Covariate-adjusted Response-adaptive Research Articles

Covariate-Adjusted Response Adaptive Designs for Competing Risk Survival Models

Often in medical research, response to a particular treatment can be classified in terms of failure from multiple causes. In such cases, a competing event precludes the observation of the main event of interest. Such scenarios in survival analysis are termed as competing risks. Covariate-adjusted response-adaptive (CARA) designs skew patient allocation towards the better-performing treatment arm, so far in a clinical trial, for a given patient’s covariate profile. When there are competing events occurring in a clinical trial, ignoring such information during the design stage may bias the results for disease-specific treatment comparison. Optimal CARA designs are developed, assuming proportional sub-distribution hazards for two-arm survival trials, where the primary endpoint encounters competing risks. The derived allocation proportions are targeted using biased coin procedure. These allocation proportions that are sequentially estimated, converge empirically to the expected target values, which are functions of the Fine and Gray (1999) model coefficients. The proposed methods are shown to be suitable alternatives to the traditional balanced designs through extensive simulation studies and have also been implemented to re-design a real-life clinical trial. Simulation results reveal the need of a theoretical procedure for more complicated semi-parametric survival response models.

Covariate-adjusted response-adaptive designs for semiparametric survivalmodels.

Covariate-adjusted responseadaptive (CARA) designs are effective in increasing the expected number of patients receiving superior treatment inan ongoing clinical trial, given a patient's covariate profile. There has recently been extensive research on CARA designs with parametric distributional assumptions on patient responses. However, the range of applications for such designs becomes limited in real clinical trials. Sverdlov etal. have pointed out that irrespective of a specific parametric form of the survival outcomes, their proposed CARA designs based on the exponential model provide valid statistical inference, provided the final analysis is performed using the appropriate accelerated failure time (AFT) model. In real survival trials, however, the planned primary analysis is rarely conducted using an AFT model. The proposed CARA designs are developed obviating any distributional assumptions about the survival responses, relying only on the proportional hazards assumption between the two treatment arms. To meet the multiple experimental objectives of a clinical trial, the proposed designs are developed based on an optimal allocation approach. The covariate-adjusted doubly adaptive biased coin design and the covariate-adjusted efficient-randomized adaptive design are used to randomize the patients to achieve the derived targets on expectation. These expected targets are functions of the Cox regression coefficients that are estimated sequentially with the arrival of every new patient into the trial. The merits of the proposed designs are assessed using extensive simulation studies of their operating characteristics and then have been implemented to re-design a real-life confirmatory clinical trial.

Incorporating treatment-covariate interaction in designing a covariate adjusted response adaptive allocation for binary response trials

Assuming binary treatment outcomes, a covariate adjusted response adaptive (CARA) design is developed for multi-arm clinical trials assuming the presence of treatment-covariate interaction. The proposed allocation skews the allocation dynamically according to the performance of the treatments and the covariate profile of any incoming subject. Relevant de- sign and precision based measures of the performance are further investigated empirically, which established the usefulness of the proposed allocation design over its competitors. Journal of Statistical Research 2022, Vol. 57, No. 1-2, pp.21-33

A Two-Stage Covariate-Adjusted Response-Adaptive Enrichment Design

In the precision medicine paradigm, it is of interest to identify subgroups that benefit most from the treatment. However, the subgroup often cannot be identified until after a large-scale clinical trial. Clinical trials are often designed under the assumption of no treatment-by-covariate interaction effect and enroll all comers. This makes many patients go through unnecessary treatment and may decrease the efficiency of the trial. We propose a two-stage enrichment design that uses covariate-adjusted response-adaptive (CARA) allocation and a novel interaction pseudo-randomization test to evaluate the interaction effect in the interim analysis for binary and continuous outcomes. A pre-defined alpha level is used as the threshold to decide whether a subgroup will be identified and recruited in the second stage. If a below-threshold interaction effect is found, a regression model will be fit and the stratum with the largest treatment effect will be chosen as the best stratum. The trial will continue to the second stage with patients from the best stratum only. If the p-value from the interim analysis is above the threshold, the trial continues with all patients. The primary aim is to test the treatment effect between treatment groups. Different CARA procedures are compared in terms of Type I error rates, power, and ethical considerations. The CARA procedure that balances better between efficiency and ethics is used in the proposed two-stage enrichment design.

