Leveraging machine learning: Covariate-adjusted Bayesian adaptive randomization and subgroup discovery in multi-arm survival trials

Clinical trials evaluate the safety and efficacy of treatments for specific diseases. Ensuring these studies are well-powered is crucial for identifying superior treatments. With the rise of personalized medicine, treatment efficacy may vary based on biomarker profiles. However, researchers often lack prior knowledge about which biomarkers are linked to varied treatment effects. Fixed or response-adaptive designs may not sufficiently account for heterogeneous patient characteristics, such as genetic diversity, potentially reducing the chance of selecting the optimal treatment for individuals. Recent advances in Bayesian nonparametric modeling pave the way for innovative trial designs that not only maintain robust power but also offer the flexibility to identify subgroups deriving greater benefits from specific treatments. Building on this inspiration, we introduce a Bayesian adaptive design for multi-arm trials focusing on time-to-event endpoints. We introduce a covariate-adjusted response adaptive randomization, updating treatment allocation probabilities grounded on causal effect estimates using a random intercept accelerated failure time BART model. After the trial concludes, we suggest employing a multi-response decision tree to pinpoint subgroups with varying treatment impacts. The performance of our design is then assessed via comprehensive simulations.

Using biomarkers to allocate patients in a response-adaptive clinical trial

In this paper, we discuss a response adaptive randomization method, and why it should be used in clinical trials for rare diseases compared to a randomized controlled trial with equal fixed randomization. The developed method uses a patient's biomarkers to alter the allocation probability to each treatment, in order to emphasize the benefit to the trial population. The method starts with an initial burn-in period of a small number of patients, who with equal probability, are allocated to each treatment. We then use a regression method to predict the best outcome of the next patient, using their biomarkers and the information from the previous patients. This estimated best treatment is assigned to the next patient with high probability. A completed clinical trial for the effect of catumaxomab on the survival of cancer patients is used as an example to demonstrate the use of the method and the differences to a controlled trial with equal allocation. Different regression procedures are investigated and compared to a randomized controlled trial, using efficacy and ethical measures.

Covariate-adjusted response-adaptive designs based on semiparametric approaches

We consider theoretical and practical issues for innovatively using a large number of covariates in clinical trials to achieve various design objectives without model misspecification. Specifically, we propose a new family of semiparametric covariate-adjusted response-adaptive randomization (CARA) designs and we use the target maximum likelihood estimation (TMLE) to analyze the correlated data from CARA designs. Our approach can flexibly achieve multiple objectives and correctly incorporate the effect of a large number of covariates on the responses without model misspecification. We also obtain the consistency and asymptotic normality of the target parameters, allocation probabilities, and allocation proportions. Numerical studies demonstrate that our approach has advantages over existing approaches, even when the data-generating distribution is complicated.

Model-based adaptive randomization procedures for heteroscedasticity of treatment responses

In clinical trials, the responses of patients usually depend on the assigned treatment as well as some important covariates, which may cause heteroscedasticity in treatment responses. As clinical trials are generally designed to demonstrate efficacy for the overall population, they are usually not adequately powered for detecting interactions. To improve the power of interaction tests, this article develops two model-based adaptive randomization procedures for heteroscedasticity of treatment responses, and derives their limiting allocation proportions, which are generalizations of the Neyman allocation. Issues of hypothesis testing and sample size estimation are also addressed. Simulation studies show that compared with complete randomization, the two model-based randomization procedures have greater power to detect differences in systematic effects, main treatment effects and treatment-covariate interactions. In addition, the validity of limiting allocation proportion is also verified through simulations.

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.

Multi-arm covariate adjusted response adaptive designs for ordinal outcome clinical trials

Covariate adjusted response adaptive designs are developed with ordinal categorical responses for phase III clinical trial involving multiple treatments. Stochastic ordering principle is used to order the treatments according to effectiveness and consequently allocation functions are developed by combining the cumulative odds ratios suitably. The performance of the proposed designs is investigated through relevant exact as well as large sample measures. To investigate the performance in a real situation, a real clinical trial involving lung cancer patients is further redesigned using the proposed allocation design.

