats, Rosenberger and Flournoy (1998) where they derived the locally c-and D-optimal design for estimating the maximum tolerated dose in a Phase I clinical trial on a restricted design space, one by Haines, Perevozskaya and Rosenberger (2003) where they extend the latter approach to Bayesian c-and D-optimal designs and one by Biedermann, Dette and Zhu (2004), which deals with optimal designs with respect to a very general class of optimality criteria for the estimation of the vector of weighted parameters (…”