Bayesian adaptive dose‐escalation procedures for binary and continuous responses utilizing a gain function

Abstract

One of the main aims of early phase clinical trials is to identify a safe dose with an indication of therapeutic benefit to administer to subjects in further studies. Ideally therefore, dose-limiting events (DLEs) and responses indicative of efficacy should be considered in the dose-escalation procedure. Several methods have been suggested for incorporating both DLEs and efficacy responses in early phase dose-escalation trials. In this paper, we describe and evaluate a Bayesian adaptive approach based on one binary response (occurrence of a DLE) and one continuous response (a measure of potential efficacy) per subject. A logistic regression and a linear log-log relationship are used respectively to model the binary DLEs and the continuous efficacy responses. A gain function concerning both the DLEs and efficacy responses is used to determine the dose to administer to the next cohort of subjects. Stopping rules are proposed to enable efficient decision making. Simulation results shows that our approach performs better than taking account of DLE responses alone. To assess the robustness of the approach, scenarios where the efficacy responses of subjects are generated from an Emax model, but modelled by the linear log-log model are also considered. This evaluation shows that the simpler log-log model leads to robust recommendations even under this model showing that it is a useful approximation to the difficulty in estimating Emax model. Additionally, we find comparable performance to alternative approaches using efficacy and safety for dose-finding.

Bayesian adaptive dose‐escalation designs for simultaneously estimating the optimal and maximum safe dose based on safety and efficacy

“…Since samples of mean efficacy responses will be generated via Markov chain Monte Carlo (MCMC) technique (described in detail in the next subsection), for consistency between the two responses, we will also generate samples of ϕ 1 and ϕ 2 via MCMC instead of using the prior or the posterior modal estimates for our evaluations. For the toxicity response and also described in Yeung et al, the joint prior distribution function of the two model parameters was derived by a change of variable assuming 2 independent beta distributions for the probabilities of DLTs at the lowest and highest dose level. The form of the joint prior distribution function was given in Tsutakawa .…”

“…( In these publications, the focus was on phase 1 dose‐finding study aiming to find the MTD with small sample sizes, and the value of 5 was considered as appropriate to obtain “accurate enough” estimates of the MTD at the end of the study. In addition, Yeung et al also used the value of 5 for the ratio for the optimal dose, the dose that represents the best trade‐off of SE. Clearly, in practice, the value chosen for the ratio should be based on the desired accuracy and the practical sample size considered.…”

“…First of all, we will evaluate the performance of the single‐objective approach. In particular, we evaluate the SE approach based on a parametric log‐log model (as described in Yeung et al and based on the flexible model described here. These approaches are also compared to a standard DLT‐based approach (SO approach) not given here but can be requested from the first author.…”

“…In a recent paper for binary DLT and continuous efficacy responses, we introduced a modified version of Zhou et al, which uses a 2‐parameter logistic regression model to describe the relationship between the probabilities of the occurrence of DLT and their corresponding dose levels. A linear log‐log model is used for the continuous dose‐efficacy relationship as a simple approximation to an E m a x model.…”

“…The paper concludes with a discussion in Section 6. Note that our focus is comparing our single‐objective against our dual‐objective approach given that different single‐objective parametric approaches have already been evaluated in Yeung et al Furthermore, no direct comparisons to other dual‐objective approaches are possible due to a lack of alternatives found in the literature. Indirect comparison of the dual‐objective approaches with other existing single‐objective approaches from the literature can be achieved by comparing results from this and our last published work …”