Adaptive two-treatment two-period crossover design for binary treatment responses incorporating carry-over effects

Adaptive designs are sometimes used in a phase III clinical trial with the goal of allocating a larger number of patients to the better treatment. In the present paper we use some adaptive designs in a two-treatment two-period crossover trial in the presence of possible carry-over effects, where the treatment responses are binary. We use some simple designs to choose between the possible treatment combinations AA, AB, BA or BB. The goal is to use the better treatment a larger proportion of times. We calculate the allocation proportions to the possible treatment combinations and their standard deviations. We also investigate related inferential problems, for which related asymptotics are derived. The proposed procedure is compared with a possible competitor. Finally we use real data sets to illustrate the applicability of our proposed design.     

On an ethical cum optimal adaptive allocation design

In the present work, we formulate a two-treatment single period two-stage adaptive allocation design for achieving larger allocation proportion to the better treatment arm in the course of the trial with increased precision of the parameter estimator. We examine some properties of the proposed rule and compare it with some of the existing allocation rules and report substantial gain in efficiency with a considerably larger number of allocations to the better treatment even for moderate sample sizes.     

Multiple-objective response-adaptive repeated measurement designs for clinical trials

In a response-adaptive design, we review and update the trial on the basis of outcomes in order to achieve a specific goal. Response-adaptive designs for clinical trials are usually constructed to achieve a single objective. In this paper, we develop a new adaptive allocation rule to improve current strategies for building response-adaptive designs to construct multiple-objective repeated measurement designs. This new rule is designed to increase estimation precision and treatment benefit by assigning more patients to a better treatment sequence. We demonstrate that designs constructed under the new proposed allocation rule can be nearly as efficient as fixed optimal designs in terms of the mean squared error, while leading to improved patient care.     

Sample size determination for cluster randomization phase II trials of dichotomous data

One of the main goals for a phase II trial is to screen and select the best treatment to proceed onto further studies in a phase III trial. Under the flexible design proposed elsewhere, we discuss for cluster randomization trials sample size calculation with a given desired probability of correct selection to choose the best treatment when one treatment is better than all the others. We develop exact procedures for calculating the minimum required number of clusters with a given cluster size (or the minimum number of patients with a given number of repeated measurements) per treatment. An approximate sample size and the evaluation of its performance for two arms are also given. To help readers employ the results presented here, tables are provided to summarize the resulting minimum required sample sizes for cluster randomization trials with two arms and three arms in a variety of situations. Finally, to illustrate the sample size calculation procedures developed here, we use the data taken from a cluster randomization trial to study the association between the dietary sodium and the blood pressure.     

A stochastically curtailed two-arm randomised phase II trial design for binary outcomes

Randomised controlled trials are considered the gold standard in trial design. However, phase II oncology trials with a binary outcome are often single-arm. Although a number of reasons exist for choosing a single-arm trial, the primary reason is that single-arm designs require fewer participants than their randomised equivalents. Therefore, the development of novel methodology that makes randomised designs more efficient is of value to the trials community. This article introduces a randomised two-arm binary outcome trial design that includes stochastic curtailment (SC), allowing for the possibility of stopping a trial before the final conclusions are known with certainty. In addition to SC, the proposed design involves the use of a randomised block design, which allows investigators to control the number of interim analyses. This approach is compared with existing designs that also use early stopping, through the use of a loss function comprised of a weighted sum of design characteristics. Comparisons are also made using an example from a real trial. The comparisons show that for many possible loss functions, the proposed design is superior to existing designs. Further, the proposed design may be more practical, by allowing a flexible number of interim analyses. One existing design produces superior design realisations when the anticipated response rate is low. However, when using this design, the probability of rejecting the null hypothesis is sensitive to misspecification of the null response rate. Therefore, when considering randomised designs in phase II, we recommend the proposed approach be preferred over other sequential designs.     

