START: single‐to‐double arm transition design for phase II clinical trials

Phase II clinical trials designed for evaluating a drug's treatment effect can be either single‐arm or double‐arm. A single‐arm design tests the null hypothesis that the response rate of a new drug is lower than a fixed threshold, whereas a double‐arm scheme takes a more objective comparison of the response rate between the new treatment and the standard of care through randomization. Although the randomized design is the gold standard for efficacy assessment, various situations may arise where a single‐arm pilot study prior to a randomized trial is necessary. To combine the single‐ and double‐arm phases and pool the information together for better decision making, we propose a Single‐To‐double ARm Transition design (START) with switching hypotheses tests, where the first stage compares the new drug's response rate with a minimum required level and imposes a continuation criterion, and the second stage utilizes randomization to determine the treatment's superiority. We develop a software package in R to calibrate the frequentist error rates and perform simulation studies to assess the trial characteristics. Finally, a metastatic pancreatic cancer trial is used for illustrating the decision rules under the proposed START design.     

Two‐stage phase II survival trial design

Recently, molecularly targeted agents and immunotherapy have been advanced for the treatment of relapse or refractory cancer patients, where disease progression‐free survival or event‐free survival is often a primary endpoint for the trial design. However, methods to evaluate two‐stage single‐arm phase II trials with a time‐to‐event endpoint are currently processed under an exponential distribution, which limits application of real trial designs. In this paper, we developed an optimal two‐stage design, which is applied to the four commonly used parametric survival distributions. The proposed method has advantages compared with existing methods in that the choice of underlying survival model is more flexible and the power of the study is more adequately addressed. Therefore, the proposed two‐stage design can be routinely used for single‐arm phase II trial designs with a time‐to‐event endpoint as a complement to the commonly used Simon's two‐stage design for the binary outcome.     

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.     

Addressing potential prior‐data conflict when using informative priors in proof‐of‐concept studies

Bayesian methods are increasingly used in proof‐of‐concept studies. An important benefit of these methods is the potential to use informative priors, thereby reducing sample size. This is particularly relevant for treatment arms where there is a substantial amount of historical information such as placebo and active comparators. One issue with using an informative prior is the possibility of a mismatch between the informative prior and the observed data, referred to as prior‐data conflict. We focus on two methods for dealing with this: a testing approach and a mixture prior approach. The testing approach assesses prior‐data conflict by comparing the observed data to the prior predictive distribution and resorting to a non‐informative prior if prior‐data conflict is declared. The mixture prior approach uses a prior with a precise and diffuse component. We assess these approaches for the normal case via simulation and show they have some attractive features as compared with the standard one‐component informative prior. For example, when the discrepancy between the prior and the data is sufficiently marked, and intuitively, one feels less certain about the results, both the testing and mixture approaches typically yield wider posterior‐credible intervals than when there is no discrepancy. In contrast, when there is no discrepancy, the results of these approaches are typically similar to the standard approach. Whilst for any specific study, the operating characteristics of any selected approach should be assessed and agreed at the design stage; we believe these two approaches are each worthy of consideration. Copyright © 2015 John Wiley & Sons, Ltd.     

Study design of single‐arm phase II immunotherapy trials with long‐term survivors and random delayed treatment effect

In the traditional study design of a single‐arm phase II cancer clinical trial, the one‐sample log‐rank test has been frequently used. A common practice in sample size calculation is to assume that the event time in the new treatment follows exponential distribution. Such a study design may not be suitable for immunotherapy cancer trials, when both long‐term survivors (or even cured patients from the disease) and delayed treatment effect are present, because exponential distribution is not appropriate to describe such data and consequently could lead to severely underpowered trial. In this research, we proposed a piecewise proportional hazards cure rate model with random delayed treatment effect to design single‐arm phase II immunotherapy cancer trials. To improve test power, we proposed a new weighted one‐sample log‐rank test and provided a sample size calculation formula for designing trials. Our simulation study showed that the proposed log‐rank test performs well and is robust of misspecified weight and the sample size calculation formula also performs well.     

