Bayesian adaptive clinical trial designs

Abstract

As the proof-of-concept stage of drug development, phase II trials focus on the evaluation of the new agent's therapeutic effects, screening out nonpromising drugs and carrying the promising ones forward to confirmative phase III trials. This thesis develops several novel Bayesian methods for phase II studies, and proposes solutions to two existing challenges in clinical trial designs.

Recent years have witnessed vast development in the statistical theories with applications to phase II clinical trial designs. Most existing phase II clinical trials use either a single- or multi-arm comparison scheme to examine the therapeutic effects of the experimental drug. Both single- and multi-arm evaluations have their own merits; for example, single-arm phase II trials are easy to conduct and often require a smaller sample size, while multi-arm trials are randomized and typically lead to a more objective comparison. To bridge the single- and double-arm schemes in one trial, two single-to-double arm designs are proposed, where the first stage takes a single-arm comparison of the experimental drug with the standard response rate (no concurrent treatment) and the second stage imposes a two-arm comparison by adding an active control arm. In the first design, the design parameters are calibrated using a new concept, the detectable treatment difference, to balance the trade-offs between futility termination, power, and sample size. In the second design, the hypotheses tests under a single-arm scheme and a double-arm scheme are different, and a Bayesian two-stage design with switching hypothesis tests to bridge the single- and double-arm schemes in one phase II clinical trial is proposed. Moreover, the “type III error rate”, defined as the probability of prematurely stopping the trial at stage 1 when the trial is supposed to move on to stage 2, is controlled. Extensive simulations on the calculations of these error rates are conducted to examine the operational characteristics of the proposed method.

One of the statistical challenges in clinical trial designs is the issue of multiplicity. Solutions to such a problem under the Bayesian paradigm are proposed. Bayesian approaches to phase II clinical trial designs are usually based on the posterior distribution of the parameter of interest and calibration of certain threshold for decision making. If the posterior probability is computed and assessed in a sequential manner, the design may involve the problem of multiplicity, which, however, is often a neglected aspect in Bayesian trial designs. To effectively maintain the overall type I error rate, solutions to the problem of multiplicity for Bayesian sequential designs and, in particular, the determination of the cutoff boundaries for the posterior probabilities, are proposed. Both theoretical and numerical methods for finding the optimal posterior probability boundaries with alpha-spending functions that mimic those of the frequentist group sequential designs are presented. The theoretical approach is based on the asymptotic properties of the posterior probability, which establishes a connection between the Bayesian trial design and the frequentist group sequential method. The numerical approach uses a sandwich-type searching algorithm, which immensely reduces the computational burden. The least-square fitting is applied to find the alpha-spending function closest to the target. The application of our method to single-arm and double-arm cases with binary and normal endpoints is discussed, and a real trial example for each case is provided.

Another challenge in clinical trial design is the inadequacy of phase II trial in screening out the ineffective treatments, as approximately 45% of all drugs that have passed phase II and entered phase III programs eventually fail. Simon's two-stage design is one of the most commonly used methods in phase II clinical trials with binary endpoints. The design tests the null hypothesis that the response rate is less than an uninteresting level, versus the alternative hypothesis that the response rate is greater than a desirable target level. From a Bayesian perspective, the posterior probabilities of the null and alternative hypotheses given that a promising result is declared in Simon's design are computed. Such a study reveals that because the frequentist hypothesis testing framework places its focus on the null hypothesis, a potentially efficacious treatment identified by rejecting the null under Simon's design could have only less than 10% posterior probability of attaining the desirable target level. Due to the indifference region between the null and alternative, rejecting the null does not necessarily mean that the drug achieves the desirable response level. To clarify such ambiguity, a Bayesian enhancement two-stage (BET) design is proposed, which guarantees a high posterior probability of the response rate reaching the target level, while allowing for early termination and sample size saving in case that the drug's response rate is smaller than the clinically uninteresting level. Moreover, the BET design can be naturally adapted to accommodate survival endpoints. Extensive simulation studies are conducted to examine the empirical performance of the design and two trial examples are presented as applications.