A novel equivalence probability weighted power prior for using historical control data in an adaptive clinical trial design: A comparison to standard methods

A standard two-arm randomised controlled trial usually compares an intervention to a control treatment with equal numbers of patients randomised to each treatment arm and only data from within the current trial are used to assess the treatment effect. Historical data are used when designing new trials and have recently been considered for use in the analysis when the required number of patients under a standard trial design cannot be achieved. Incorporating historical control data could lead to more efficient trials, reducing the number of controls required in the current study when the historical and current control data agree. However, when the data are inconsistent, there is potential for biased treatment effect estimates, inflated type I error and reduced power. We introduce two novel approaches for binary data which discount historical data based on the agreement with the current trial controls, an equivalence approach and an approach based on tail area probabilities. An adaptive design is used where the allocation ratio is adapted at the interim analysis, randomising fewer patients to control when there is agreement. The historical data are down-weighted in the analysis using the power prior approach with a fixed power. We compare operating characteristics of the proposed design to historical data methods in the literature: the modified power prior; commensurate prior; and robust mixture prior. The equivalence probability weight approach is intuitive and the operating characteristics can be calculated exactly. Furthermore, the equivalence bounds can be chosen to control the maximum possible inflation in type I error.     

Bayesian two-stage design for drug screening trials with switching hypothesis tests based on continuous endpoints

Abstract

In this paper, we propose a Bayesian two-stage design with changing hypothesis test by bridging a single-arm study and a double-arm randomized trial in one phase II clinical trial based on continuous endpoints rather than binary endpoints. We have also calibrated with respect to frequentist and Bayesian error rates. The proposed design minimizes the Bayesian expected sample size if the new candidate has low or high efficacy activity subject to the constraint upon error rates in both frequentist and Bayesian perspectives. Tables of designs for various combinations of design parameters are also provided.     

Sample size determination for testing equality in frequency data under an incomplete block crossover design

When there are more than two treatments under comparison, we may consider the use of the incomplete block crossover design (IBCD) to save the number of patients needed for a parallel groups design and reduce the duration of a crossover trial. We develop an asymptotic procedure for simultaneously testing equality of two treatments versus a control treatment (or placebo) in frequency data under the IBCD with two periods. We derive a sample size calculation procedure for the desired power of detecting the given treatment effects at a nominal-level and suggest a simple ad hoc adjustment procedure to improve the accuracy of the sample size determination when the resulting minimum required number of patients is not large. We employ Monte Carlo simulation to evaluate the finite-sample performance of the proposed test, the accuracy of the sample size calculation procedure, and that with the simple ad hoc adjustment suggested here. We use the data taken as a part of a crossover trial comparing the number of exacerbations between using salbutamol or salmeterol and a placebo in asthma patients to illustrate the sample size calculation procedure.     

An Optimality Probability Index for Correlated Multiple Responses

In the real problems, there are many cases which have correlated quality characteristics so multiple response optimization can be more realistic if we can consider correlation structure of responses. In this study we propose a new method which uses multivariate normal probability to find the optimal treatment in an experimental design. Moreover, a heuristic method is used to find better factors’ level in all possible combinations in the designs with large number of controllable factors and their levels. Some simulated numerical examples and a real case were studied by the proposed approach and the comparison of the results with previous methods show efficiency of the proposed method.     

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.     

A Hybrid Geometric Phase II/III Clinical Trial Design based on Treatment Failure Time and Toxicity

The problem of comparing several experimental treatments to a standard arises frequently in medical research. Various multi-stage randomized phase II/III designs have been proposed that select one or more promising experimental treatments and compare them to the standard while controlling overall Type I and Type II error rates. This paper addresses phase II/III settings where the joint goals are to increase the average time to treatment failure and control the probability of toxicity while accounting for patient heterogeneity. We are motivated by the desire to construct a feasible design for a trial of four chemotherapy combinations for treating a family of rare pediatric brain tumors. We present a hybrid two-stage design based on two-dimensional treatment effect parameters. A targeted parameter set is constructed from elicited parameter pairs considered to be equally desirable. Bayesian regression models for failure time and the probability of toxicity as functions of treatment and prognostic covariates are used to define two-dimensional covariate-adjusted treatment effect parameter sets. Decisions at each stage of the trial are based on the ratio of posterior probabilities of the alternative and null covariate-adjusted parameter sets. Design parameters are chosen to minimize expected sample size subject to frequentist error constraints. The design is illustrated by application to the brain tumor trial.     

