On Recent Advances in Optimal Allocation Designs in Clinical Trials

Cluster Randomized Trials Designed to Support Generalizable Inferences

When planning a cluster randomized trial, evaluators often have access to an enumerated cohort representing the target population of clusters. Practicalities of conducting the trial, such as the need to oversample clusters with certain characteristics in order to improve trial economy or support inferences about subgroups of clusters, may preclude simple random sampling from the cohort into the trial, and thus interfere with the goal of producing generalizable inferences about the target population. We describe a nested trial design where the randomized clusters are embedded within a cohort of trial-eligible clusters from the target population and where clusters are selected for inclusion in the trial with known sampling probabilities that may depend on cluster characteristics (e.g., allowing clusters to be chosen to facilitate trial conduct or to examine hypotheses related to their characteristics). We develop and evaluate methods for analyzing data from this design to generalize causal inferences to the target population underlying the cohort. We present identification and estimation results for the expectation of the average potential outcome and for the average treatment effect, in the entire target population of clusters and in its non-randomized subset. In simulation studies, we show that all the estimators have low bias but markedly different precision. Cluster randomized trials where clusters are selected for inclusion with known sampling probabilities that depend on cluster characteristics, combined with efficient estimation methods, can precisely quantify treatment effects in the target population, while addressing objectives of trial conduct that require oversampling clusters on the basis of their characteristics.

Response-adaptive randomization in clinical trials: from myths to practical considerations

Response-Adaptive Randomization (RAR) is part of a wider class of data-dependent sampling algorithms, for which clinical trials are typically used as a motivating application. In that context, patient allocation to treatments is determined by randomization probabilities that change based on the accrued response data in order to achieve experimental goals. RAR has received abundant theoretical attention from the biostatistical literature since the 1930's and has been the subject of numerous debates. In the last decade, it has received renewed consideration from the applied and methodological communities, driven by well-known practical examples and its widespread use in machine learning. Papers on the subject present different views on its usefulness, and these are not easy to reconcile. This work aims to address this gap by providing a unified, broad and fresh review of methodological and practical issues to consider when debating the use of RAR in clinical trials.

Optimal Weighted Multiple-Testing Procedure for Clinical Trials

This paper describes a new method for testing randomized clinical trials with binary outcomes, which combines the O’Brien and Fleming (1979) multiple-testing procedure with optimal allocations and unequal weighted samples simultaneously. The O’Brien and Fleming method of group sequential testing is a simple and effective method with the same Type I error and power as a fixed one-stage chi-square test, with the option to terminate early if one treatment is clearly superior to another. This study modified the O’Brien and Fleming procedure, resulting in a more flexible new procedure, where the optimal allocation assists in allocating more subjects to the winning treatment without compromising the integrity of the study, while unequal weighting allows for different samples to be chosen for different stages of a trial. The new optimal weighted multiple-testing procedure (OWMP), based on simulation studies, is relatively robust to the added features because it showed a high preference for decreasing the Type I error and maintaining the power. In addition, the procedure was illustrated using simulated and real-life examples. The outcomes of the current study suggest that the new procedure is as effective as the original. However, it is more flexible.

A roadmap to using randomization in clinical trials

BACKGROUND

Randomization is the foundation of any clinical trial involving treatment comparison. It helps mitigate selection bias, promotes similarity of treatment groups with respect to important known and unknown confounders, and contributes to the validity of statistical tests. Various restricted randomization procedures with different probabilistic structures and different statistical properties are available. The goal of this paper is to present a systematic roadmap for the choice and application of a restricted randomization procedure in a clinical trial.

METHODS

We survey available restricted randomization procedures for sequential allocation of subjects in a randomized, comparative, parallel group clinical trial with equal (1:1) allocation. We explore statistical properties of these procedures, including balance/randomness tradeoff, type I error rate and power. We perform head-to-head comparisons of different procedures through simulation under various experimental scenarios, including cases when common model assumptions are violated. We also provide some real-life clinical trial examples to illustrate the thinking process for selecting a randomization procedure for implementation in practice.

