Bootstrap methods for adaptive designs

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.

Inference in response-adaptive clinical trials when the enrolled population varies over time

A common assumption of data analysis in clinical trials is that the patient population, as well as treatment effects, do not vary during the course of the study. However, when trials enroll patients over several years, this hypothesis may be violated. Ignoring variations of the outcome distributions over time, under the control and experimental treatments, can lead to biased treatment effect estimates and poor control of false positive results. We propose and compare two procedures that account for possible variations of the outcome distributions over time, to correct treatment effect estimates, and to control type-I error rates. The first procedure models trends of patient outcomes with splines. The second leverages conditional inference principles, which have been introduced to analyze randomized trials when patient prognostic profiles are unbalanced across arms. These two procedures are applicable in response-adaptive clinical trials. We illustrate the consequences of trends in the outcome distributions in response-adaptive designs and in platform trials, and investigate the proposed methods in the analysis of a glioblastoma study.

A new inferential approach for response-adaptive clinical trials: the variance-stabilized bootstrap

This paper discusses disadvantages and limitations of the available inferential approaches in sequential clinical trials for treatment comparisons managed via response-adaptive randomization. Then, we propose an inferential methodology for response-adaptive designs which, by exploiting a variance stabilizing transformation into a bootstrap framework, is able to overcome the above-mentioned drawbacks, regardless of the chosen allocation procedure as well as the desired target. We derive the theoretical properties of the suggested proposal, showing its superiority with respect to likelihood, randomization and design-based inferential approaches. Several illustrative examples and simulation studies are provided in order to confirm the relevance of our results.

A simple solution to the inadequacy of asymptotic likelihood-based inference for response-adaptive clinical trials

The present paper discusses drawbacks and limitations of likelihood-based inference in sequential clinical trials for treatment comparisons managed via Response-Adaptive Randomization. Taking into account the most common statistical models for the primary outcome—namely binary, Poisson, exponential and normal data—we derive the conditions under which (i) the classical confidence intervals degenerate and (ii) the Wald test becomes inconsistent and strongly affected by the nuisance parameters, also displaying a non monotonic power. To overcome these drawbacks, we provide a very simple solution that could preserve the fundamental properties of likelihood-based inference. Several illustrative examples and simulation studies are presented in order to confirm the relevance of our results and provide some practical recommendations.

Adding experimental arms to platform clinical trials: randomization procedures and interim analyses

Multi-arm clinical trials use a single control arm to evaluate multiple experimental treatments. In most cases this feature makes multi-arm studies considerably more efficient than two-arm studies. A bottleneck for implementation of a multi-arm trial is the requirement that all experimental treatments have to be available at the enrollment of the first patient. New drugs are rarely at the same stage of development. These limitations motivate our study of statistical methods for adding new experimental arms after a clinical trial has started enrolling patients. We consider both balanced and outcome-adaptive randomization methods for experimental designs that allow investigators to add new arms, discuss their application in a tuberculosis trial, and evaluate the proposed designs using a set of realistic simulation scenarios. Our comparisons include two-arm studies, multi-arm studies, and the proposed class of designs in which new experimental arms are added to the trial at different time points.

Bayesian response-adaptive designs for basket trials

We develop a general class of response-adaptive Bayesian designs using hierarchical models, and provide open source software to implement them. Our work is motivated by recent master protocols in oncology, where several treatments are investigated simultaneously in one or multiple disease types, and treatment efficacy is expected to vary across biomarker-defined subpopulations. Adaptive trials such as I-SPY-2 (Barker et al., 2009) and BATTLE (Zhou et al., 2008) are special cases within our framework. We discuss the application of our adaptive scheme to two distinct research goals. The first is to identify a biomarker subpopulation for which a therapy shows evidence of treatment efficacy, and to exclude other subpopulations for which such evidence does not exist. This leads to a subpopulation-finding design. The second is to identify, within biomarker-defined subpopulations, a set of cancer types for which an experimental therapy is superior to the standard-of-care. This goal leads to a subpopulation-stratified design. Using simulations constructed to faithfully represent ongoing cancer sequencing projects, we quantify the potential gains of our proposed designs relative to conventional non-adaptive designs.

Clinical data combined with radiological imaging improves the accuracy of TNM staging of pancreatic body and tail adenocarcinoma

PURPOSE

Pancreatic body and tail adenocarcinoma (PBTA) remains one of the deadliest cancers, and current radiological modalities still have limitations on the staging of PBTA. Improving PBTA staging will contribute to the management of this disease.

PATIENTS AND METHODS

Clinicopathological characteristics of 91 surgically treated PBTA patients were retrospectively retrieved. Clinical data associated with postoperative tumor staging (pTNM) were assessed using ordinal logistic regression model. Discriminant analysis was performed using function formula based on multivariate analysis results; further cross-validation was conducted by Bootstrap methods.

RESULTS

Multivariate analysis showed that carbohydrate antigen 19-9 ≥955.0 U/L, albumin, and alkaline phosphatase/total bilirubin ratio were independent factors contributing to improved accuracy of pTNM staging. Discriminant analysis exhibited better performance and showed that the probability of accurate prediction of pTNM stage was 90.6% and the probability of cross-validation was 85.9%. After excluding patients with preoperative diagnosis of stage IV disease, the probability of accurate prediction of pTNM stage was 86.1% and the probability of cross-validation was 75.0%.

CONCLUSION

The combination of imaging and clinical data has higher accuracy in staging PBTA than radiological data alone. A model proposed in this study will improve the management of PBTA.

