This thesis deals with sequential and adaptive methods for clinical trials, and how such methods can be used to achieve efficient clinical trial designs. The efficiency gains that can be achieved through non-adaptive group sequential methods are well established, while the newer adaptive methods seek to combine the best of the classical group sequential framework with an approach that gives increased flexibility. Our results show that the adaptive methods can provide some additional efficiency, as well as increased possibilities to respond to new internal and external information. Care is however needed when applying adaptive methods. While sub-optimal rules for adaptation can lead to inefficiencies, the logistical challenges can also be considerable. Efficient non-adaptive group sequential designs are often easier to implement in practice, and have for the cases we have considered been quite competitive in terms of efficiency. The four problems that are presented in this thesis are very relevant to how clinical trials are run in practice. The solutions that we present are either new approaches to problems that have not previously been solved, or methods that are more efficient than the ones currently available in the literature. Several challenging optimisation problems are solved through numerical computations. The optimal designs that are achieved can be used to benchmark new methods proposed in this thesis as well as methods available in the statistical literature. The problem that is solved in Chapter 5 can be viewed as a natural extension to the other problems. It brings together methods that we have used to the design of individual trials, to solve the more complex problem of designing a sequence of trials that are the core part of a clinical development program. The expected utility that is maximised is motivated by how the development of new medicines works in practice.

Adaptive clinical trials for new drugs or treatment options promise substantial benefits to both the pharmaceutical industry and the patients, but complicate resource allocation decisions. In this dissertation, we focus on sequential adaptive clinical trials with binary response, which allow for early termination of drug testing for benefit or futility at interim analysis points. The option to stop the trial early enables the trial sponsor to mitigate investment risks on ineffective drugs, and to shorten the development time line of effective drugs, hence reducing expenditures and expediting patient access to these new therapies. In this setting, decision makers need to determine a testing schedule, or the number of patients to recruit at each interim analysis point, and stopping criteria that inform their decision to continue or stop the trial, considering performance measures that include drug misclassification risk, time-to-market, and expected profit. In the first manuscript, we model current practices of sequential adaptive trials, so as to quantify the magnitude of drug misclassification risk. Towards this end, we build a simulation model to realistically represent the current decision-making process, including the utilization of the triangular test, a widely implemented sequential methodology. We find that current practices lead to a high risk of incorrectly terminating the development of an effective drug, thus, to unrecoverable expenses for the sponsor, and unfulfilled patient needs. In the second manuscript, we study the sequential resource allocation decision, in terms of a testing schedule and stopping criteria, so as to quantify the impact of interim analyses on the aforementioned performance measures. Towards this end, we build a stochastic dynamic programming model, integrated with a Bayesian learning framework for updating the drug’s estimated efficacy. The resource allocation decision is characterized by endogenous uncertainty, and a trade-off between the incentive to establish that the drug is effective early on (exploitation), due to a time-decreasing market revenue, and the benefit from collecting some information on the drug’s efficacy prior to committing a large budget (exploration). We derive important structural properties of an optimal resource allocation strategy and perform a numerical study based on realistic data, and show that sequential adaptive trials with interim analyses substantially outperform traditional trials. Finally, the third manuscript integrates the first two models, and studies the benefits of an optimal resource allocation decision over current practices. Our findings indicate that our optimal testing schedules outperform different types of fixed testing schedules under both perfect and imperfect information. / Ph. D.