Permutation tests for adaptive clinical trials

Planning a confirmatory clinical trial involves a large number of decisions: suitable clinical endpoints have to be chosen; treatment doses and regimens have to be selected; sample sizes and allocation ratios have to be specified. These decisions typically depend on assumptions about the distribution of observations such as the variability of outcomes, the size of treatment differences, or the dose-response relationship. At the time of planning, however, often little information is available on which those assumptions may be based on. Adaptive designs address this problem as they permit to learn from and use information emerging from the ongoing experiment to perform mid-trial design modifications. To control the type I error rate, however, most currently available test procedures for adaptive designs require restrictive assumptions about the distribution of outcome measures and test statistics. In this project I propose to develop nonparametric tests for confirmatory adaptive designs. Specifically, I propose to extend the conditional error rate approach - a general statistical principle for confirmatory adaptive designs - to permutation and re-randomization tests. I will consider adaptive permutation tests for univariate data as well as adaptive permutation tests for multivariate data and corresponding multiple testing procedures. I will use analytic derivations to establish formal conditions for type I error control, perform simulation studies to assess the operating characteristics of specific test procedures and devise case studies to illustrate applications to specific problems. The proposed approach requires less assumptions about the distribution of observations and test statistics, while providing similar flexibility for interim design modifications as existing adaptive test procedures. Moreover, the proposed methods do not rely on asymptotic properties, which are only satisfied in large samples. Therefore, they are especially suited for clinical trials with small and moderate sample sizes. 1

Planning a clinical trial with the objective to demonstrate the efficacy of new therapies involves a large number of decisions whose impact on the success probability of the trial depends on statistical properties of the data. Conventionally, these decisions have to be made before the start of the trial. Adaptive trial designs, however, permit to perform interim analyses during an ongoing trial and to adapt the design of the trial and statistical analysis plan,. For example, during an interim analysis the number of patients to be included in the remainder of the trial can be changed based on preliminary results from the trial. The increased complexity of adaptive designs, however, needs to be reflected in the statistical analysis of the results. Especially strict control of the probability of a false positive result and the unbiasedness of effect size estimates need to be guaranteed.To this end, statistical methods for the analysis of adaptive clinical trials have been proposed. The operating characteristics under deviations from the underlying statistical model assumptions, however, has gotten little attention in the literature, so far. Results of this project show that the probability to demonstrate the efficacy of an active treatment relies heavily on restrictive assumptions about the statistical properties of the data, especially, if the number of patients included in the trial is small.We have, therefore, developed novel statistical methods for the analysis of confirmatory adaptive designs that require a minimum of assumptions about statistical properties of the data and therefore perform well across a wide range of statistical models. Especially, if the number of patients included in trial is small, do the proposed procedures provide substantial gains in terms of the probability to demonstrate the efficacy of an active treatment. One disadvantage of the approach is that the initially planned number of patients may not be reduced. Consequently, we propose corresponding methods to determine to which extent the number of patients included in the remainder of the trial should be increased. We show that using such rules one requires on average fewer patients to demonstrate the efficacy of an active treatment with the same probability as if a corresponding non-adaptive trials where used.The results of the project provide a comprehensive framework of statistical methods for the analysis of adaptive designs with minimal assumptions about the statistical properties of outcome variables. The methods provide a promising alternative to established methods, especially in research areas where small sample sizes are common, like the development of new treatments for rare diseases.