A Bayesian predictive two‐stage design for phase II clinical trials

Abstract

In this paper, we propose a Bayesian two-stage design for phase II clinical trials, which represents a predictive version of the single threshold design (STD) recently introduced by Tan and Machin. The STD two-stage sample sizes are determined specifying a minimum threshold for the posterior probability that the true response rate exceeds a pre-specified target value and assuming that the observed response rate is slightly higher than the target. Unlike the STD, we do not refer to a fixed experimental outcome, but take into account the uncertainty about future data. In both stages, the design aims to control the probability of getting a large posterior probability that the true response rate exceeds the target value. Such a probability is expressed in terms of prior predictive distributions of the data. The performance of the design is based on the distinction between analysis and design priors, recently introduced in the literature. The properties of the method are studied when all the design parameters vary.

Bayesian vs Frequentist Power Functions to Determine the Optimal Sample Size: Testing One Sample Binomial Proportion Using Exact Methods

“…[8] to construct single-arm two-stage design for phase II of clinical trials based on binary data. In Ref.…”

“…An essential element of the method is the use of two different prior distributions for the parameter of interest, which play two distinct roles in the criteria. The importance of this distinction in sample size determination problems has been stressed by several authors (see, for instance, [4][5][6][7][8][9] among others). The rest of the chapter is organized as follows: in Section 2, we review both the frequentist conditional and predictive procedures based on power analysis to determine the optimal sample size.…”

Simulating Correlated Ordinal and Discrete Variables with Assigned Marginal Distributions

“…The Bayesian predictive approach we develop adjusts the two-stage design proposed by Sambucini (2008) to the continuous setup. In essence, in both stages we choose the optimal sample sizes in order to control the predictive probabilities of obtaining a large posterior probability that θ exceeds the target θ , under the assumption that the treatment is actually effective.…”

A randomized two‐stage design for phase II clinical trials based on a Bayesian predictive approach

“…For instance, Tan and Machin [2] proposed a Bayesian two-stage phase II design based on the posterior probability that the true response rate of the experimental treatment exceeds a target value of interest. A predictive version of this design was offered by Sambucini [3], whereas Wang et al [4] introduced a Bayesian version of Simon's designs that takes into consideration Bayesian and frequentist error rates. The simultaneous control of these two kinds of error rates was also suggested in [5].…”

“…To obtain optimal values for (n 1 , a 1 , n, a) with the use of a suitable Bayesian criterion, we resort to the two-stage single-arm design of Sambucini [3]: this was originally proposed as a predictive version of a Bayesian design developed by Tan and Machin [2] and called the Single Threshold Design (STD). For this reason, we will refer to it as the predictive STD (PSTD) (see also [22]).…”