Personalized Risk-Based Screening Design for Comparative Two-Arm Group Sequential Clinical Trials

Personalized medicine has been emerging to take into account individual variability in genes and environment. In the era of personalized medicine, it is critical to incorporate the patients’ characteristics and improve the clinical benefit for patients. The patients’ characteristics are incorporated in adaptive randomization to identify patients who are expected to get more benefit from the treatment and optimize the treatment allocation. However, it is challenging to control potential selection bias from using observed efficacy data and the effect of prognostic covariates in adaptive randomization. This paper proposes a personalized risk-based screening design using Bayesian covariate-adjusted response-adaptive randomization that compares the experimental screening method to a standard screening method based on indicators of having a disease. Personalized risk-based allocation probability is built for adaptive randomization, and Bayesian adaptive decision rules are calibrated to preserve error rates. A simulation study shows that the proposed design controls error rates and yields a much smaller number of failures and a larger number of patients allocated to a better intervention compared to existing randomized controlled trial designs. Therefore, the proposed design performs well for randomized controlled clinical trials under personalized medicine.

Comparative Effectiveness Research using Bayesian Adaptive Designs for Rare Diseases: Response Adaptive Randomization Reusing Participants

Slow accrual rate is a major challenge in clinical trials for rare diseases and is identified as the most frequent reason for clinical trials to fail. This challenge is amplified in comparative effectiveness research where multiple treatments are compared to identify the best treatment. Novel efficient clinical trial designs are in urgent need in these areas. Our proposed response adaptive randomization (RAR) reusing participants trial design mimics the real-world clinical practice that allows patients to switch treatments when desired outcome is not achieved. The proposed design increases efficiency by two strategies: 1) Allowing participants to switch treatments so that each participant can have more than one observation and hence it is possible to control for participant specific variability to increase statistical power; and 2) Utilizing RAR to allocate more participants to the promising arms such that ethical and efficient studies will be achieved. Extensive simulations were conducted and showed that, compared with trials where each participant receives one treatment, the proposed participants reusing RAR design can achieve comparable power with a smaller sample size and a shorter trial duration, especially when the accrual rate is low. The efficiency gain decreases as the accrual rate increases.

Incorporating covariates information in adaptive clinical trials for precision medicine

Precision medicine is the systematic use of information that pertains to an individual patient to select or optimize that patient's preventative and therapeutic care. Recent studies have classified biomarkers into predictive and prognostic biomarkers based on their roles in clinical studies. To design a clinical trial for precision medicine, predictive biomarkers and prognostic biomarkers should both be included. In statistical analysis, biomarkers are mathematically treated as covariates. We first classify covariates into predictive and prognostic covariates according to their roles. We then provide a brief review of recent advances in adaptive designs that incorporate covariates. However, the literature includes no designs that incorporate both prognostic covariates and predictive covariates simultaneously. In this paper, we propose a new family of covariate-adjusted response-adaptive (CARA) designs that incorporate both prognostic and predictive covariates and the responses. It is important to note that the predictive biomarkers and prognostic biomarkers play different roles in the new designs. The advantages of the proposed methods are demonstrated via numerical studies, and some further statistical issues are also discussed.

Adding flexibility to clinical trial designs: an example-based guide to the practical use of adaptive designs

Adaptive designs for clinical trials permit alterations to a study in response to accumulating data in order to make trials more flexible, ethical, and efficient. These benefits are achieved while preserving the integrity and validity of the trial, through the pre-specification and proper adjustment for the possible alterations during the course of the trial. Despite much research in the statistical literature highlighting the potential advantages of adaptive designs over traditional fixed designs, the uptake of such methods in clinical research has been slow. One major reason for this is that different adaptations to trial designs, as well as their advantages and limitations, remain unfamiliar to large parts of the clinical community. The aim of this paper is to clarify where adaptive designs can be used to address specific questions of scientific interest; we introduce the main features of adaptive designs and commonly used terminology, highlighting their utility and pitfalls, and illustrate their use through case studies of adaptive trials ranging from early-phase dose escalation to confirmatory phase III studies.

