Adaptive Biased Coin Design Research Articles

Group Response-Adaptive Randomization With Delayed and Missing Responses.

Response-adaptive randomization (RAR) procedures have been extensively studied in the literature, but most of the procedures rely on updating therandomization after each response, which is impractical in many clinical trials. In this article, we propose a new family of RAR procedures that dynamically update based on the responses of a group of individuals, either when available or at fixed time intervals (weekly or biweekly). We show that the proposed design retains the essential theoretical properties of Hu and Zhang's doubly adaptive biased coin designs (DBCD), and performs well in scenarios involving delayed and randomly missing responses. Numerical studies have been conducted to demonstrate that the new proposed group doubly adaptive biased coin design has similar properties to the Hu and Zhang's DBCDs in different situations. We also apply the new design to a real clinical trial, highlighting its advantages and practicality. Our findings open the door to studying the properties of other group response adaptive designs, such as urn models, and facilitate the application of response-adaptive randomized clinical trials in practice.

Robustness of response-adaptive randomization.

Doubly adaptive biased coin design (DBCD), a response-adaptive randomization scheme, aims to skew subject assignment probabilities based on accrued responses for ethical considerations. Recent years have seen substantial advances in understanding DBCD's theoretical properties, assuming correct model specification for the responses. However, concerns have been raised about the impact of model misspecification on its design and analysis. In this paper, we assess the robustness to both design model misspecification and analysis model misspecification under DBCD. On one hand, we confirm that the consistency and asymptotic normality of the allocation proportions can be preserved, even when the responses follow a distribution other than the one imposed by the design model during the implementation of DBCD. On the other hand, we extensively investigate three commonly used linear regression models for estimating and inferring the treatment effect, namely difference-in-means, analysis of covariance (ANCOVA) I, and ANCOVA II. By allowing these regression models to be arbitrarily misspecified, thereby not reflecting the true data generating process, we derive the consistency and asymptotic normality of the treatment effect estimators evaluated from the three models. The asymptotic properties show that the ANCOVA II model, which takes covariate-by-treatment interaction terms into account, yields the most efficient estimator. These results can provide theoretical support for using DBCD in scenarios involving model misspecification, thereby promoting the widespread application of this randomization procedure.

Doubly adaptive biased coin design to improve Bayesian clinical trials with time-to-event endpoints.

Clinical trialists often face the challenge of balancing scientific questions with other design features, such as improving efficiency, minimizing exposure to inferior treatments, and simultaneously comparing multiple treatments. While Bayesian response adaptive randomization (RAR) is a popular and effective method for achieving these objectives, it is known to have large variability and a lack of explicit theoretical results, making its use in clinical trials a subject of concern. It is desirable to propose a design that targets the same allocation proportion as Bayesian RAR and achieves the above objectives but addresses the concerns over Bayesian RAR. We propose the frequentist doubly adaptive biased coin designs (DBCD) targeting ethical allocation proportions from the Bayesian framework to satisfy different objectives in clinical trials with time-to-event endpoints. We derive the theoretical properties of the proposed adaptive randomization design and show through comprehensive numerical simulations that it can achieve ethical objectives without sacrificing efficiency. Our combined theoretical and numerical results offer a strong foundation for the practical use of RAR in real clinical trials.

Seamless Clinical Trials with Doubly Adaptive Biased Coin Designs

In addition to scientific questions, clinical trialists often explore or require other design features, such as increasing the power while controlling the type I error rate, minimizing unnecessary exposure to inferior treatments, and comparing multiple treatments in one clinical trial. We propose implementing adaptive seamless design (ASD) with response adaptive randomization (RAR) to satisfy various clinical trials’ design objectives. However, the combination of ASD and RAR poses a challenge in controlling the type I error rate. In this paper, we investigated how to utilize the advantages of the two adaptive methods and control the type I error rate. We offered the theoretical foundation for this procedure. Numerical studies demonstrated that our methods could achieve efficient and ethical objectives while controlling the type I error rate.