Confidence intervals for the difference between two median survival times for clustered survival data

Clustered survival data arise often in clinical trial design, where the correlated subunits from the same cluster are randomized to different treatment groups. Under such design, we consider the problem of constructing confidence interval for the difference of two median survival time given the covariates. We use Cox gamma frailty model to account for the within-cluster correlation. Based on the conditional confidence intervals, we can identify the possible range of covariates over which the two groups would provide different median survival times. The associated coverage probability and the expected length of the proposed interval are investigated via a simulation study. The implementation of the confidence intervals is illustrated using a real data set.     

Crossover design in clinical trials for binary response

In this paper, we consider a binary response model for the analysis of the two-treatment, two-period and four-sequence crossover design. We have introduced intra-patient drug dependency parameter in the model and provide two tests for the hypothesis of equality of treatment effects. We employ Monte Carlo simulation to compare our tests and a test that works under parallel design on the basis of type I error rate and power. We find that our procedures are dominant over the competitor with respect to power. Finally, we use a data set to illustrate the applicability of our procedure.     

Variable Selection for Qualitative Interactions

In this article we discuss variable selection for decision making with focus on decisions regarding when to provide treatment and which treatment to provide. Current variable selection techniques were developed for use in a supervised learning setting where the goal is prediction of the response. These techniques often downplay the importance of interaction variables that have small predictive ability but that are critical when the ultimate goal is decision making rather than prediction. We propose two new techniques designed specifically to find variables that aid in decision making. Simulation results are given along with an application of the methods on data from a randomized controlled trial for the treatment of depression.     

Adaptive phase I/II clinical trials for drug combination assessment in oncology using the outcomes of each cycle

Many new anticancer agents can be combined with existing drugs, as combining a number of drugs may be expected to have a better therapeutic effect than monotherapy owing to synergistic effects. Furthermore, to drive drug development and to reduce the associated cost, there has been a growing tendency to combine these as phase I/II trials. With respect to phase I/II oncology trials for the assessment of dose combinations, in the existing methodologies in which efficacy based on tumor response and safety based on toxicity are modeled as binary outcomes, it is not possible to enroll and treat the next cohort of patients unless the best overall response has been determined in the current cohort. Thus, the trial duration might be potentially extended to an unacceptable degree. In this study, we proposed a method that randomizes the next cohort of patients in the phase II part to the dose combination based on the estimated response rate using all the available observed data upon determination of the overall response in the current cohort. We compared the proposed method to the existing method using simulation studies. These demonstrated that the percentage of optimal dose combinations selected in the proposed method is not less than that in the existing method and that the trial duration in the proposed method is shortened compared to that in the existing method. The proposed method meets both ethical and financial requirements, and we believe it has the potential to contribute to expedite drug development.     

A signature enrichment design with Bayesian adaptive randomization

Clinical trials in the era of precision cancer medicine aim to identify and validate biomarker signatures which can guide the assignment of individually optimal treatments to patients. In this article, we propose a group sequential randomized phase II design, which updates the biomarker signature as the trial goes on, utilizes enrichment strategies for patient selection, and uses Bayesian response-adaptive randomization for treatment assignment. To evaluate the performance of the new design, in addition to the commonly considered criteria of Type I error and power, we propose four new criteria measuring the benefits and losses for individuals both inside and outside of the clinical trial. Compared with designs with equal randomization, the proposed design gives trial participants a better chance to receive their personalized optimal treatments and thus results in a higher response rate on the trial. This design increases the chance to discover a successful new drug by an adaptive enrichment strategy, i.e. identification and selective enrollment of a subset of patients who are sensitive to the experimental therapies. Simulation studies demonstrate these advantages of the proposed design. It is illustrated by an example based on an actual clinical trial in non-small-cell lung cancer.     