Maximum likelihood estimation of generalized linear models for adaptive designs: Applications and asymptotics

Due to increasing discoveries of biomarkers and observed diversity among patients, there is growing interest in personalized medicine for the purpose of increasing the well-being of patients (ethics) and extending human life. In fact, these biomarkers and observed heterogeneity among patients are useful covariates that can be used to achieve the ethical goals of clinical trials and improving the efficiency of statistical inference. Covariate-adjusted response-adaptive (CARA) design was developed to use information in such covariates in randomization to maximize the well-being of participating patients as well as increase the efficiency of statistical inference at the end of a clinical trial. In this paper, we establish conditions for consistency and asymptotic normality of maximum likelihood (ML) estimators of generalized linear models (GLM) for a general class of adaptive designs. We prove that the ML estimators are consistent and asymptotically follow a multivariate Gaussian distribution. The efficiency of the estimators and the performance of response-adaptive (RA), CARA, and completely randomized (CR) designs are examined based on the well-being of patients under a logit model with categorical covariates. Results from our simulation studies and application to data from a clinical trial on stroke prevention in atrial fibrillation (SPAF) show that RA designs lead to ethically desirable outcomes as well as higher statistical efficiency compared to CARA designs if there is no treatment by covariate interaction in an ideal model. CARA designs were however more ethical than RA designs when there was significant interaction.

A class of Covariate-Adjusted Response-Adaptive Allocation Designs for Multitreatment Binary Response Trials

A class of covariate-adjusted response-adaptive randomization procedures is developed for binary treatment outcomes in a phase III clinical trial set up involving multiple treatments. The target allocation is developed by combining the ethical aspects with statistical precision under the existence of treatment covariate interaction. Relevant measures of the performance for the proposed allocation designs are studied and compared.

Response-adaptive designs for binary responses: How to offer patient benefit while being robust to time trends?

Response‐adaptive randomisation (RAR) can considerably improve the chances of a successful treatment outcome for patients in a clinical trial by skewing the allocation probability towards better performing treatments as data accumulates. There is considerable interest in using RAR designs in drug development for rare diseases, where traditional designs are not either feasible or ethically questionable. In this paper, we discuss and address a major criticism levelled at RAR: namely, type I error inflation due to an unknown time trend over the course of the trial. The most common cause of this phenomenon is changes in the characteristics of recruited patients—referred to as patient drift. This is a realistic concern for clinical trials in rare diseases due to their lengthly accrual rate. We compute the type I error inflation as a function of the time trend magnitude to determine in which contexts the problem is most exacerbated. We then assess the ability of different correction methods to preserve type I error in these contexts and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations as to which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the 2‐armed and the multi‐armed case. We further propose a RAR design for multi‐armed clinical trials, which is computationally efficient and robust to several time trends considered.

Covariate-adjusted response-adaptive randomization for multi-arm clinical trials using a modified forward looking Gittins index rule

We introduce a non-myopic, covariate-adjusted response adaptive (CARA) allocation design for multi-armed clinical trials. The allocation scheme is a computationally tractable procedure based on the Gittins index solution to the classic multi-armed bandit problem and extends the procedure recently proposed in Villar et al. (2015). Our proposed CARA randomization procedure is defined by reformulating the bandit problem with covariates into a classic bandit problem in which there are multiple combination arms, considering every arm per each covariate category as a distinct treatment arm. We then apply a heuristically modified Gittins index rule to solve the problem and define allocation probabilities from the resulting solution. We report the efficiency, balance, and ethical performance of our approach compared to existing CARA methods using a recently published clinical trial as motivation. The net savings in terms of expected number of treatment failures is considerably larger and probably enough to make this design attractive for certain studies where known covariates are expected to be important, stratification is not desired, treatment failures have a high ethical cost, and the disease under study is rare. In a two-armed context, this patient benefit advantage comes at the expense of increased variability in the allocation proportions and a reduction in statistical power. However, in a multi-armed context, simple modifications of the proposed CARA rule can be incorporated so that an ethical advantage can be offered without sacrificing power in comparison with balanced designs.