Response‐adaptive treatment allocation for clinical studies with recurrent event and terminal event data

In long-term clinical studies, recurrent event data are frequently collected to contrast the efficacy of two different treatments. However, the recurrent event process can be stopped by a terminal event, such as death. For analyzing recurrent event and terminal event data, joint frailty modeling has recently received considerable attention because it makes it possible to study the joint evolution over time of both recurrent and terminal event processes and gives consistent and efficient parameters. For a two-arm clinical trial design based on these data sets, there has been limited research on investigating the balanced design, let alone adaptive treatment allocation. Although equal sample size allocation obtained for both treatments is intuitively first adopted in a trial design, if one treatment is expected to be superior, it may be desirable to allocate more subjects to the effective treatment. In this article, we calculate the required sample size based on restricted randomization and then propose a target response-adaptive randomization procedure for recurrent and terminal event outcomes based on the joint frailty model. A randomization procedure, the doubly adaptive biased coin design that targets some optimal allocations, is implemented. The proposed adaptive treatment allocation schemes have been shown to be capable of reducing the number of trial participants who receive inferior treatment while simultaneously reaching an optimal target, as well as retaining a comparable test power as compared to a restricted randomization design. Finally, two clinical studies, the COAPT trial and the A-HeFT trial, are used to illustrate the advantages of adopting the proposed procedure.

A practical response adaptive block randomization (RABR) design with analytic type I error protection

Response adaptive randomization (RAR) is appealing from methodological, ethical, and pragmatic perspectives in the sense that subjects are more likely to be randomized to better performing treatment groups based on accumulating data. However, applications of RAR in confirmatory drug clinical trials with multiple active arms are limited largely due to its complexity, and lack of control of randomization ratios to different treatment groups. To address the aforementioned issues, we propose a Response Adaptive Block Randomization (RABR) design allowing arbitrarily prespecified randomization ratios for the control and high-performing groups to meet clinical trial objectives. We show the validity of the conventional unweighted test in RABR with a controlled type I error rate based on the weighted combination test for sample size adaptive design invoking no large sample approximation. The advantages of the proposed RABR in terms of robustly reaching target final sample size to meet regulatory requirements and increasing statistical power as compared with the popular Doubly Adaptive Biased Coin Design are demonstrated by statistical simulations and a practical clinical trial design example.

Adaptive treatment allocation for comparative clinical studies with recurrent events data.

In long-term clinical studies, recurrent event data are sometimes collected and used to contrast the efficacies of two different treatments. The event reoccurrence rates can be compared using the popular negative binomial model, which incorporates information related to patient heterogeneity into a data analysis. For treatment allocation, a balanced approach in which equal sample sizes are obtained for both treatments is predominately adopted. However, if one treatment is superior, then it may be desirable to allocate fewer subjects to the less-effective treatment. To accommodate this objective, a sequential response-adaptive treatment allocation procedure is derived based on the doubly adaptive biased coin design. Our proposed treatment allocation schemes have been shown to be capable of reducing the number of subjects receiving the inferior treatment while simultaneously retaining a test power level that is comparable to that of a balanced design. The redesign of a clinical study illustrates the advantages of using our procedure.

Response-adaptive treatment allocation for clinical studies with ordinal responses.

Ordinal responses are common in clinical studies. Although the proportional odds model is a popular option for analyzing ordered-categorical data, it cannot control the type I error rate when the proportional odds assumption fails to hold. The latent Weibull model was recently shown to be a superior candidate for modeling ordinal data, with remarkably better performance than the latent normal model when the data are highly skewed. In clinical trials with ordinal responses, a balanced design is common, with equal sample allocation for each treatment. However, a more ethical approach is to adopt a response-adaptive allocation scheme in which more patients receive the better treatment. In this paper, we propose the use of the doubly adaptive biased coin design to generate treatment allocations that benefit the trial participants. The proposed treatment allocation scheme not only allows more patients to receive the better treatment, it also maintains compatible test power for the comparison of treatment efficiencies. A clinical example is used to illustrate the proposed procedure.

