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.     

A Clinical Trial Design With Covariate-Adjusted Response-Adaptive Randomization Using Superiority Confidence of Treatments

Abstract

Adaptive randomization using response outcome or covariate is commonly used in the literature. However, the performance of these designs has not been thoroughly studied, especially when there are various interactions between the covariate and treatment. We have conducted simulations to evaluate the performance of commonly used designs under two-arm and multiple-arm situations. When a predictive factor exists, in the phase II trial conduction using adaptive designs, such as the BATTLE-1, BATTLE-2 trial, and ISPY-2 trials, researchers evaluate the operating characteristics using the traditional power assessment. In this article, new criteria are used in a general modeling frame work to incorporate the complicated interaction. Based on our evaluation, the covariate-adjusted and response-adaptive randomization (Sc-ca) results in a greater total number of responders. Additionally, the design can detect the treatment effect difference in subgroups, and consistently assign patients to the most beneficial treatment according to their covariate profiles. This translates into a higher proportion of individuals receiving optimized treatments compared with other commonly used designs. This adaptive design is a step toward personalized therapy to benefit each patient enrolled in a prospective clinical trial, when there is the strong evidence that predictive factors exist.     

A Graphical Comparison of Response-Adaptive Randomization Procedures

Response-adaptive randomization procedures have a dual goal of estimating the treatment effect and randomizing patients with a higher probability of receiving the superior treatment. These are competing objectives, and no procedure in the literature is “perfect” with respect to both objectives. For clinical trials of two treatments, we discuss metrics for comparing response-adaptive randomization procedures that can be represented graphically to compare designs. These metrics involve the simulated distribution of the set of jointly sufficient statistics for estimating functions of the unknown parameters. We explore the binary response and normal cases, and compare numerous procedures found in the literature. We distinguish between metrics of efficiency and metrics that measure ethical cost. Each of these is a function of the joint sufficient statistics. When graphed against each other, we can gauge competing designs in obtaining these competing objectives. We find that, contrary to asymptotic results, tuning parameters that affect the variability of the procedure do not have much impact in the finite case. In the binary response case, we find that procedures that target an optimal allocation based on ethical and efficiency considerations generally provide a better compromise design than procedures that do not. In the normal response case, a randomly reinforced urn tends to provide a good compromise procedure.     

Response-Adaptive Allocation for Circular Data

Response-adaptive designs are used in phase III clinical trials to allocate a larger proportion of patients to the better treatment. Circular data is a natural outcome in many clinical trial setup, e.g., some measurements in opthalmologic studies, degrees of rotation of hand or waist, etc. There is no available work on response-adaptive designs for circular data. With reference to a dataset on cataract surgery we provide some response-adaptive designs where the responses are of circular nature and propose some test statistics for treatment comparison under adaptive data allocation procedure. Detailed simulation study and the analysis of the dataset, including redesigning the cataract surgery data, are carried out.     

An Adaptive Timeline Determination of Survival Trials

Adaptive design of survival trials often faces a dilemma. If the target is to use all the event information in the final analysis, there is a limitation on the interim information that may be used for the adaptations. If one wants to use all the interim information for a better stage 2 design, some event information may need to be discarded in the final analysis to properly control Type I error. This article proposes an adaptive design method to bridge this gap. This method allows the use of all the interim information for stage 2 design and the use of all the event information in the final analysis. We prove that a sufficient condition for proper Type I error control for this method is that the final analysis time, potentially depending on all the interim data, converges to some fixed point. We illustrate that such condition is valid in many applications. Because the proposed method uses all the event information, it is more powerful than the existing methods that sacrifice some event information to control the error rate. Simulation study shows our method performs satisfactorily.     

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 Rosenberger , W. F. , Vidyashankar , A. N. , Agarwal , D. K. ( 2001 ). Covariate-adjusted response-adaptive designs for binary response . J. Biopharm. Stat. 11 : 227 – 236 .[Taylor &; Francis Online] , [Google Scholar]) 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.     