Information-adaptive clinical trials with selective recruitment and binary outcomes

Selective recruitment designs preferentially recruit individuals who are estimated to be statistically informative onto a clinical trial. Individuals who are expected to contribute less information have a lower probability of recruitment. Furthermore, in an information-adaptive design, recruits are allocated to treatment arms in a manner that maximises information gain. The informativeness of an individual depends on their covariate (or biomarker) values, and how information is defined is a critical element of information-adaptive designs. In this paper, we define and evaluate four different methods for quantifying statistical information. Using both experimental data and numerical simulations, we show that selective recruitment designs can offer a substantial increase in statistical power compared with randomised designs. In trials without selective recruitment, we find that allocating individuals to treatment arms according to information-adaptive protocols also leads to an increase in statistical power. Consequently, selective recruitment designs can potentially achieve successful trials using fewer recruits thereby offering economic and ethical advantages. Copyright © 2017 John Wiley & Sons, Ltd.

Comparing three regularization methods to avoid extreme allocation probability in response-adaptive randomization

We examine three variations of the regularization methods for response-adaptive randomization (RAR) and compare their operating characteristics. A power transformation (PT) is applied to refine the randomization probability. The clip method is used to bound the randomization probability within specified limits. A burn-in period of equal randomization (ER) can be added before adaptive randomization (AR). For each method, more patients are assigned to the superior arm and overall response rate increase as the scheme approximates simple AR, while statistical power increases as it approximates ER. We evaluate the performance of the three methods by varying the tuning parameter to control the extent of AR to achieve the same statistical power. When there is no early stopping rule, PT method generally performed the best in yielding higher proportion to the superior arm and higher overall response rate, but with larger variability. The burn-in method showed smallest variability compared with the clip method and the PT method. With the efficacy early stopping rule, all three methods performed more similarly. The PT and clip methods are better than the burn-in method in achieving higher proportion randomized to the superior arm and higher overall response rate but burn-in method required fewer patients in the trial. By carefully choosing the method and the tuning parameter, RAR methods can be tailored to strike a balance between achieving the desired statistical power and enhancing the overall response rate.

A Unified Family of Covariate-Adjusted Response-Adaptive Designs Based on Efficiency and Ethics

Response-adaptive designs have recently attracted more and more attention in the literature because of its advantages in efficiency and medical ethics. To develop personalized medicine, covariate information plays an important role in both design and analysis of clinical trials. A challenge is how to incorporate covariate information in response-adaptive designs while considering issues of both efficiency and medical ethics. To address this problem, we propose a new and unified family of covariate-adjusted response-adaptive (CARA) designs based on two general measurements of efficiency and ethics. Important properties (including asymptotic properties) of the proposed procedures are studied under categorical covariates. This new family of designs not only introduces new desirable CARA designs, but also unifies several important designs in the literature. We demonstrate the proposed procedures through examples, simulations, and a discussion of related earlier work.

Simulation study for evaluating the performance of response-adaptive randomization

A response-adaptive randomization (RAR) design refers to the method in which the probability of treatment assignment changes according to how well the treatments are performing in the trial. Holding the promise of treating more patients with the better treatments, RARs have been successfully implemented in clinical trials. We compared equal randomization (ER) with three RARs: Bayesian adaptive randomization, sequential maximum likelihood, and sequential posterior mean. We fixed the total number of patients, considered as patient horizon, but varied the number of patients in the trial. Among the designs, we compared the proportion of patients assigned to the superior arm, overall response rate, statistical power, and total patients enrolled in the trial with and without adding an efficacy early stopping rule. Without early stopping, ER is preferred when the number of patients beyond the trial is much larger than the number of patients in the trial. RAR is favored for large treatment difference or when the number of patients beyond the trial is small. With early stopping, the difference between these two types of designs was reduced. By carefully choosing the design parameters, both RAR and ER methods can achieve the desirable statistical properties. Within three RAR methods, we recommend SPM considering the larger proportion in the better arm and higher overall response rate than BAR and similar power and trial size with ER. The ultimate choice of RAR or ER methods depends on the investigator's preference, the trade-off between group ethics and individual ethics, and logistic considerations in the trial conduct, etc.