RESULTS

Restricted randomization procedures targeting 1:1 allocation vary in the degree of balance/randomness they induce, and more importantly, they vary in terms of validity and efficiency of statistical inference when common model assumptions are violated (e.g. when outcomes are affected by a linear time trend; measurement error distribution is misspecified; or selection bias is introduced in the experiment). Some procedures are more robust than others. Covariate-adjusted analysis may be essential to ensure validity of the results. Special considerations are required when selecting a randomization procedure for a clinical trial with very small sample size.

CONCLUSIONS

The choice of randomization design, data analytic technique (parametric or nonparametric), and analysis strategy (randomization-based or population model-based) are all very important considerations. Randomization-based tests are robust and valid alternatives to likelihood-based tests and should be considered more frequently by clinical investigators.

A simple solution to the inadequacy of asymptotic likelihood-based inference for response-adaptive clinical trials

The present paper discusses drawbacks and limitations of likelihood-based inference in sequential clinical trials for treatment comparisons managed via Response-Adaptive Randomization. Taking into account the most common statistical models for the primary outcome—namely binary, Poisson, exponential and normal data—we derive the conditions under which (i) the classical confidence intervals degenerate and (ii) the Wald test becomes inconsistent and strongly affected by the nuisance parameters, also displaying a non monotonic power. To overcome these drawbacks, we provide a very simple solution that could preserve the fundamental properties of likelihood-based inference. Several illustrative examples and simulation studies are presented in order to confirm the relevance of our results and provide some practical recommendations.

Optimal and ethical designs for hypothesis testing in multi-arm exponential trials

Multi-arm clinical trials are complex experiments which involve several objectives. The demand for unequal allocations in a multi-treatment context is growing and adaptive designs are being increasingly used in several areas of medical research. For uncensored and censored exponential responses, we propose a constrained optimization approach in order to derive the design maximizing the power of the multivariate test of homogeneity, under a suitable ethical constraint. In the absence of censoring, we obtain a very simple closed-form solution that dominates the balanced design in terms of power and ethics. Our suggestion can also accommodate delayed responses and staggered entries, and can be implemented via response adaptive rules. While other targets proposed in the literature could present an unethical behavior, the suggested optimal allocation is frequently unbalanced by assigning more patients to the best treatment, both in the absence and presence of censoring. We evaluate the operating characteristics of our proposal theoretically and by simulations, also redesigning a real lung cancer trial, showing that the constrained optimal target guarantees very good performances in terms of ethical demands, power and estimation precision. Therefore, it is a valid and useful tool in designing clinical trials, especially oncological trials and clinical experiments for grave and novel infectious diseases, where the ethical concern is of primary importance.

The Bayesian Design of Adaptive Clinical Trials

This paper presents a brief overview of the recent literature on adaptive design of clinical trials from a Bayesian perspective for statistically not so sophisticated readers. Adaptive designs are attracting a keen interest in several disciplines, from a theoretical viewpoint and also—potentially—from a practical one, and Bayesian adaptive designs, in particular, have raised high expectations in clinical trials. The main conceptual tools are highlighted here, with a mention of several trial designs proposed in the literature that use these methods, including some of the registered Bayesian adaptive trials to this date. This review aims at complementing the existing ones on this topic, pointing at further interesting reading material.

A web application for the design of multi-arm clinical trials

BACKGROUND

Multi-arm designs provide an effective means of evaluating several treatments within the same clinical trial. Given the large number of treatments now available for testing in many disease areas, it has been argued that their utilisation should increase. However, for any given clinical trial there are numerous possible multi-arm designs that could be used, and choosing between them can be a difficult task. This task is complicated further by a lack of available easy-to-use software for designing multi-arm trials.

RESULTS

To aid the wider implementation of multi-arm clinical trial designs, we have developed a web application for sample size calculation when using a variety of popular multiple comparison corrections. Furthermore, the application supports sample size calculation to control several varieties of power, as well as the determination of optimised arm-wise allocation ratios. It is built using the Shiny package in the R programming language, is free to access on any device with an internet browser, and requires no programming knowledge to use. It incorporates a variety of features to make it easier to use, including help boxes and warning messages. Using design parameters motivated by a recently completed phase II oncology trial, we demonstrate that the application can effectively determine and evaluate complex multi-arm trial designs.