Characterization of dose‐response for count data using a generalized MCP‐Mod approach in an adaptive dose‐ranging trial

Understanding the dose–response relationship is a key objective in Phase II clinical development. Yet, designing a dose‐ranging trial is a challenging task, as it requires identifying the therapeutic window and the shape of the dose–response curve for a new drug on the basis of a limited number of doses. Adaptive designs have been proposed as a solution to improve both quality and efficiency of Phase II trials as they give the possibility to select the dose to be tested as the trial goes. In this article, we present a ‘shapebased’ two‐stage adaptive trial design where the doses to be tested in the second stage are determined based on the correlation observed between efficacy of the doses tested in the first stage and a set of pre‐specified candidate dose–response profiles. At the end of the trial, the data are analyzed using the generalized MCP‐Mod approach in order to account for model uncertainty. A simulation study shows that this approach gives more precise estimates of a desired target dose (e.g. ED70) than a single‐stage (fixed‐dose) design and performs as well as a two‐stage D‐optimal design. We present the results of an adaptive model‐based dose‐ranging trial in multiple sclerosis that motivated this research and was conducted using the presented methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

A mixture model using likelihood‐based and Bayesian approaches for identifying responders and non‐responders in longitudinal clinical trials

A longitudinal mixture model for classifying patients into responders and non‐responders is established using both likelihood‐based and Bayesian approaches. The model takes into consideration responders in the control group. Therefore, it is especially useful in situations where the placebo response is strong, or in equivalence trials where the drug in development is compared with a standard treatment. Under our model, a treatment shows evidence of being effective if it increases the proportion of responders or increases the response rate among responders in the treated group compared with the control group. Therefore, the model has flexibility to accommodate different situations. The proposed method is illustrated using simulation and a depression clinical trial dataset for the likelihood‐based approach, and the same depression clinical trial dataset for the Bayesian approach. The likelihood‐based and Bayesian approaches generated consistent results for the depression trial data. In both the placebo group and the treated group, patients are classified into two components with distinct response rate. The proportion of responders is shown to be significantly higher in the treated group compared with the control group, suggesting the treatment paroxetine is effective. Copyright © 2014 John Wiley & Sons, Ltd.     

Bayesian sample size determination for phase IIA clinical trials using historical data and semi‐parametric prior's elicitation

The Simon's two‐stage design is the most commonly applied among multi‐stage designs in phase IIA clinical trials. It combines the sample sizes at the two stages in order to minimize either the expected or the maximum sample size. When the uncertainty about pre‐trial beliefs on the expected or desired response rate is high, a Bayesian alternative should be considered since it allows to deal with the entire distribution of the parameter of interest in a more natural way. In this setting, a crucial issue is how to construct a distribution from the available summaries to use as a clinical prior in a Bayesian design. In this work, we explore the Bayesian counterparts of the Simon's two‐stage design based on the predictive version of the single threshold design. This design requires specifying two prior distributions: the analysis prior, which is used to compute the posterior probabilities, and the design prior, which is employed to obtain the prior predictive distribution. While the usual approach is to build beta priors for carrying out a conjugate analysis, we derived both the analysis and the design distributions through linear combinations of B‐splines. The motivating example is the planning of the phase IIA two‐stage trial on anti‐HER2 DNA vaccine in breast cancer, where initial beliefs formed from elicited experts' opinions and historical data showed a high level of uncertainty. In a sample size determination problem, the impact of different priors is evaluated.     

A Bayesian sequential design with adaptive randomization for 2‐sided hypothesis test

Bayesian sequential and adaptive randomization designs are gaining popularity in clinical trials thanks to their potentials to reduce the number of required participants and save resources. We propose a Bayesian sequential design with adaptive randomization rates so as to more efficiently attribute newly recruited patients to different treatment arms. In this paper, we consider 2‐arm clinical trials. Patients are allocated to the 2 arms with a randomization rate to achieve minimum variance for the test statistic. Algorithms are presented to calculate the optimal randomization rate, critical values, and power for the proposed design. Sensitivity analysis is implemented to check the influence on design by changing the prior distributions. Simulation studies are applied to compare the proposed method and traditional methods in terms of power and actual sample sizes. Simulations show that, when total sample size is fixed, the proposed design can obtain greater power and/or cost smaller actual sample size than the traditional Bayesian sequential design. Finally, we apply the proposed method to a real data set and compare the results with the Bayesian sequential design without adaptive randomization in terms of sample sizes. The proposed method can further reduce required sample size.     

