The value of a two-armed Bayesian response adaptive randomization trial

We investigate the value of a two-armed Bayesian response adaptive randomization (RAR) design to investigate early preterm birth rates of high versus low dose of docosahexaenoic acid during pregnancy. Unexpectedly, the COVID-19 pandemic forced recruitment to pause at 1100 participants rather than the planned 1355. The difference in power between number of participants at the pause and planned was 87% and 90% respectively. We decided to stop the study. This paper describes how the RAR was used to execute the study. The value of RAR in two-armed studies is quite high and their use in the future is promising.

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.

Using Adaptive Designs to Avoid Selecting the Wrong Arms in Multiarm Comparative Effectiveness Trials

Limited resources are a challenge when planning comparative effectiveness studies of multiple promising treatments, often prompting study planners to reduce the sample size to meet the financial constraints. The practical solution is often to increase the efficiency of this sample size by selecting a pair of treatments among the pool of promising treatments before the clinical trial begins. The problem with this approach is that the investigator may inadvertently leave out the most beneficial treatment. This paper demonstrates a possible solution to this problem by using Bayesian adaptive designs. We use a planned comparative effectiveness clinical trial of treatments for sialorrhea in amyotrophic lateral sclerosis as an example of the approach. Rather than having to guess at the two best treatments to compare based on limited data, we suggest putting more arms in the trial and letting response adaptive randomization (RAR) determine better arms. To ground this study relative to previous literature we first compare RAR, adaptive equal randomization (ER), arm(s) dropping, and a fixed design. Given the goals of this trial we demonstrate that we may avoid 'type III errors' - inadvertently leaving out the best treatment - with little loss in power compared to a two-arm design, even when choosing the correct two arms for the two-armed design. There are appreciable gains in power when the two arms are prescreened at random.

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.

Is the classical Wald test always suitable under response-adaptive randomization?

The aim of this paper is to analyze the impact of response-adaptive randomization rules for normal response trials intended to test the superiority of one of two available treatments. Taking into account the classical Wald test, we show how response-adaptive methodology could induce a consistent loss of inferential precision. Then, we suggest a modified version of the Wald test which, by using the current allocation proportion to the treatments as a consistent estimator of the target, avoids some degenerate scenarios and so it should be preferable to the classical test. Furthermore, we show both analytically and via simulations how some target allocations may induce a locally decreasing power function. Thus, we derive the conditions on the target guaranteeing its monotonicity and we show how a correct choice of the initial sample size allows one to overcome this drawback regardless of the adopted target.