Can response-adaptive randomization increase participation in acute stroke trials?

BACKGROUND AND PURPOSE

A response-adaptive randomization (RAR) trial design actively adjusts the ratio of participants assigned to each trial arm, favoring the better performing treatment by using outcome data from participants already in the trial. Compared with a standard clinical trial, an RAR study design has the potential to improve patient participation in acute stroke trials.

METHODS

This cross-sectional randomized survey included adult emergency department patients, age≥18, without symptoms of stroke or other critical illness. A standardized protocol was used, and subjects were randomized to either an RAR or standard hypothetical acute stroke trial. After viewing the video describing the hypothetical trial (http://youtu.be/cKIWduCaPZc), reviewing the consent form, and having questions answered, subjects indicated whether they would consent to the trial. A multivariable logistic regression model was fitted to estimate the impact of RAR while controlling for demographic factors and patient understanding of the design.

RESULTS

A total of 418 subjects (210 standard and 208 RAR) were enrolled. All baseline characteristics were balanced between groups. There was significantly higher participation in the RAR trial (67.3%) versus the standard trial (54.5%), absolute increase: 12.8% (95% confidence interval, 3.7-22.2). The RAR group had a higher odds ratio of agreeing to research (odds ratio, 1.89; 95% confidence interval, 1.2-2.9) while adjusting for patient level factors. Trial designs were generally well understood by the participants.

CONCLUSIONS

The hypothetical RAR trial attracted more research participation than standard randomization. RAR has the potential to increase recruitment and offer benefit to future trial participants.

Estimation and testing in targeted goup sequential covariate-adjusted randomized clinical trials

This article is devoted to the construction and asymptotic study of adaptive group sequential covariate-adjusted randomized clinical trials analyzed through the prism of the semipara-metric methodology of targeted maximum likelihood estimation (TMLE). We show how to build, as the data accrue group-sequentially, a sampling design which targets a user-supplied optimal design. We also show how to carry out a sound TMLE statistical inference based on such an adaptive sampling scheme (therefore extending some results known in the i.i.d setting only so far), and how group-sequential testing applies on top of it. The procedure is robust (i.e., consistent even if the working model is misspecified). A simulation study confirms the theoretical results, and validates the conjecture that the procedure may also be efficient.

A covariate-adjusted response-adaptive allocation in clinical trials for a general class of responses

A class of covariate-adjusted adaptive allocation procedures is developed for a general class of responses with an aim to satisfy relevant clinical requirements. Some exact and asymptotic properties of the procedures, proposed and a reasonable competitor, are studied and compared under the presence of treatment-covariate interaction.

Multiple-stage sampling procedure for covariate-adjusted response-adaptive designs

Covariate-adjusted response-adaptive (CARA) design becomes an important statistical tool for evaluating and comparing the performance of treatments when targeted medicine and adaptive therapy become important medical innovations. Due to the nature of the adaptive therapies of interest and how subjects accrue to a sampling procedure, it is of interest how to control the sample size sequentially such that the estimates of treatment effects have satisfactory precision in addition to its asymptotic properties. In this paper, we apply a multiple-stage sequential sampling method to CARA design in such a way that the control of the sample size is more feasible. The theoretical properties of the proposed method, including the estimates of regression parameters and the allocation probabilities under this randomly stopped sampling procedure, are discussed. The numerical results based on synthesized data and a real example are presented.