Testing treatment‐by‐period interaction in four‐period crossover trials

Statistical analyses of crossover clinical trials have mainly focused on assessing the treatment effect, carryover effect, and period effect. When a treatment‐by‐period interaction is plausible, it is important to test such interaction first before making inferences on differences among individual treatments. Considerably less attention has been paid to the treatment‐by‐period interaction, which has historically been aliased with the carryover effect in two‐period or three‐period designs. In this article, from the data of a newly developed four‐period crossover design, we propose a statistical method to compare the effects of two active drugs with respect to two response variables. We study estimation and hypothesis testing considering the treatment‐by‐period interaction. Constrained least squares is used to estimate the treatment effect, period effect, and treatment‐by‐period interaction. For hypothesis testing, we extend a general multivariate method for analyzing the crossover design with multiple responses. Results from simulation studies have shown that this method performs very well. We also illustrate how to apply our method to the real data problem.     

Bayesian inference in two‐arm trials using relative belief ratios

Various methodologies proposed for some inference problems associated with two‐arm trails are known to suffer from difficulties, as documented in Senn (2001). We propose an alternative Bayesian approach to these problems that deals with these difficulties through providing an explicit measure of statistical evidence and the strength of this evidence. Bayesian methods are often criticized for their intrinsic subjectivity. We show how these concerns can be dealt with through assessing the bias induced by a prior model checking and checking for prior‐data conflict. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian adaptive dose‐escalation designs for simultaneously estimating the optimal and maximum safe dose based on safety and efficacy

The main purpose of dose‐escalation trials is to identify the dose(s) that is/are safe and efficacious for further investigations in later studies. In this paper, we introduce dose‐escalation designs that incorporate both the dose‐limiting events and dose‐limiting toxicities (DLTs) and indicative responses of efficacy into the procedure. A flexible nonparametric model is used for modelling the continuous efficacy responses while a logistic model is used for the binary DLTs. Escalation decisions are based on the combination of the probabilities of DLTs and expected efficacy through a gain function. On the basis of this setup, we then introduce 2 types of Bayesian adaptive dose‐escalation strategies. The first type of procedures, called “single objective,” aims to identify and recommend a single dose, either the maximum tolerated dose, the highest dose that is considered as safe, or the optimal dose, a safe dose that gives optimum benefit risk. The second type, called “dual objective,” aims to jointly estimate both the maximum tolerated dose and the optimal dose accurately. The recommended doses obtained under these dose‐escalation procedures provide information about the safety and efficacy profile of the novel drug to facilitate later studies. We evaluate different strategies via simulations based on an example constructed from a real trial on patients with type 2 diabetes, and the use of stopping rules is assessed. We find that the nonparametric model estimates the efficacy responses well for different underlying true shapes. The dual‐objective designs give better results in terms of identifying the 2 real target doses compared to the single‐objective designs.     

The impact of period effects on dose level contrasts in alternating cross‐over designs for first‐time‐in‐human studies

For first‐time‐in‐human studies with small molecules alternating cross‐over designs are often employed and at study end are analyzed using linear models. We discuss the impact of including a period effect in the model on the precision with which dose level contrasts can be estimated and quantify the bias of least squares estimators if a period effect is inherent in the data that is not accounted for in the model. We also propose two alternative designs that allow a more precise estimation of dose level contrasts compared with the standard design when period effects are included in the model. Copyright © 2010 John Wiley & Sons, Ltd.     

Dose finding when the target dose is on a plateau of a dose–response curve: comparison of fully sequential designs

Consider the problem of estimating a dose with a certain response rate. Many multistage dose‐finding designs for this problem were originally developed for oncology studies where the mean dose–response is strictly increasing in dose. In non‐oncology phase II dose‐finding studies, the dose–response curve often plateaus in the range of interest, and there are several doses with the mean response equal to the target. In this case, it is usually of interest to find the lowest of these doses because higher doses might have higher adverse event rates. It is often desirable to compare the response rate at the estimated target dose with a placebo and/or active control. We investigate which of the several known dose‐finding methods developed for oncology phase I trials is the most suitable when the dose–response curve plateaus. Some of the designs tend to spread the allocation among the doses on the plateau. Others, such as the continual reassessment method and the t‐statistic design, concentrate allocation at one of the doses with the t‐statistic design selecting the lowest dose on the plateau more frequently. Copyright © 2013 John Wiley & Sons, Ltd.     

Gaining acceptability for the Bayesian decision‐theoretic approach in dose‐escalation studies

There has recently been increasing demand for better designs to conduct first‐into‐man dose‐escalation studies more efficiently, more accurately and more quickly. The authors look into the Bayesian decision‐theoretic approach and use simulation as a tool to investigate the impact of compromises with conventional practice that might make the procedures more acceptable for implementation. Copyright © 2005 John Wiley & Sons, Ltd.     

