Adaptive designs for clinical trials permit alterations to a study in response to accumulating data in order to make trials more flexible, ethical, and efficient. These benefits are achieved while preserving the integrity and validity of the trial, through the pre-specification and proper adjustment for the possible alterations during the course of the trial. Despite much research in the statistical literature highlighting the potential advantages of adaptive designs over traditional fixed designs, the uptake of such methods in clinical research has been slow. One major reason for this is that different adaptations to trial designs, as well as their advantages and limitations, remain unfamiliar to large parts of the clinical community. The aim of this paper is to clarify where adaptive designs can be used to address specific questions of scientific interest; we introduce the main features of adaptive designs and commonly used terminology, highlighting their utility and pitfalls, and illustrate their use through case studies of adaptive trials ranging from early-phase dose escalation to confirmatory phase III studies.

The COVID-19 pandemic has led to an unprecedented response in terms of clinical research activity. An important part of this research has been focused on randomized controlled clinical trials to evaluate potential therapies for COVID-19. The results from this research need to be obtained as rapidly as possible. This presents a number of challenges associated with considerable uncertainty over the natural history of the disease and the number and characteristics of patients affected, and the emergence of new potential therapies. These challenges make adaptive designs for clinical trials a particularly attractive option. Such designs allow a trial to be modified on the basis of interim analysis data or stopped as soon as sufficiently strong evidence has been observed to answer the research question, without compromising the trial’s scientific validity or integrity. In this paper we describe some of the adaptive design approaches that are available and discuss particular issues and challenges associated with their use in the pandemic setting. Our discussion is illustrated by details of four ongoing COVID-19 trials that have used adaptive designs.

Summary: For many years phase I and phase II clinical trials have been conducted separately, but there has been a recent shift to combine these phases. Although a variety of phase I–II model-based designs for cytotoxic agents have been proposed in the literature, methods for molecularly targeted agents (TAs) are just starting to develop. The main challenge of the TA setting is the unknown dose–efficacy relationship that can have either an increasing, plateau or umbrella shape. To capture these, approaches with more parameters are needed or, alternatively, more orderings are required to account for the uncertainty in the dose–efficacy relationship. As a result, designs for more complex clinical trials, e.g. trials looking at schedules of a combination treatment involving TAs, have not been extensively studied yet. We propose a novel regimen finding design which is based on a derived efficacy–toxicity trade-off function. Because of its special properties, an accurate regimen selection can be achieved without any parametric or monotonicity assumptions. We illustrate how this design can be applied in the context of a complex combination–schedule clinical trial. We discuss practical and ethical issues such as coherence, delayed and missing efficacy responses, safety and futility constraints.

Squared error loss remains the most commonly used loss function for constructing a Bayes estimator of the parameter of interest. However, it can lead to suboptimal solutions when a parameter is defined on a restricted space. It can also be an inappropriate choice in the context when an extreme overestimation and/or underestimation results in severe consequences and a more conservative estimator is preferred. We advocate a class of loss functions for parameters defined on restricted spaces which infinitely penalize boundary decisions like the squared error loss does on the real line. We also recall several properties of loss functions such as symmetry, convexity and invariance. We propose generalizations of the squared error loss function for parameters defined on the positive real line and on an interval. We provide explicit solutions for corresponding Bayes estimators and discuss multivariate extensions. Four well-known Bayesian estimation problems are used to demonstrate inferential benefits the novel Bayes estimators can provide in the context of restricted estimation.

Summary: The question of selecting the ‘best’ among different choices is a common problem in statistics. In drug development, our motivating setting, the question becomes, for example, which treatment gives the best response rate. Motivated by recent developments in the theory of context-dependent information measures, we propose a flexible response-adaptive experimental design based on a novel criterion governing treatment arm selections which can be used in adaptive experiments with simple (e.g. binary) and complex (e.g. co-primary, ordinal or nested) end points. It was found that, for specific choices of the context-dependent measure, the criterion leads to a reliable selection of the correct arm without any parametric or monotonicity assumptions and provides noticeable gains in settings with costly observations. The asymptotic properties of the design are studied for different allocation rules, and the small sample size behaviour is evaluated in simulations in the context of phase II clinical trials with different end points. We compare the proposed design with currently used alternatives and discuss its practical implementation.