Adaptive randomization for clinical trials

In February 2010, the U.S. Food and Drug Administration (FDA, 2010 ) drafted guidance that discusses the statistical, clinical, and regulatory aspects of various adaptive designs for clinical trials. An important class of adaptive designs is adaptive randomization, which is considered very briefly in subsection VI.B of the guidance. The objective of this paper is to review several important new classes of adaptive randomization procedures and convey information on the recent developments in the literature on this topic. Much of this literature has been focused on the development of methodology to address past criticisms and concerns that have hindered the broader use of adaptive randomization. We conclude that adaptive randomization is a very broad area of experimental design that has important application in modern clinical trials.

An urn based covariate adjusted response adaptive allocation design

An urn based covariate adjusted response adaptive allocation design with dichotomous responses is proposed incorporating the ordered nature of the covariate. The allocation procedure is assessed both numerically and theoretically. The performance of the allocation design is also investigated in a relevant hypothetical clinical trial.

Covariate-adjusted response-adaptive designs for longitudinal treatment responses: PEMF trial revisited

Response-adaptive designs have become popular for allocation of the entering patients among two or more competing treatments in a phase III clinical trial. Although there are a lot of designs for binary treatment responses, the number of designs involving covariates is very small. Sometimes the patients give repeated responses. The only available response-adaptive allocation design for repeated binary responses is the urn design by Biswas and Dewanji [Biswas A and Dewanji AA. Randomized longitudinal play-the-winner design for repeated binary data. ANZJS 2004; 46: 675–684; Biswas A and Dewanji A. Inference for a RPW-type clinical trial with repeated monitoring for the treatment of rheumatoid arthritis. Biometr J 2004; 46: 769–779.], although it does not take care of the covariates of the patients in the allocation design. In this article, a covariate-adjusted response-adaptive randomisation procedure is developed using the log-odds ratio within the Bayesian framework for longitudinal binary responses. The small sample performance of the proposed allocation procedure is assessed through a simulation study. The proposed procedure is illustrated using some real data set.

Response-adaptive randomization for clinical trials with adjustment for covariate imbalance

In clinical trials with a small sample size, the characteristics (covariates) of patients assigned to different treatment arms may not be well balanced. This may lead to an inflated type I error rate. This problem can be more severe in trials that use response-adaptive randomization rather than equal randomization because the former may result in smaller sample sizes for some treatment arms. We have developed a patient allocation scheme for trials with binary outcomes to adjust the covariate imbalance during response-adaptive randomization. We used simulation studies to evaluate the performance of the proposed design. The proposed design keeps the important advantage of a standard response-adaptive design, that is to assign more patients to the better treatment arms, and thus it is ethically appealing. On the other hand, the proposed design improves over the standard response-adaptive design by controlling covariate imbalance between treatment arms, maintaining the nominal type I error rate, and offering greater power.

A simulation study for comparing testing statistics in response-adaptive randomization

Background

Response-adaptive randomizations are able to assign more patients in a comparative clinical trial to the tentatively better treatment. However, due to the adaptation in patient allocation, the samples to be compared are no longer independent. At large sample sizes, many asymptotic properties of test statistics derived for independent sample comparison are still applicable in adaptive randomization provided that the patient allocation ratio converges to an appropriate target asymptotically. However, the small sample properties of commonly used test statistics in response-adaptive randomization are not fully studied.

Methods

Simulations are systematically conducted to characterize the statistical properties of eight test statistics in six response-adaptive randomization methods at six allocation targets with sample sizes ranging from 20 to 200. Since adaptive randomization is usually not recommended for sample size less than 30, the present paper focuses on the case with a sample of 30 to give general recommendations with regard to test statistics for contingency tables in response-adaptive randomization at small sample sizes.