Sample size determination and treatment screening in two‐stage phase II clinical trials via ROC curve

In pharmaceutical‐related research, we usually use clinical trials methods to identify valuable treatments and compare their efficacy with that of a standard control therapy. Although clinical trials are essential for ensuring the efficacy and postmarketing safety of a drug, conducting clinical trials is usually costly and time‐consuming. Moreover, to allocate patients to the little therapeutic effect treatments is inappropriate due to the ethical and cost imperative. Hence, there are several 2‐stage designs in the literature where, for reducing cost and shortening duration of trials, they use the conditional power obtained from interim analysis results to appraise whether we should continue the lower efficacious treatments in the next stage. However, there is a lack of discussion about the influential impacts on the conditional power of a trial at the design stage in the literature. In this article, we calculate the optimal conditional power via the receiver operating characteristic curve method to assess the impacts on the quality of a 2‐stage design with multiple treatments and propose an optimal design using the minimum expected sample size for choosing the best or promising treatment(s) among several treatments under an optimal conditional power constraint. In this paper, we provide tables of the 2‐stage design subject to optimal conditional power for various combinations of design parameters and use an example to illustrate our methods.     

Marginal Regression for Binary Longitudinal Data in Adaptive Clinical Trials

Abstract.  In an adaptive clinical trial research, it is common to use certain data-dependent design weights to assign individuals to treatments so that more study subjects are assigned to the better treatment. These design weights must also be used for consistent estimation of the treatment effects as well as the effects of the other prognostic factors. In practice, there are however situations where it may be necessary to collect binary responses repeatedly from an individual over a period of time and to obtain consistent estimates for the treatment effect as well as the effects of the other covariates in such a binary longitudinal set up. In this paper, we introduce a binary response-based longitudinal adaptive design for the allocation of individuals to a better treatment and propose a weighted generalized quasi-likelihood approach for the consistent and efficient estimation of the regression parameters including the treatment effects.     

Some practical considerations in three‐arm non‐inferiority trial design

Non‐inferiority trials aim to demonstrate whether an experimental therapy is not unacceptably worse than an active reference therapy already in use. When applicable, a three‐arm non‐inferiority trial, including an experiment therapy, an active reference therapy, and a placebo, is often recommended to assess assay sensitivity and internal validity of a trial. In this paper, we share some practical considerations based on our experience from a phase III three‐arm non‐inferiority trial. First, we discuss the determination of the total sample size and its optimal allocation based on the overall power of the non‐inferiority testing procedure and provide ready‐to‐use R code for implementation. Second, we consider the non‐inferiority goal of ‘capturing all possibilities’ and show that it naturally corresponds to a simple two‐step testing procedure. Finally, using this two‐step non‐inferiority testing procedure as an example, we compare extensively commonly used frequentist p ‐value methods with the Bayesian posterior probability approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Sample Size Requirements and Study Duration for Testing Main Effects and Interactions in Completely Randomized Factorial Designs When Time to Event is the Outcome

In this paper, we develop the methodology for designing clinical trials with any factorial arrangement when the primary outcome is time to event. We provide a matrix formulation for calculating the sample size and study duration necessary to test any effect with a prespecified type I error rate and power. Assuming that a time to event follows an exponential distribution, we describe the relationships between the effect size, the power, and the sample size. We present examples for illustration purposes. We provide a simulation study to verify the numerical calculations of the expected number of events and the duration of the trial. The change in the power produced by a reduced number of observations or by accruing no patients to certain factorial combinations is also described.