Bayesian selective response‐adaptive design using the historical control

High quality historical control data, if incorporated, may reduce sample size, trial cost, and duration. A too optimistic use of the data, however, may result in bias under prior‐data conflict. Motivated by well‐publicized two‐arm comparative trials in stroke, we propose a Bayesian design that both adaptively incorporates historical control data and selectively adapt the treatment allocation ratios within an ongoing trial responsively to the relative treatment effects. The proposed design differs from existing designs that borrow from historical controls. As opposed to reducing the number of subjects assigned to the control arm blindly, this design does so adaptively to the relative treatment effects only if evaluation of cumulated current trial data combined with the historical control suggests the superiority of the intervention arm. We used the effective historical sample size approach to quantify borrowed information on the control arm and modified the treatment allocation rules of the doubly adaptive biased coin design to incorporate the quantity. The modified allocation rules were then implemented under the Bayesian framework with commensurate priors addressing prior‐data conflict. Trials were also more frequently concluded earlier in line with the underlying truth, reducing trial cost, and duration and yielded parameter estimates with smaller standard errors.

Response-adaptive treatment allocation for non-inferiority trials with heterogeneous variances

In clinical studies, patients usually accrue sequentially. The response-adaptive design has been shown to be a valuable treatment allocation apparatus that skews the treatment allocation probabilities to achieve certain objectives such as reducing the number of patients who receive inferior treatments. The doubly adaptive biased coin design was successfully derived for the three-arm non-inferiority (NI) trial. For an NI study, an experimental treatment can be considered a possible substitute for the standard treatment if the loss of clinically tolerable efficacy is compensated by benefits such as the alleviation of side effects. Previous applications of the doubly adaptive biased coin design in NI trials were developed only for homogeneous treatment variances. However, it is worth to examine the more complicated, but nevertheless popular, scenarios in which the treatment variances are heterogeneous. The proposed treatment allocation scheme is superior when the treatment variances differ and remains very competitive when they are homogeneous. A clinical example is given for demonstrative purposes.

Palliative chemoradiotherapy versus radiotherapy alone for dysphagia in advanced oesophageal cancer: a multicentre randomised controlled trial (TROG 03.01)

A short course of radiotherapy is commonly prescribed for palliative relief of malignant dysphagia in patients with incurable oesophageal cancer. We compared chemoradiotherapy with radiotherapy alone for dysphagia relief in the palliative setting. This multicentre randomised controlled trial included patients with advanced or metastatic oesophageal cancer who were randomly assigned (1:1) through a computer-generated adaptive biased coin design to either palliative chemoradiotherapy or radiotherapy alone for treatment of malignant dysphagia at 22 hospitals in Australia, Canada, New Zealand, and the UK. Eligible patients had biopsy-proven oesophageal cancer that was unsuitable for curative treatment, symptomatic dysphagia, Eastern Cooperative Oncology Group performance status 0-2, and adequate haematological and renal function. Patients were stratified by hospital, dysphagia score (Mellow scale 1-4), and presence of metastases. The radiotherapy dose was 35 Gy in 15 fractions over 3 weeks for patients in Australia and New Zealand and 30 Gy in ten fractions over 2 weeks for patients in Canada and the UK. Chemotherapy consisted of one cycle of intravenous cisplatin (either 80 mg/m2 on day 1 or 20 mg/m2 per day on days 1-4 of radiotherapy at clinician's discretion) and intravenous fluorouracil 800 mg/m2 per day on days 1-4 of radiotherapy in week 1. Patients were assessed weekly during treatment. The primary endpoint was dysphagia relief (defined as ≥1 point reduction on the Mellow scale at 9 weeks and maintained 4 weeks later), and key secondary endpoints were dysphagia progression-free survival (defined as a worsening of at least 1 point on the Mellow scale from baseline or best response) and overall survival. These endpoints were analysed in the intention-to-treat population. This study is registered at ClinicalTrials.gov, number NCT00193882. This trial is closed. Between July 7, 2003, and March 21, 2012, 111 patients were randomly assigned to chemoradiotherapy and 109 patients to radiotherapy. One patient in the chemoradiotherapy group was omitted from analysis because of ineligibility. 50 (45%, 95% CI 36-55) patients in the chemoradiotherapy group and 38 (35%, 26-44) in the radiotherapy group obtained dysphagia relief (difference 10·6%, 95% CI -2 to 23; p=0·13). Median dysphagia progression-free survival was 4·1 months (95% CI 3·5-4·8) versus 3·4 months (3·1-4·3) in the chemoradiotherapy and radiotherapy groups, respectively (p=0·58), and median overall survival was 6·9 months (95% CI 5·1-8·3) versus 6·7 months (4·9-8·0), respectively (p=0·88). Of the 211 patients who commenced radiotherapy, grade 3-4 acute toxicity occurred in 38 (36%) patients in the chemoradiotherapy group and in 17 (16%) patients in the radiotherapy group (p=0·0017). Anaemia, thrombocytopenia, neutropenia, oesophagitis, diarrhoea, nausea and vomiting, and mucositis were significantly worse in patients who had chemoradiotherapy than in patients who had radiotherapy. Palliative chemoradiotherapy showed a modest, but not statistically significant, increase in dysphagia relief compared with radiotherapy alone, with minimal improvement in dysphagia progression-free survival and overall survival with chemoradiotherapy but at a cost of increased toxicity. A short course of radiotherapy alone should be considered a safe and well tolerated treatment for malignant dysphagia in the palliative setting. National Health and Medical Research Council, Canadian Cancer Society Research Institute, Canadian Cancer Trials Group, Trans Tasman Radiation Oncology Group, and Cancer Australia.