Estimating Covariate-Adjusted Log Hazard Ratios for Multiple Time Intervals in Clinical Trials Using Nonparametric Randomization Based ANCOVA

The hazard ratio is a useful tool in randomized clinical trials for comparing time-to-event outcomes for two groups. Although better power is often achieved for assessments of the hazard ratio via model-based methods that adjust for baseline covariates, such methods make relatively strong assumptions, which can be problematic in regulatory settings that require prespecified analysis plans. This article introduces a nonparametric method for producing covariate-adjusted estimates of the log weighted average hazard ratio for nonoverlapping time intervals under minimal assumptions. The proposed methodology initially captures the means of baseline covariables for each group and the means of indicators for risk and survival for each interval and group. These quantities are used to produce estimates of interval-specific log weighted average hazard ratios and the difference in means for baseline covariables between two groups, with a corresponding covariance matrix. Randomization-based analysis of covariance is applied to produce covariate-adjusted estimates for the interval-specific log hazard ratios through forcing the difference in means for baseline covariables to zero, and there is variance reduction for these adjusted estimates when the time to event has strong correlations with the covariates. The method is illustrated on data from a clinical trial of a noncurable neurologic disorder.     

Blinded versus Unblinded Covariate Selection in Confirmatory Survival Trials

Adjustment for covariates and specification of the correct covariate set are important issues in the analysis of clinical trials. Edwards (1999 Edwards , D. ( 1999 ). On model prespecification in confirmatory randomized studies . Statistics in Medicine 18 : 771 – 785 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) proposes a model selection approach where the model is chosen on the final data set, which remains blinded for treatment group allocation. We investigate this method for time-to-event endpoints and compare its performance to variable selection within an adaptive design. This adaptive design integrates the methods of Schäfer and Müller (2001 Schäfer , H. , Müller , H.-H. (2001). Modification of the sample size and the schedule of interim analyses in survival trials based on data inspections. Statistics in Medicine 20:3741–3751.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and Keiding et al. (1987 Keiding , N. , Bayer , T. , Watt-Boolsen , S. ( 1987 ). Confirmatory analysis of survival data using left truncation of the life times of primary survivors . Statistics in Medicine 6 : 939 – 944 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and allows variable selection on the unblinded data during an interim analysis. Monte Carlo simulation shows that Edwards’ method—though blinded—outperforms the adaptive method in terms of ability to select the survival relevant covariates and power. The application of the methods is illustrated by a clinical trial example.     

Adaptive Allocation and Failure Saving in Randomised Clinical Trials

In the present work, we develop a randomized two-treatment single period response adaptive design by combining two contrasting aspects (i.e., ethics and optimality), where optimality is defined in a meaningful way. We compare this rule with some of the existing rules by computing various performance measures of the rules.     

Estimating Covariate-Adjusted Log Hazard Ratios in Randomized Clinical Trials Using Cox Proportional Hazards Models and Nonparametric Randomization Based Analysis of Covariance

In the context of randomized clinical trials with time-to-event outcomes, estimates of covariate-adjusted log hazard ratios for comparing two treatments are obtained via nonparametric analysis of covariance by forcing the difference in means for covariables to zero. The method avoids the assumption of proportional hazards for each of the covariates, and it provides an adjusted analysis for the same population average treatment effect that the unadjusted analysis addresses. It is primarily useful in regulatory clinical trials that require analyses to be specified a priori. To illustrate, the method is applied to a study of lung disease with multivariate time-to-event outcomes.     

Sample Size Calculations for Combination Drugs of Two Monotherapies With One Approved Dose Level

In this article, we consider sample size calculations for combination drugs of two monotherapies that each has only one approved dose level. We modify the method of Laska and Meiner by employing the asymptotic joint distribution of test statistics to derive the power function and using unequal allocation to minimize the total sample sizes. Two cases are investigated. In the first case, each monotherapy has the same indication. A heuristic method, the method of Laska and Meiner, and the proposed method are compared in terms of the total sample sizes. We show that the proposed method produces the smallest total sample sizes. In the second case, each monotherapy has a different indication. While the method of Laska and Meiner cannot be applied in this case, we show that the proposed method can be employed and that it produces smaller total sample sizes than a heuristic method.     

