On the efficiency of two-stage response-adaptive designs

Opportunity for efficiency in clinical development: An overview of adaptive clinical trial designs and innovative machine learning tools, with examples from the cardiovascular field

Modern data analysis tools and statistical modeling techniques are increasingly used in clinical research to improve diagnosis, estimate disease progression and predict treatment outcomes. What seems less emphasized is the importance of the study design, which can have a serious impact on the study cost, time and statistical efficiency. This paper provides an overview of different types of adaptive designs in clinical trials and their applications to cardiovascular trials. We highlight recent proliferation of work on adaptive designs over the past two decades, including some recent regulatory guidelines on complex trial designs and master protocols. We also describe the increasing role of machine learning and use of metaheuristics to construct increasingly complex adaptive designs or to identify interesting features for improved predictions and classifications.

Optimal dose-finding for efficacy-safety models

Dose-finding is an important part of the clinical development of a new drug. The purpose of dose-finding studies is to determine a suitable dose for future development based on both efficacy and safety. Optimal experimental designs have already been used to determine the design of this kind of studies, however, often that design is focused on efficacy only. We consider an efficacy-safety model, which is a simplified version of the bivariate Emax model. We use here the clinical utility index concept, which provides the desirable balance between efficacy and safety. By maximizing the utility of the patients, we get the estimated dose. This desire leads us to locally c -optimal designs. An algebraic solution for c -optimal designs is determined for arbitrary c vectors using a multivariate version of Elfving's method. The solution shows that the expected therapeutic index of the drug is a key quantity determining both the number of doses, the doses itself, and their weights in the optimal design. A sequential design is proposed to solve the complication of parameter dependency, and it is illustrated in a simulation study.

Convergence of least squares estimators in the adaptive Wynn algorithm for some classes of nonlinear regression models

The paper continues the authors’ work (Freise et al. The adaptive Wynn-algorithm in generalized linear models with univariate response. arXiv:1907.02708, 2019) on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper the asymptotics of adaptive least squares estimators under the adaptive Wynn algorithm is studied. Strong consistency and asymptotic normality are derived for two classes of nonlinear models: firstly, for the class of models satisfying a condition of ‘saturated identifiability’, which was introduced by Pronzato (Metrika 71:219–238, 2010); secondly, a class of generalized linear models. Further essential assumptions are compactness of the experimental region and of the parameter space together with some natural continuity assumptions. For asymptotic normality some further smoothness assumptions and asymptotic homoscedasticity of random errors are needed and the true parameter point is required to be an interior point of the parameter space.

Implementing Optimal Designs for Dose-Response Studies Through Adaptive Randomization for a Small Population Group

In dose-response studies with censored time-to-event outcomes, D-optimal designs depend on the true model and the amount of censored data. In practice, such designs can be implemented adaptively, by performing dose assignments according to updated knowledge of the dose-response curve at interim analysis. It is also essential that treatment allocation involves randomization-to mitigate various experimental biases and enable valid statistical inference at the end of the trial. In this work, we perform a comparison of several adaptive randomization procedures that can be used for implementing D-optimal designs for dose-response studies with time-to-event outcomes with small to moderate sample sizes. We consider single-stage, two-stage, and multi-stage adaptive designs. We also explore robustness of the designs to experimental (chronological and selection) biases. Simulation studies provide evidence that both the choice of an allocation design and a randomization procedure to implement the target allocation impact the quality of dose-response estimation, especially for small samples. For best performance, a multi-stage adaptive design with small cohort sizes should be implemented using a randomization procedure that closely attains the targeted D-optimal design at each stage. The results of the current work should help clinical investigators select an appropriate randomization procedure for their dose-response study.

Adaptive Optimal Designs for Dose-Finding Studies with Time-to-Event Outcomes

We consider optimal design problems for dose-finding studies with censored Weibull time-to-event outcomes. Locally D-optimal designs are investigated for a quadratic dose-response model for log-transformed data subject to right censoring. Two-stage adaptive D-optimal designs using maximum likelihood estimation (MLE) model updating are explored through simulation for a range of different dose-response scenarios and different amounts of censoring in the model. The adaptive optimal designs are found to be nearly as efficient as the locally D-optimal designs. A popular equal allocation design can be highly inefficient when the amount of censored data is high and when the Weibull model hazard is increasing. The issues of sample size planning/early stopping for an adaptive trial are investigated as well. The adaptive D-optimal design with early stopping can potentially reduce study size while achieving similar estimation precision as the fixed allocation design.

The effect of using a robust optimality criterion in model based adaptive optimization

Optimizing designs using robust (global) optimality criteria has been shown to be a more flexible approach compared to using local optimality criteria. Additionally, model based adaptive optimal design (MBAOD) may be less sensitive to misspecification in the prior information available at the design stage. In this work, we investigate the influence of using a local (lnD) or a robust (ELD) optimality criterion for a MBAOD of a simulated dose optimization study, for rich and sparse sampling schedules. A stopping criterion for accurate effect prediction is constructed to determine the endpoint of the MBAOD by minimizing the expected uncertainty in the effect response of the typical individual. 50 iterations of the MBAODs were run using the MBAOD R-package, with the concentration from a one-compartment first-order absorption pharmacokinetic model driving the population effect response in a sigmoidal EMAX pharmacodynamics model. The initial cohort consisted of eight individuals in two groups and each additional cohort added two individuals receiving a dose optimized as a discrete covariate. The MBAOD designs using lnD and ELD optimality with misspecified initial model parameters were compared by evaluating the efficiency relative to an lnD-optimal design based on the true parameter values. For the explored example model, the MBAOD using ELD-optimal designs converged quicker to the theoretically optimal lnD-optimal design based on the true parameters for both sampling schedules. Thus, using a robust optimality criterion in MBAODs could reduce the number of adaptations required and improve the practicality of adaptive trials using optimal design.