A Bayesian response-adaptive trial in tuberculosis: The endTB trial

PURPOSE

To evaluate the use of Bayesian adaptive randomization for clinical trials of new treatments for multidrug-resistant tuberculosis.

METHODS

We built a response-adaptive randomization procedure, adapting on two preliminary outcomes for tuberculosis patients in a trial with five experimental regimens and a control arm. The primary study outcome is treatment success after 73 weeks from randomization; preliminary responses are culture conversion at 8 weeks and treatment success at 39 weeks. We compared the adaptive randomization design with balanced randomization using hypothetical scenarios.

RESULTS

When we compare the statistical power under adaptive randomization and non-adaptive designs, under several hypothetical scenarios we observe that adaptive randomization requires fewer patients than non-adaptive designs. Moreover, adaptive randomization consistently allocates more participants to effective arm(s). We also show that these advantages are limited to scenarios consistent with the assumptions used to develop the adaptive randomization algorithm.

CONCLUSION

Given the objective of evaluating several new therapeutic regimens in a timely fashion, Bayesian response-adaptive designs are attractive for tuberculosis trials. This approach tends to increase allocation to the effective regimens.

Combining progression-free survival and overall survival as a novel composite endpoint for glioblastoma trials

BACKGROUND

The use of auxiliary endpoints may provide efficiencies for clinical trial design, but such endpoints may not have intrinsic clinical relevance or clear linkage to more meaningful endpoints. The purpose of this study was to generate a novel endpoint that considers both overall survival (OS) and earlier events such as progression-free survival (PFS) and determine whether such an endpoint could increase efficiency in the design of glioblastoma clinical trials.

METHODS

Recognizing that the association between PFS and OS varies depending on therapy and tumor type, we developed a statistical model to predict OS based on PFS as the trial progresses. We then evaluated the efficiency of our model using simulations of adaptively randomized trials incorporating PFS and OS distributions from prior published trials in neuro-oncology.

RESULTS

When treatment effects on PFS and OS are concordant, our proposed approach results in efficiency gains compared with randomization based on OS alone while sacrificing minimal efficiency compared with using PFS as the primary endpoint. When treatment effects are limited to PFS, our approach provides randomization probabilities that are close to those based on OS alone.

CONCLUSION

Use of OS as the primary endpoint, combined with statistical modeling of the relationship between OS and PFS during the course of the trial, results in more robust and efficient trial designs than using either endpoint alone.

Bayesian adaptive randomized trial design for patients with recurrent glioblastoma

PURPOSE

To evaluate whether the use of Bayesian adaptive randomized (AR) designs in clinical trials for glioblastoma is feasible and would allow for more efficient trials.

PATIENTS AND METHODS

We generated an adaptive randomization procedure that was retrospectively applied to primary patient data from four separate phase II clinical trials in patients with recurrent glioblastoma. We then compared AR designs with more conventional trial designs by using realistic hypothetical scenarios consistent with survival data reported in the literature. Our primary end point was the number of patients needed to achieve a desired statistical power.

RESULTS

If our phase II trials had been a single, multiarm trial using AR design, 30 fewer patients would have been needed compared with a multiarm balanced randomized (BR) design to attain the same power level. More generally, Bayesian AR trial design for patients with glioblastoma would result in trials with fewer overall patients with no loss in statistical power and in more patients being randomly assigned to effective treatment arms. For a 140-patient trial with a control arm, two ineffective arms, and one effective arm with a hazard ratio of 0.6, a median of 47 patients would be randomly assigned to the effective arm compared with 35 in a BR trial design.

CONCLUSION

Given the desire for control arms in phase II trials, an increasing number of experimental therapeutics, and a relatively short time for events, Bayesian AR designs are attractive for clinical trials in glioblastoma.

Estimation following group-sequential response-adaptive clinical trials

A sequential clinical trial model is considered in which two treatments with immediate normally distributed responses are to be compared. The class of one-sided group-sequential tests with response-adaptive sampling developed by Jennison and Turnbull is used to investigate which of the treatments has the larger mean response. The power function for this class of tests is the same as that under nonadaptive sampling, and significant decreases in the inferior treatment number can be achieved with only minor increases in the average total sample number. Two inferential methods are considered following the design. Approximate confidence intervals for the treatment mean difference and the individual means are constructed using the pivotal method of Woodroofe, and an approximation to the bias of the maximum likelihood estimator of the treatment mean difference is studied based on the work of Whitehead. Simulation is used to assess the accuracy of both methods for various stopping boundaries and numbers of interim analyses.

Efficient trial designs to reduce placebo requirements

This brief discussion summarizes possible trial design changes that could be utilized to reduce the number of subjects exposed to ineffective treatment--in this case placebo; however, these designs are fairly complex and have not been implemented sufficiently to judge their utility. Clearly, such studies are essential before embarking on these paradigms as a primary method for assessing antidepressant efficacy.

Randomized play-the-winner clinical trials: review and recommendations

The randomized play-the-winner rule is an adaptive randomized design, based on an urn model, that is used occasionally in clinical trials. This paper discusses practical and theoretical issues arising from its use, including stratification, delayed response, operating characteristics, selection of urn parameters, and inference. The paper also discusses recent experience with adaptive clinical trials within the pharmaceutical industry. The author concludes that the randomized play-the-winner rule is appropriate for some clinical trials, but intense and thoughtful planning must take place in the design phase. Such planning should incorporate considerations of variability, power, and appropriate techniques.