Three influential design quantities on the power of Wald-type tests for treatment comparisons in clinical trials

In clinical trials, efficient statistical inference is critical to the well-being of future patients. We therefore construct Wald-type tests for the hypothesis of treatment-by-covariate interaction when treatments are assigned to patients by an adaptive design and the true model is a generalized linear model. Our measure of efficiency is the power of the test while ethics of a trial or well-being of participating patients is measured by the success rate of treatments. We demonstrate that the power of the test depends on the target allocation proportion, the bias of the randomization procedure from the target, and the variability induced by the randomization process (design variability) for adaptive designs. We prove that these quantities influence the power when the trial involves two treatments and a single covariate. We also show that, in this case, as design variability decreases the power increases. Due to the complexity of the problem, we demonstrate by simulation that this result still holds when more than one covariate is present in the model. In simulation studies, we compare the measures of efficiency and ethics under response-adaptive (RA), covariate-adjusted responseadaptive (CARA), and completely randomized (CR) designs. The methods are applied to data from a clinical trial on stroke prevention in atrial fibrillation (SPAF).
 Journal of Statistical Research 2022, Vol. 56, No. 1, pp. 11-36

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.

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.

Nonparametric covariate-adjusted response-adaptive design based on a functional urn model

In this paper we propose a general class of covariate-adjusted response-adaptive (CARA) designs based on a new functional urn model. We prove strong consistency concerning the functional urn proportion and the proportion of subjects assigned to the treatment groups, in the whole study and for each covariate profile, allowing the distribution of the responses conditioned on covariates to be estimated nonparametrically. In addition, we establish joint central limit theorems for the above quantities and the sufficient statistics of features of interest, which allow to construct procedures to make inference on the conditional response distributions. These results are then applied to typical situations concerning Gaussian and binary responses.

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

SummaryWe 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.

Comparison of sequential estimation in response-adaptive designs with and without covariate-adjustment

Subjects on one side of the covariate population can be allocated to the inferior treatment when there is interaction between the covariate and treatment along with a response-adaptive (RA) design without covariate adjustment. An RA design allows a newly entered subject to have a better chance so that the subject is treated by a superior treatment based on cumulative information from previous subjects. A covariate-adjusted responseadaptive (CARA) is the same as RA design and additionally adjusts the allocation based on individual covariate information. A comparison has been made for the sequential estimation procedure with and without covariate adjustment to see how ignoring significantly interactive covariate affects the correct treatment allocation. Using logistic models, we present simulation results regarding the coverage probability of treatment effect, correct allocation, and stopping time.

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.

Covariate‐adjusted response adaptive designs incorporating covariates with and without treatment interactions

AbstractThe covariate‐adjusted response adaptive (CARA) design has been shown to be better than traditional designs in terms of both ethics and efficiency. However, its mechanism for allocating subjects makes certain stochastic processes such as allocated response sequences very complicated. Consequently, the validation of statistical inference is usually challenging, and few theoretical results have been obtained. In this paper we systematically solve some fundamental problems for statistical inference with CARA designs. First, we obtain the conditional independence and distribution of allocated response sequences, which is the basis for further theoretical investigation. Second, we propose a new family of CARA designs, which is extensively applicable. We more importantly provide a framework for new CARA designs with unified asymptotic results for statistical inference. The numerical results demonstrate the advantages of the proposed CARA designs. Our findings are crucial in understanding the CARA design as well as its development and application. The Canadian Journal of Statistics 43: 534–553; 2015 © 2015 Statistical Society of Canada

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.