Adaptive designs: The Swiss Army knife among clinical trial designs?

There has been considerable progress in the development and implementation of adaptive designs over the past 30 years. A major driver for this class of novel designs is the possibility to increase the information value of clinical trial data to enable better decisions, leading to more efficient drug development processes and improved late-stage success rates. In the first part of this article, we review the development of adaptive designs from different perspectives. We trace back key historical papers, report on landmark adaptive design clinical trials, review major cross-industry collaborations, and highlight key regulatory guidance documents. In the second, more technical part of this article, we address the question of whether it is possible to define factors which guide the choice between a fixed or an adaptive design for a given trial. We show that in non-linear regression models with a moderate variance of the responses, the first-stage sample size of an adaptive design should be chosen sufficiently large in order to address variability in the interim parameter estimate. In conclusion, the choice between an adaptive and a fixed design depends in a sensitive manner on the specific statistical problem under investigation.

Optimal designs for comparing curves

We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions. Optimal design theory (equivalence theorems, efficiency bounds) is developed for this non standard design problem and for some commonly used dose response models optimal designs are found explicitly. The results are illustrated in several examples modeling dose response relationships. It is demonstrated that the optimal pair of designs for the comparison of the regression curves is not the pair of the optimal designs for the individual models. In particular it is shown that the use of the optimal designs proposed in this paper instead of commonly used "non-optimal" designs yields a reduction of the width of the confidence band by more than 50%.

Rationale and study design of the Adaptive study of IL-2 dose on regulatory T cells in type 1 diabetes (DILT1D): a non-randomised, open label, adaptive dose finding trial

INTRODUCTION

CD4 T regulatory cells (Tregs) are crucial for the maintenance of self-tolerance and are deficient in many common autoimmune diseases such as type 1 diabetes (T1D). Interleukin 2 (IL-2) plays a major role in the activation and function of Tregs and treatment with ultra-low dose (ULD) IL-2 could increase Treg function to potentially halt disease progression in T1D. However, prior to embarking on large phase II/III clinical trials it is critical to develop new strategies for determining the mechanism of action of ULD IL-2 in participants with T1D. In this mechanistic study we will combine a novel trial design with a clinical grade Treg assay to identify the best doses of ULD IL-2 to induce targeted increases in Tregs.

METHOD AND ANALYSIS

Adaptive study of IL-2 dose on regulatory T cells in type 1 diabetes (DILT1D) is a single centre non-randomised, single dose, open label, adaptive dose-finding trial. The primary objective of DILT1D is to identify the best doses of IL-2 to achieve a minimal or maximal Treg increase in participants with T1D (N=40). The design has an initial learning phase where pairs of participants are assigned to five preassigned doses followed by an interim analysis to determine the two Treg targets for the reminder of the trial. This will then be followed by an adaptive phase which is fully sequential with an interim analysis after each participant is observed to determine the choice of dose based on the optimality criterion to minimise the determinant of covariance of the estimated target doses. A dose determining committee will review all data available at the interim(s) and then provide decisions regarding the choice of dose to administer to subsequent participants.

ETHICS AND DISSEMINATION

Ethical approval for the study was granted on 18 February 2013.

RESULTS

The results of this study will be reported through peer-reviewed journals, conference presentations and an internal organisational report.

TRIAL REGISTRATION NUMBERS

NCT01827735, ISRCTN27852285, DRN767.

Dose-finding studies, MCP-Mod, model selection, and model averaging: Two applications in the real world

BACKGROUND

Phase II clinical trials are important milestones to determine whether a dose-effect exists and to decide on future doses to use in confirmatory studies. To take into account the overall shape of the dose-response curve, modeling the relationship by linear or non-linear models is preferable to the classical pair-wise comparisons of the effect of each dose versus the placebo or the comparator. The multiple comparisons and modeling approach has been developed within the last 10 years to address this important question in the clinical development of drugs. Despite some recent publications referring to this methodology, few detailed applications have been shown so far and several practical questions remain to be addressed.

METHODS

Starting from a set of candidate models, model selection using classical methods criteria is possible. However, it suffers some limitations, not taking into account the uncertainty of the selection process itself. An attractive solution is to use model averaging, which applies appropriate weights to the parameters (e.g., the minimum effective dose) obtained from each model.

RESULTS

A discussion of the selection criteria is first presented. Through two real examples, how to proceed with model selection and model averaging is presented and discussed.

LIMITATIONS

The first multiple comparisons and modeling approach papers addressed normal responses. More recently, an extension of this methodology has been proposed to deal with other types of responses, in particular binary, time-to-event and longitudinal data. Questions that remain are concerned with the choice of the candidate models and of their parameters' guesstimates.

CONCLUSIONS

The analysis of clinical dose-finding studies using a modeling of the entire curve offers a promising alternative as compared with the classical multiple comparisons methods, while not compromising the necessary rigor of the analysis.