Bayesian doubly adaptive randomization in clinical trials

Bayesian adaptive randomization has attracted increasingly attention in the literature and has been implemented in many phase II clinical trials. Doubly adaptive biased coin design (DBCD) is a superior choice in response-adaptive designs owing to its promising properties. In this paper, we propose a randomized design by combining Bayesian adaptive randomization with doubly adaptive biased coin design. By selecting a fixed tuning parameter, the proposed randomization procedure can target an explicit allocation proportion, and assign more patients to the better treatment simultaneously. Moreover, the proposed randomization is efficient to detect treatment differences. We illustrate the proposed design by its applications to both discrete and continuous responses, and evaluate its operating features through simulation studies.

Adaptive Designs for Non-inferiority Trials with Multiple Experimental Treatments.

The increase in the popularity of non-inferiority clinical trials represents the increasing need to search for substitutes for some reference (standard) treatments. A new treatment would be preferred to the standard treatment if the benefits of adopting it outweigh a possible clinically insignificant reduction in treatment efficacy (non-inferiority margin). Statistical procedures have recently been developed for treatment comparisons in non-inferiority clinical trials that have multiple experimental (new) treatments. An ethical concern for non-inferiority trials is that some patients undergo the less effective treatments; this problem is more serious when multiple experimental treatments are included in a balanced trial in which the sample sizes are the same for all experimental treatments. With the aim of giving fewer patients the inferior treatments, we propose a response-adaptive treatment allocation scheme that is based on the doubly adaptive biased coin design. The proposed adaptive design is also shown to be superior to the balanced design in terms of testing power.

Outcome-adaptive randomization for a delayed outcome with a short-term predictor: imputation-based designs.

Delay in the outcome variable is challenging for outcome-adaptive randomization, as it creates a lag between the number of subjects accrued and the information known at the time of the analysis. Motivated by a real-life pediatric ulcerative colitis trial, we consider a case where a short-term predictor is available for the delayed outcome. When a short-term predictor is not considered, studies have shown that the asymptotic properties of many outcome-adaptive randomization designs are little affected unless the lag is unreasonably large relative to the accrual process. These theoretical results assumed independent identical delays, however, whereas delays in the presence of a short-term predictor may only be conditionally homogeneous. We consider delayed outcomes as missing and propose mitigating the delay effect by imputing them. We apply this approach to the doubly adaptive biased coin design (DBCD) for motivating pediatric ulcerative colitis trial. We provide theoretical results that if the delays, although non-homogeneous, are reasonably short relative to the accrual process similarly as in the iid delay case, the lag is also asymptotically ignorable in the sense that a standard DBCD that utilizes only observed outcomes attains target allocation ratios in the limit. Empirical studies, however, indicate that imputation-based DBCDs performed more reliably in finite samples with smaller root mean square errors. The empirical studies assumed a common clinical setting where a delayed outcome is positively correlated with a short-term predictor similarly between treatment arm groups. We varied the strength of the correlation and considered fast and slow accrual settings.

