Bayesian adaptive designs in multi-arm multi-stage clinical trials

Clinical trial seek to investigate novel treatments, asses the relative benefits of competing therapies, and establish optimal treatment combinations. Statistical models provide an explicit way to models patients response to a treatment, and make inference about the clinical utility of therapies which guides clinical decision making. Statistical designs for clinical trials are a formal procedure the aim to maximize the the quality of generated information on the performance of experimental treatment. We explore a particular class of clinical trial design called adaptive design, which allows modifications of one or more specified aspects of the design based on the analysis of information (usually interim data) collected from subjects in the study. The interest in adaptive design studies arises from the belief that these methods provide a promising new venue in the task of improving drug development compared to conventional non-adaptive statistical methods for the design of clinical experiments. In particular, the approach of adaptive design may increase the likelihood of a patient to be treated with a successful drug and may reduce the uncertainty on the treatment effect. The class of adaptive designs includes adaptive randomization procedures, sample size re-estimations, and sequential or group-sequential interim analysis. The Bayesian approach is ideally suited to dynamically adapt the design as information arises during a trial. Accumulated data can be used at any time to modify the design of the trial, for instance, by stopping treatment assignments to ineffective arms or unbalancing randomization towards arms with strong evidence of treatment superiority. In this thesis we focus on two particular sub-classes of Bayesian adaptive designs:Two-stage designs for phase II clinical trials and Response-adaptive randomization designs for multi arm (multi-stage) clinical trial. A bayesian approach for randomized two-stage designs: Two-stage designs are commonly used in phase II clinical trials, especially in cancer clinical trials. Standard two-stage designs, introduced in Chapter 1, involve one single experimental arm that is compared to a pre-fixed desired level. However, the rate of failure in phase III oncology trials is surprisingly high, partly owing to inadequate phase II studies. Recently, the use of randomized designs in phase II has been increasingly recommended to avoid such limitations. With the supervision of Prof. Valeria Sambucini, we proposed a randomized version of a Bayesian two-stage design due to Tan and Machin [120] (see Chapter 2 of the thesis). The design selects the two-stage sample sizes by ensuring a large posterior probability that the true response rate of the experimental treatment exceeds that of the standard agent, assuming that the experimental treatment is actually more effective (see Cellamare et al. [35]). This optimistic assumption is realized by fixing virtual outcomes in favor of the experimental arm. However, the design does not account for the uncertainty about future data. Therefore, in Chapter 3 we propose a two-arm two-stage design based on a Bayesian predictive approach (see Cellamare and Sambucini [34]). The idea is to ensure a large probability, expressed in terms of the prior predictive probability of the data, of obtaining a substantial posterior evidence in favour of the experimental treatment under the assumption that it is actually more effective than the standard agent. This design is a randomized version of the two-stage design that has been proposed for single-arm phase II trials by Sambucini [104]. We examine the main features of our novel design as all the parameters involved vary and compare our approach with Jung’s minimax and optimal designs [76]. A potential limitation of the proposed design is that the second stage sample size is determined before observing the first stage data. It can produce some paradoxical situations in which a second stage analysis is performed and additional patients recruited, despite the first stage results were already sufficient to make a final decision. As also suggested by Sambucini[105], we solve this potential problem by using an adaptive version of the Bayesian predictive two-arm two-stage design, in which the second stage sample size is selected after the first stage results have been observed. Bayesian response-adaptive design for multi-arm clinical trials: In the planning of a clinical trial, the randomization of patients to either the experimental or control groups is among the most important advances in the history of medical research. Randomization prevents confounding due to latents factors that are correlated with the health outcome and control potential bias of the treatment effect estimates by balancing patients among the treatment arms . However, this property could be sometimes in conflict with ethical assumptions. As experiments on human subjects, clinical trials are characterized by the necessity of finding a balance between collective ethics and individual ethics. When the observation of a failure represents an extreme outcome (i.e. death), the traditional balanced randomization becomes ethically infeasible because of unjustifiable sacrifice of individual ethics. In this context, response-adaptive randomization designs represent a class of designs in which the probability of treatment assignment changes according to patient’s outcome and treating more patients with effective arms compared to fixed randomization. Response-adaptive designs have been widely studied in literature and we provide a review of them in either frequentist or Bayesian framework in Chapter 4. Under the supervision of Prof. Lorenzo Trippa and Prof. Steffen Ventz at the Harvard School of Public Health (and Dana Farber Cancer Institute), we studied the use of Bayesian adaptive randomization (BAR) design in the context of multi-arm clinical trials, in which multiple experimental arms are compared to a common control arm (see Chapter 5). In collaboration with Dr. Carole D. Mitnick and motivated by a multi-arm randomized clinical trial for fluoroquinolone-susceptible multi-drug resistant tuberculosis (MDR-TB)5 called endTb, we build a response-adaptive clinical trial in which the randomization procedure is updated using two preliminary outcomes. The primary study outcome is treatment success after 72 weeks from treatment and two preliminary responses are measured after 8 and 39 weeks (see Cellamare et al. [36]). We compared the proposed design with a standard multi-arm multi-stage design through hypothetical scenarios based on historical data. Our simulations show how BAR may be more efficient than standard multi-arm multi-stage designs. In particular, when we compare the statistical power of BAR to that of non-adaptive designs under a variety of realistic hypothetical scenarios, we observe that our design requires less patients than non-adaptive designs to ensure a fixed predefine power. Moreover, BAR consistently allocates more participants to effective arm(s). In conclusion, given the objective of evaluating several new therapeutic regimens in a timely fashion, Bayesian response adaptive designs seem more appealing for MDR-TB trials. This approach offers the resource benefit of requiring fewer participants and tends to increase allocation to the effective regimens. Despite the attractive operating characteristics of response adaptive design in the multi arm settings, as shown in the case of the endTb trial, multi-arm clinical trials design presented in literature are generally based on the assumption that all experimental treatments are available at the enrollment of the first patient. In several real situations, new drugs are rarely at the same stage of development and multi-arm designs may delay in the clinical evaluation of new treatments. These limitations motivate our study of statistical methods for adding new experimental arms after a clinical trial started enrolling patients (see Chapter 6). We consider both balanced and response-adaptive randomization for experimental designs that allow investigators to add new arms during the course of the trial (see Ventz, Cellamare et al [134]). We discuss their application in the endTb context and we evaluate the proposed experimental designs using a set of realistic simulation scenarios. Our results showed that adding treatments to an ongoing trial yield substantial gain in efficacy compared to multiple independent two-arms trials. The use of standard response-adaptive algorithms can behave poorly in this setting and adjustments of the procedures are required. Moreover, we found that, despite the complexity and the computational burden, response-adaptive algorithms can potentially outperform the balanced algorithm