Evaluation of a multi-arm multi-stage Bayesian design for phase II drug selection trials - an example in hemato-oncology

Abstract

Background: Multi-Arm Multi-Stage designs aim at comparing several new treatments to a common reference, in order to select or drop any treatment arm to move forward when such evidence already exists based on interim analyses. We redesigned a Bayesian adaptive design initially proposed for dose-finding, focusing our interest in the comparison of multiple experimental drugs to a control on a binary criterion measure.

Methods: We redesigned a phase II clinical trial that randomly allocates patients across three (one control and two experimental) treatment arms to assess dropping decision rules. We were interested in dropping any arm due to futility, either based on historical control rate (first rule) or comparison across arms (second rule), and in stopping experimental arm due to its ability to reach a sufficient response rate (third rule), using the difference of response probabilities in Bayes binomial trials between the treated and control as a measure of treatment benefit. Simulations were then conducted to investigate the decision operating characteristics under a variety of plausible scenarios, as a function of the decision thresholds.

Results: Our findings suggest that one experimental treatment was less efficient than the control and could have been dropped from the trial based on a sample of approximately 20 instead of 40 patients. In the simulation study, stopping decisions were reached sooner for the first rule than for the second rule, with close mean estimates of response rates and small bias. According to the decision threshold, the mean sample size to detect the required 0.15 absolute benefit ranged from 63 to 70 (rule 3) with false negative rates of less than 2 % (rule 1) up to 6 % (rule 2). In contrast, detecting a 0.15 inferiority in response rates required a sample size ranging on average from 23 to 35 (rules 1 and 2, respectively) with a false positive rate ranging from 3.6 to 0.6 % (rule 3).

Conclusion: Adaptive trial design is a good way to improve clinical trials. It allows removing ineffective drugs and reducing the trial sample size, while maintaining unbiased estimates. Decision thresholds can be set according to predefined fixed error decision rates.

Trial registration: ClinicalTrials.gov Identifier: NCT01342692 .

Keywords: Adaptive design; Bayesian; Drop/select drug; MAMS.

Figures

Fig. 1

Guide calibration of the prior variance according to the prior mean and the prior information translated into the so-called effective sample size (ESS) – For instance, when prior mean is 0.50, the variance is 0.125, 0.083, 0.042, and 0.027 for a prior effective sample size of 1, 2, 5 and 10, respectively

Fig. 2

MDS trial- Sensitivity analyses of the distribution of response rate in each treatment arm according to the prior choice in terms of location (non-informative centered on 0.5, skeptical centered on 0.3 or enthusiastic centered on 0.45) and effective sample size (ESS ranging from 1–5 in experimental arms up to 10 in control). Upper plots display the prior densities while lower plots display the posterior densities. The left plots refer to the non-informative situation in which all of the three priors are uniform over [0,1] (Be (1,1)) or distributed according to Jeffreys prior (Be (1/2,1/2); the middle and right plots refer to the situations in which the priors were either skeptical (middle plots) or enthusiastic (right plots); each uses various effective sample sizes (ESS) denoting various amounts of prior information

Fig. 3

Results of the MDS trial- Bayesian analyses using non-informative uniform priors, the minimum required treatment response rate at MRT=0.3 (Rule 1), the targeted minimal response rate at Δ=0 (Rule 2), and a sufficient treatment response rate at STR=0.15 (Rule 3), with the cut-off probability thresholds for rules 1–3 set at 0.9, 0.1 and 0.9, respectively

Fig. 4

Posterior stopping rules according to the actual treatment benefit and sample size; the left plots refer to decision criterion 1 with p0=0.15, the middle plots refer to criterion 2 with Δ=0, and the right plots refer to criterion 3 with δ*=0.15. The mean estimates are from N=10,000 independent simulations for each actual benefit (dB)