Multi-objective optimal designs in comparative clinical trials with covariates: The reinforced doubly adaptive biased coin design

The present paper deals with the problem of allocating patients to two competing treatments in the presence of covariates or prognostic factors in order to achieve a good trade-off among ethical concerns, inferential precision and randomness in the treatment allocations. In particular we suggest a multipurpose design methodology that combines efficiency and ethical gain when the linear homoscedastic model with both treatment/covariate interactions and interactions among covariates is adopted. The ensuing compound optimal allocations of the treatments depend on the covariates and their distribution on the population of interest, as well as on the unknown parameters of the model. Therefore, we introduce the reinforced doubly adaptive biased coin design, namely a general class of covariate-adjusted response-adaptive procedures that includes both continuous and discontinuous randomization functions, aimed to target any desired allocation proportion. The properties of this proposal are described both theoretically and through simulations.

Doubly adaptive biased coin designs for balancing competing objectives in time-to-event trials

Doubly adaptive biased coin designs for balancing competing objectives in time-to-event trials

Frequentist performance of Bayesian inference with response‐adaptive designs

In controlled clinical trials, where minimizing treatment failures is crucial, response-adaptive designs are attractive competitors to 1:1 randomized designs for comparing the success rates φ(1) and φ(2) of two treatments. In these designs each new treatment assignment depends on previous outcomes through some predefined rule. Here Play-The-Winner (PW), Randomized Play-The-Winner (RPW), Drop-The-Loser, Generalized Drop-the-Loser and Doubly adaptive Biased Coin Designs are considered for new treatment assignments. As frequentist inference relies on complex sampling distributions in those designs, we investigate how Bayesian inference, based on two independent Beta prior distributions, performs from a frequentist point-of-view. Performance is assessed through coverage probabilities of interval estimation procedures, power and minimization of failure count. It is shown that Bayesian inference can be favorably compared to frequentist procedures where the latter are available. The power of response-adaptive designs is generally very close to the power of 1:1 randomized design. However, failure count savings are generally small, except for the PW and Doubly adaptive Biased Coin designs in particular ranges of the true success rates. The RPW assignment rule has the worst performance, while PW, Generalized Drop-the-Loser or Doubly adaptive Biased Coin Designs may outperform other designs depending on different particular ranges of the true success rates.

An optimal response adaptive biased coin design with k heteroscedastic treatments

For comparing treatments in clinical trials, Atkinson (1982) introduced optimal biased coins for balancing patients across treatment assignments by using D-optimality under the assumption of homoscedastic responses of different treatments. However, this assumption can be violated in many real applications. In this paper, we relax the homoscedasticity assumption in the k treatments setting with k > 2 . A general family of optimal response adaptive biased coin designs are proposed following Atkinson's procedure. Asymptotic properties of the proposed designs are obtained. Some advantages of the proposed design are discussed.

Doubly adaptive biased coin designs with heterogeneous responses

Doubly adaptive biased coin design (DBCD) is an important family of response-adaptive randomization procedures for clinical trials. It uses sequentially updated estimation to skew the allocation probability to favor the treatment that has performed better thus far. An important assumption for the DBCD is the homogeneity assumption for the patient responses. However, this assumption may be violated in many sequential experiments. Here we prove the robustness of the DBCD against certain time trends in patient responses. Strong consistency and asymptotic normality of the design are obtained under some widely satisfied conditions. Also, we propose a general weighted likelihood method to reduce the bias caused by the heterogeneity in the inference after a trial. Some numerical studies are also presented to illustrate the finite sample properties of DBCD.

Doubly adaptive biased coin designs with delayed responses

AbstractIn clinical studies, patients are usually accrued sequentially. Response‐adaptive designs are then useful tools for assigning treatments to incoming patients as a function of the treatment responses observed thus far. In this regard, doubly adaptive biased coin designs have advantageous properties under the assumption that their responses can be obtained immediately after testing. However, it is a common occurrence that responses are observed only after a certain period of time. The authors examine the effect of delayed responses on doubly adaptive biased coin designs and derive some of their asymptotic properties. It turns out that these designs are relatively insensitive to delayed responses under widely satisfied conditions. This is illustrated with a simulation study.