Asymptotic properties of randomized clinical trials designs

Nowadays, we are witnessing changes in the traditional clinical trial landscape: many methods have been proposed as a compromise between uncontrolled trials and randomized trials and a large number of adaptive randomization procedures have been developed for various studies, including multi-arm trials, dose-finding trials and platform trials. Adaptive designs often require time-consuming and computationally intensive Monte Carlo simulations to establish operating characteristics, particularly type I error probability and power. These statistical properties should be thoroughly investigated in order that the designs achieve regulatory approval. In particular, the estimated operating characteristics need to cover different scenarios, varying key parameters, such as enrollment rates and treatment effects. This makes routine applications of adaptive designs challenging. Also, at present new data sources are becoming available that can supplement data generated in standard randomized clinical trials. Externally-controlled clinical trials designs incorporate existing data about the control treatment available from external sources as external controls. So far, these designs have been evaluated mainly according to qualitative arguments or simulation studies. In the first part of this PhD thesis, we focus on asymptotic properties of the designs of response-adaptive clinical trials, that is characteristics of these designs obtained under the assumption that the number of patients enrolled in the studies is large. Approximations of the operating characteristics, beyond simulations, leveraging asymptotic properties, could allow a fast comparison of designs across plausible scenarios. In the second part of this PhD thesis, we investigate the statistical properties of externally-controlled randomized clinical trial designs, adopting a quantitative approach, and question whether these designs could shorten study length and benefit more patients being treated with a better treatment. The aims of our research are threefold: to determine appropriate methodology that can be used in the assessment of asymptotic properties of the designs of response-adaptive clinical trials; to develop a quantitative framework to compare externally-controlled randomized clinical trial designs to standard randomized clinical trial designs; and finally to examine the identified methods and verify our results via simulation studies, across a variety of scenarios and endpoints. The key contributions of our work are: proposing a novel methodology to derive asymptotic results for the randomization probabilities and allocation proportions of patients to various arms in a broad class of Bayesian response-adaptive randomized clinical trials designs, by combining tools from the classical foundations of statistical inference and probability theory with mathematical techniques such as stochastic approximation; showing that asymptotic analyses of adaptive procedures simplify the design of clinical trials and reduce the need for time-consuming simulations to evaluate operating characteristics across potential trial scenarios; proving that externally-controlled clinical trials can increase power compared to randomized clinical trials by leveraging additional information from outside the trial rather than committing resources to an internal control.