Minimax A‐ and D‐optimal integer‐valued wavelet designs for estimation

The author discusses integer‐valued designs for wavelet estimation of nonparametric response curves in the possible presence of heteroscedastic noise using a modified wavelet version of the Gasser‐Müller kernel estimator or weighted least squares estimation. The designs are constructed using a minimax treatment and the simulated annealing algorithm. The author presents designs for three case studies in experiments for investigating Gompertz's theory on mortality rates, nitrite utilization in bush beans and the impact of crash helmets in motorcycle accidents.     

Dose‐escalation strategies which use subgroup information

Dose‐escalation trials commonly assume a homogeneous trial population to identify a single recommended dose of the experimental treatment for use in future trials. Wrongly assuming a homogeneous population can lead to a diluted treatment effect. Equally, exclusion of a subgroup that could in fact benefit from the treatment can cause a beneficial treatment effect to be missed. Accounting for a potential subgroup effect (ie, difference in reaction to the treatment between subgroups) in dose‐escalation can increase the chance of finding the treatment to be efficacious in a larger patient population. A standard Bayesian model‐based method of dose‐escalation is extended to account for a subgroup effect by including covariates for subgroup membership in the dose‐toxicity model. A stratified design performs well but uses available data inefficiently and makes no inferences concerning presence of a subgroup effect. A hypothesis test could potentially rectify this problem but the small sample sizes result in a low‐powered test. As an alternative, the use of spike and slab priors for variable selection is proposed. This method continually assesses the presence of a subgroup effect, enabling efficient use of the available trial data throughout escalation and in identifying the recommended dose(s). A simulation study, based on real trial data, was conducted and this design was found to be both promising and feasible.     

Cost‐efficient higher‐order crossover designs for two‐treatment clinical trials

Higher‐order crossover designs have drawn considerable attention in clinical trials, because of their ability to test direct treatment effects in the presence of carry‐over effects. The important question, when applying higher‐order crossover designs in practice, is how to choose a design with both statistical and cost efficiencies from various alternatives. In this paper, we propose a general cost function and compare five statistically optimal or near‐optimal designs with this cost function for a two‐treatment study under different carry‐over models. Based on our study, to achieve both statistical and cost efficiencies, a four‐period, four‐sequence crossover design is generally recommended under the simple carry‐over or no carry‐over models, and a three‐period, two‐sequence crossover design is generally recommended under the steady‐state carry‐over models. Copyright © 2005 John Wiley & Sons, Ltd.     

Properties of the weighted log‐rank test in the design of confirmatory studies with delayed effects

Proportional hazards are a common assumption when designing confirmatory clinical trials in oncology. This assumption not only affects the analysis part but also the sample size calculation. The presence of delayed effects causes a change in the hazard ratio while the trial is ongoing since at the beginning we do not observe any difference between treatment arms, and after some unknown time point, the differences between treatment arms will start to appear. Hence, the proportional hazards assumption no longer holds, and both sample size calculation and analysis methods to be used should be reconsidered. The weighted log‐rank test allows a weighting for early, middle, and late differences through the Fleming and Harrington class of weights and is proven to be more efficient when the proportional hazards assumption does not hold. The Fleming and Harrington class of weights, along with the estimated delay, can be incorporated into the sample size calculation in order to maintain the desired power once the treatment arm differences start to appear. In this article, we explore the impact of delayed effects in group sequential and adaptive group sequential designs and make an empirical evaluation in terms of power and type‐I error rate of the of the weighted log‐rank test in a simulated scenario with fixed values of the Fleming and Harrington class of weights. We also give some practical recommendations regarding which methodology should be used in the presence of delayed effects depending on certain characteristics of the trial.     

Single‐arm phase II trial design under parametric cure models

The current practice of designing single‐arm phase II survival trials is limited under the exponential model. Trial design under the exponential model may not be appropriate when a portion of patients are cured. There is no literature available for designing single‐arm phase II trials under the parametric cure model. In this paper, a test statistic is proposed, and a sample size formula is derived for designing single‐arm phase II trials under a class of parametric cure models. Extensive simulations showed that the proposed test and sample size formula perform very well under different scenarios. Copyright © 2015 John Wiley & Sons, Ltd.