Group Sequential Survival Trial Design and Monitoring Using the Log-Rank Test

For randomized group sequential survival trial designs with unbalanced treatment allocation, the widely used Schoenfeld formula is inaccurate, and the commonly used information time as the ratio of number of events at interim look to the number of events at the end of trial can be biased. In this article, a sample size formula for the two-sample log-rank test under the proportional hazards model is proposed that provides more accurate sample size calculation for unbalanced survival trial designs. Furthermore, a new information time is introduced for the sequential survival trials such that the new information time is more accurate than the traditional information time when the allocation of enrollments is unbalanced in groups. Finally, we demonstrate the monitoring process using the sequential conditional probability ratio test and compare it with two other well-known group sequential procedures. An example is given to illustrate unbalanced survival trial design using available software. Supplementary materials for this article are available online.     

Covariate-Adjusted Adaptive Designs for Continuous Responses in a Phase III Clinical Trial: Recommendation for Practice

In this paper we propose a Bayesian method to combine safety data collected from two separate drug development programs using the same active drug substance but for different indications, formulations, or patient populations. The objective of combining the data across the programs is to better define the level of safety risk associated with the new indication or target population. There may be adverse events (AEs) observed in the new program that represent new safety signals. Our method is to explore the AEs using data from both development programs. Our approach utilizes data collected previously to assist in analyzing safety data from the new program. It is assumed that the frequency of a certain AE follows a distribution with a parameter that characterizes the safety risk level. The parameter is assumed to follow a distribution function. In the Bayesian framework, this distribution function is called a prior distribution in the absence of data and posterior distribution when updated by real data. The key concept behind our method is to use data from the previous program to construct a posterior distribution that will in turn serve as a prior distribution for the new program. The construction of this updated prior down weights data from the previous program to emphasize the new program and thus avoids simple pooling of the data across programs. Such “soft use” of previous information minimizes the potential for undue influence of previous data on the analysis. Data from the new program are used to update the prior distribution and compute the posterior distribution for the new program. Key statistics are then calculated from the posterior distribution to quantify the risk level for the new program. We have tested the proposed approach using data from a real Phase 2 study that was conducted as part of a clinical development program for a new indication of an approved drug. The results indicate that the estimated risk level was affected both by the observed event rates and the extents of exposure across the two development programs. This approach appropriately characterizes the safety profile across the two development programs and properly contextualizes new safety signals from the new program.     

Optimal Adaptive Designs for Binary Response Trials With Three Treatments

A fundamental question in response–adaptive randomization is: What allocation proportion should we target to achieve required power while resulting in fewer treatment failures? For comparing two treatments, such optimal allocations are well studied in the literature. However, few authors address the question for multiple treatments and the generalization of optimal allocations is necessary in practice. We are interested in finding the optimal allocation proportion, which achieves a required power of a multivariate test of homogeneity in binary response experiments while minimizing expected treatment failures at the same time. We propose such an optimal allocation for three treatments by giving an analytical solution for the optimization problem. Numerical studies show that a response–adaptive randomization procedure that targets proposed optimal allocation is superior to complete randomization. We also discuss some future research topics and additional issues on optimal adaptive designs.     

Strategies for Including Patients Recruited During Interim Analysis of Clinical Trials

In clinical trials a periodical check of safety and efficacy data is often needed. For organizational reasons it is rarely desirable to stop a trial during such an interim analysis. Therefore, new study patients are included in the trial while the interim analysis is ongoing. Disregarding the additional information provided by these interim patients would be unsatisfactory, especially for an office of regulatory affairs. Consequently, the rules for group sequential or adaptive decisions must be adjusted to the recruitment of interim patients. In this paper, two strategies for modifying study designs to consider the analysis of interim patients are proposed.     

Designing Issues in Confirmatory Adaptive Population Enrichment Trials

Adaptive population enrichment designs enable the data-driven selection of one or more pre-specified subpopulations in an interim analysis, and the confirmatory proof of efficacy in the selected subset at the end of the trial. Sample size reassessment and other adaptive design changes can be performed as well. Strong control of the experimentwise Type I error rate is guaranteed by use of the combination testing principle together with the closed testing argument. In this paper the general methodology and designing issues when planning such a design are reviewed. It is shown how to derive overall confidence intervals and p-values. Criteria for assessing the operating characteristics of these designs are given, and the application is illustrated by examples.     