Results

Among all asymptotic test statistics, the Cook's correction to chi-square test (T_MC) is the best in attaining the nominal size of hypothesis test. The William's correction to log-likelihood ratio test (T_ML) gives slightly inflated type I error and higher power as compared with T_MC, but it is more robust against the unbalance in patient allocation. T_MC and T_ML are usually the two test statistics with the highest power in different simulation scenarios. When focusing on T_MC and T_ML, the generalized drop-the-loser urn (GDL) and sequential estimation-adjusted urn (SEU) have the best ability to attain the correct size of hypothesis test respectively. Among all sequential methods that can target different allocation ratios, GDL has the lowest variation and the highest overall power at all allocation ratios. The performance of different adaptive randomization methods and test statistics also depends on allocation targets. At the limiting allocation ratio of drop-the-loser (DL) and randomized play-the-winner (RPW) urn, DL outperforms all other methods including GDL. When comparing the power of test statistics in the same randomization method but at different allocation targets, the powers of log-likelihood-ratio, log-relative-risk, log-odds-ratio, Wald-type Z, and chi-square test statistics are maximized at their corresponding optimal allocation ratios for power. Except for the optimal allocation target for log-relative-risk, the other four optimal targets could assign more patients to the worse arm in some simulation scenarios. Another optimal allocation target, R_RSIHR, proposed by Rosenberger and Sriram (Journal of Statistical Planning and Inference, 1997) is aimed at minimizing the number of failures at fixed power using Wald-type Z test statistics. Among allocation ratios that always assign more patients to the better treatment, R_RSIHR usually has less variation in patient allocation, and the values of variation are consistent across all simulation scenarios. Additionally, the patient allocation at R_RSIHR is not too extreme. Therefore, R_RSIHR provides a good balance between assigning more patients to the better treatment and maintaining the overall power.

Conclusion

The Cook's correction to chi-square test and Williams' correction to log-likelihood-ratio test are generally recommended for hypothesis test in response-adaptive randomization, especially when sample sizes are small. The generalized drop-the-loser urn design is the recommended method for its good overall properties. Also recommended is the use of the R_RSIHR allocation target.

An urn model for odds-ratio-based response-adaptive phase III clinical trials for two or more treatments

Adaptive data-dependent allocation designs are used in phase III clinical trials having two or more competing treatments with sequential entrance of patients, in order to allocate a larger number of patients to the better treatment. The odds ratio is a popular concept for biomedical practitioners; hence, odds-ratio-based adaptive designs could be very useful in practice. Rosenberger et al. (2001) introduced an odds-ratio-based two-treatment response-adaptive design; however, they did not study the properties in details. In this article, we describe these designs by means of urn models and provide limiting results for them. Some properties of the design are also studied numerically. We compare the performance of the proposed design with some possible competitors with respect to a few criteria. A real dataset is used to illustrate the applicability of the proposed design. Thus, we provide a base for using odds-ratio-based response-adaptive designs in practice. We extend our design for covariates and also for more than two treatments. In particular, we study the three-treatment design in this article.

A two stage conditional power adaptive design adjusting for treatment by covariate interaction

During the design and planning phase of clinical trials, researchers often assume that no covariate by treatment interaction exists. This assumption has led to many trials being underpowered to detect such interactions and perhaps inaccurate interpretation of treatment effects. We propose a two-stage adaptive design that incorporates the likely existence of a treatment by covariate interaction into the design and implementation of the clinical trial. The information in stage 1 is used to test for the presence of the covariate by treatment interaction. A statistically significant interaction influences how the second stage of the trial will be implemented, thereby aiding in the full understanding and consequently, an accurate interpretation of the treatment effect. We examine the statistical properties of the proposed design using a binary outcome under different types of covariate by treatment interactions and treatment allocation schemes. A conditional power approach is used to prevent inflation of the overall trial type I error rate while maintaining adequate statistical power conditional on the statistically significant interaction.

How practical are adaptive designs likely to be for confirmatory trials?

This is a discussion of the following papers appearing in this special issue on adaptive designs: 'Confirmatory Seamless Phase II/III Clinical trials with Hypotheses Selection at Interim: General Concepts' by Frank Bretz, Heinz Schmidli, Franz König, Amy Racine and Willi Maurer; and 'Confirmatory Seamless Phase II/III Clinical Trials with Hypotheses Selection at Interim: Applications and Practical Considerations' by Heinz Schmidli, Frank Bretz, Amy Racine and Willi Maurer.