CONCLUSIONS

The application provides the core information required by statisticians and clinicians to review the operating characteristics of a chosen multi-arm clinical trial design. The range of designs supported by the application is broader than other currently available software solutions. Its primary limitation, particularly from a regulatory agency point of view, is its lack of validation. However, we present an approach to efficiently confirming its results via simulation.

Design of experiments for a confirmatory trial of precision medicine

Precision medicine, aka stratified/personalized medicine, is becoming more pronounced in the medical field due to advancement in computational ability to learn about patient genomic backgrounds. A biomaker, i.e. a type of biological process indicator, is often used in precision medicine to classify patient population into several subgroups. The aim of precision medicine is to tailor treatment regimes for different patient subgroups who suffer from the same disease. A multi-arm design could be conducted to explore the effect of treatment regimes on different biomarker subgroups. However, if treatments work only on certain subgroups, which is often the case, enrolling all patient subgroups in a confirmatory trial would increase the burden of a study. Having observed a phase II trial, we propose a design framework for finding an optimal design that could be implemented in a phase III study or a confirmatory trial. We consider two elements in our approach: Bayesian data analysis of observed data, and design of experiments. The first tool selects subgroups and treatments to be enrolled in the future trial whereas the second tool provides an optimal treatment randomization scheme for each selected/enrolled subgroups. Considering two independent treatments and two independent biomarkers, we illustrate our approach using simulation studies. We demonstrate efficiency gain, i.e. high probability of recommending truly effective treatments in the right subgroup, of the optimal design found by our framework over a randomized controlled trial and a biomarker–treatment linked trial.

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A classical randomized controlled trial fails to identify subgroup treatment effect.

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Standard enriched designs may miss out potential patient subgroups.

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A standard multi-arm design could be inefficient for a trial of precision medicine.

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A data-driven design framework could provide efficient designs for future trials.

Optimal designs for testing hypothesis in multiarm clinical trials

The present paper deals with the problem of designing randomized multiarm clinical trials for treatment comparisons in order to achieve a suitable trade-off among inferential precision and ethical concerns. Although the large majority of the literature is focused on the estimation of the treatment effects, in particular for the case of two treatments with binary outcomes, the present paper takes into account the inferential goal of maximizing the power of statistical tests to detect correct conclusions about the treatment effects for normally response trials. After discussing the allocation optimizing the power of the classical multivariate test of homogeneity, we suggest a multipurpose design methodology, based on constrained optimization, which maximizes the power of the test under a suitable ethical constraint reflecting the effectiveness of the treatments. The ensuing optimal allocation depends in general on the unknown model parameters but, contrary to the unconstrained optimal solution or to some targets proposed in the literature, it is a non-degenerate continuous function of the treatment contrasts, and therefore it can be approached by standard response-adaptive randomization procedures. The properties of this constrained optimal allocation are described both theoretically and through suitable examples, showing good performances both in terms of ethical gain and statistical efficiency, taking into account estimation precision as well.

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.

Optimal treatment allocation for placebo-treatment comparisons in trials with discrete-time survival endpoints

In many randomized controlled trials, treatment groups are of equal size, but this is not necessarily the best choice. This paper provides a methodology to calculate optimal treatment allocations for longitudinal trials when we wish to compare multiple treatment groups with a placebo group, and the comparisons may have unequal importance. The focus is on trials with a survival endpoint measured in discrete time. We assume the underlying survival process is Weibull and show that values for the parameters in the Weibull distribution have an impact on the optimal treatment allocation scheme in an interesting way. Additionally, we incorporate different cost considerations at the subject and measurement levels and determine the optimal number of time periods. We also show that when many events occur at the beginning of the trial, fewer time periods are more efficient. As an application, we revisit a risperidone maintenance treatment trial in schizophrenia and use our proposed methodology to redesign it and compare merits of our optimal design.