An Adaptive Dose-Finding Design Based on Both Safety and Immunologic Responses in Cancer Clinical Trials

Dose-finding in cancer clinical trials has been dominated by algorithmic designs on the principle that the highest tolerable dose is also the most effective dose. This assumption no longer applies to the biologic treatments that are characterized by different toxicity and/or efficacy profiles to the extent that the best therapeutic dose might be well below any dose that produces serious toxicity. As such, we propose a two-stage design with focus on immunotherapy trials, incorporating both safety and efficacy information. The first stage establishes the safety profile of each dose, with escalation decisions based on likelihood principles. Continuous immunologic outcomes are used to evaluate the relative efficacy of the doses. The second stage employs an adaptive randomization to assign patients to doses showing higher efficacy. Safety is being continuously monitored throughout Stage 2, where some doses may be ‘closed’ due to unacceptable toxicity. The proposed design is compared to the modified toxicity probability interval (mTPI) design using percent dose allocation and estimation of outcomes under different scenarios. We show that by using an efficacy-driven adaptive randomization with safety constraints, the allocation distribution is skewed towards more efficacious doses, and thus limit the number of patients exposed to toxic or non-therapeutic doses. Supplementary materials for this article are available online.     

基于FDA新版指南草案浅谈适应性设计的发展

摘 要在过去的二、三十年中,适应性设计一直是临床研究设计的热点。继2010年美国食品药品管理局（FDA）发布第一版适应性设计指南草案后,2018年9月FDA再次发布了第二版适应性设计指南草案：“Adaptive Designs for Clinical Trials of Drugs and Biologics Guidance for Industry”（以下简称“新版指南草案”）。此次颁布的指南草案在2010年版的基础上增加了临床试验中适应性设计的原则、适应性设计的类型、与适应性设计有关的注意事项及主题,如适应性设计计划中的模拟问题、贝叶斯适应性设计以及终点考虑和安全性考虑等内容,为临床试验的研究者们提供了非常重要的蓝本。本文将基于该新版指南草案内容,同时结合国内外适应性设计的发展概况,对适应性设计类型等相关的问题进行浅析,以期为相关研究人员提供参考。     

Optimal Interim Decision Rules Based on a Binary Surrogate Outcome for Adaptive Biomarker-Based Trials in Oncology

ABSTRACT

Adaptive enrichment designs represent a promising approach to evaluate targeted therapies, for example, in oncology. They allow selection of the most promising target population in an interim analysis and then combination of the data from the two trial stages for the final proof of efficacy. Application of these designs is motivated by the assumption that there might be a biomarker-defined subgroup of patients with an increased treatment benefit as compared to the total patient population. If the primary outcome is a time-to-event variable and the respective event takes a relatively long time to be observed, it could be beneficial to select the most promising patient population based on an earlier available binary surrogate, for example, response, to save time and costs. We propose an adaptive enrichment design which allows us to implement such a trial setting. For this design, optimal decision rules are derived minimizing the expected loss incurred due to a false interim decision. These rules are compared to ad hoc rules in terms of selection probability and power within a simulation study which is motivated by a clinical trial example. Furthermore, the impact of the correlation between surrogate and primary outcome on power is investigated. Supplementary materials for this article are available online.     

Statistical Considerations for Testing Multiple Endpoints in Group Sequential or Adaptive Clinical Trials

Many clinical trials are designed with a fixed sample size or total number of events to detect a postulated size of treatment effect on a primary efficacy endpoint. When the trial is completed and the primary efficacy endpoint achieves statistical significance, formal statistical testing of other clinically important secondary endpoints often follows in order for the statistically and clinically significant results of these endpoints to be included in the label of the test pharmaceutical product. In conventional fixed designs without any interim analysis or trial extension, these endpoints are often tested in a pre-specified hierarchical order, following the closed testing principle. This testing strategy ensures a strong control of the overall type I error. However, when trials are conducted using a group-sequential design with interim analyses or can be extended using an adaptive design with an increase of sample size or total number of events, this conventional hierarchical testing strategy may violate the closure principle and the overall type I error rate may not be controlled in the strong sense.