Utility of Covariate-Adjusted Response-Adaptive Randomization in Survival Trials

Covariate-adjusted response-adaptive (CARA) randomization is used in clinical trials to balance the competing goals of assigning a greater number of study subjects to the better treatment and achieving high statistical efficiency in estimating treatment effects in the presence of covariates, while maintaining randomness in treatment assignments. In this article, we propose CARA randomization procedures for survival intervention trials with two treatment arms when the primary outcomes follow an exponential regression model. We demonstrate, through extensive simulation, that our CARA procedures can achieve some reduction in the number of events in the study without compromising power and Type I error, compared with balanced randomization designs, including in situations when the exponential model is misspecified. We conclude that the proposed CARA procedures can be suitable alternatives to the traditional balanced randomization designs in survival trials, provided response data are available during the recruitment phase to enable adaptations in the design. We illustrate the proposed methodology by redesigning two survival trials from the literature.

Randomization in clinical trials: can we eliminate bias?

Randomization plays a fundamental role in clinical trials. While many modern clinical trials employ restricted, stratified or covariate-adaptive randomization designs that pursue balance in treatment assignments and balance across important covariates, some clinical trials call for response-adaptive or covariate-adjusted response-adaptive (CARA) randomization designs to address multiple experimental objectives primarily related to statistical efficiency and ethical considerations. In this paper, we elicit key principles of the well-conducted randomized clinical trial and explore the role of randomization and other important design tools in achieving valid and credible results. We give special attention to response-adaptive and CARA randomization designs, which have a firm theoretical basis, but are more complex and more vulnerable to operational biases than traditional randomization designs. We conclude that modern advances in information technology, rigorous planning, and adherence to the key principles ...

Sequential estimation for covariate-adjusted response-adaptive designs

In clinical trials, a covariate-adjusted response-adaptive (CARA) design allows a subject newly entering a trial a better chance of being allocated to a superior treatment regimen based on cumulative information from previous subjects, and adjusts the allocation according to individual covariate information. Since this design allocates subjects sequentially, it is natural to apply a sequential method for estimating the treatment effect in order to make the data analysis more efficient. In this paper, we study the sequential estimation of treatment effect for a general CARA design. A stopping criterion is proposed such that the estimates satisfy a prescribed precision when the sampling is stopped. The properties of estimates and stopping time are obtained under the proposed stopping rule. In addition, we show that the asymptotic properties of the allocation function, under the proposed stopping rule, are the same as those obtained in the non-sequential/fixed sample size counterpart. We then illustrate the performance of the proposed procedure with some simulation results using logistic models. The properties, such as the coverage probability of treatment effect, correct allocation proportion and average sample size, for diverse combinations of initial sample sizes and tuning parameters in the utility function are discussed.

Handling Covariates in the Design of Clinical Trials

There has been a split in the statistics community about the need for taking covariates into account in the design phase of a clinical trial. There are many advocates of using stratification and covariate-adaptive randomization to promote balance on certain known covariates. However, balance does not always promote efficiency or ensure more patients are assigned to the better treatment. We describe these procedures, including model-based procedures, for incorporating covariates into the design of clinical trials, and give examples where balance, efficiency and ethical considerations may be in conflict. We advocate a new class of procedures, covariate-adjusted response-adaptive (CARA) randomization procedures that attempt to optimize both efficiency and ethical considerations, while maintaining randomization. We review all these procedures, present a few new simulation studies, and conclude with our philosophy.

Asymptotic properties of covariate-adjusted response-adaptive designs

Response-adaptive designs have been extensively studied and used in clinical trials. However, there is a lack of a comprehensive study of response-adaptive designs that include covariates, despite their importance in clinical trials. Because the allocation scheme and the estimation of parameters are affected by both the responses and the covariates, covariate-adjusted response-adaptive (CARA) designs are very complex to formulate. In this paper, we overcome the technical hurdles and lay out a framework for general CARA designs for the allocation of subjects to K (≥2) treatments. The asymptotic properties are studied under certain widely satisfied conditions. The proposed CARA designs can be applied to generalized linear models. Two important special cases, the linear model and the logistic regression model, are considered in detail.