Phase II trial design with growth modulation index as the primary endpoint

Molecularly targeted, genomic‐driven, and immunotherapy‐based clinical trials continue to be advanced for the treatment of relapse or refractory cancer patients, where the growth modulation index (GMI) is often considered a primary endpoint of treatment efficacy. However, there little literature is available that considers the trial design with GMI as the primary endpoint. In this article, we derived a sample size formula for the score test under a log‐linear model of the GMI. Study designs using the derived sample size formula are illustrated under a bivariate exponential model, the Weibull frailty model, and the generalized treatment effect size. The proposed designs provide sound statistical methods for a single‐arm phase II trial with GMI as the primary endpoint.     

SPIRIT: A seamless phase I/II randomized design for immunotherapy trials

Immunotherapy—treatments that enlist the immune system to battle tumors—has received widespread attention in cancer research. Due to its unique features and mechanisms for treating cancer, immunotherapy requires novel clinical trial designs. We propose a Bayesian seamless phase I/II randomized design for immunotherapy trials (SPIRIT) to find the optimal biological dose (OBD) defined in terms of the restricted mean survival time. We jointly model progression‐free survival and the immune response. Progression‐free survival is used as the primary endpoint to determine the OBD, and the immune response is used as an ancillary endpoint to quickly screen out futile doses. Toxicity is monitored throughout the trial. The design consists of two seamlessly connected stages. The first stage identifies a set of safe doses. The second stage adaptively randomizes patients to the safe doses identified and uses their progression‐free survival and immune response to find the OBD. The simulation study shows that the SPIRIT has desirable operating characteristics and outperforms the conventional design.     

Bayesian single-to-double arm transition design using both short-term and long-term endpoints

The choice between single-arm designs versus randomized double-arm designs has been contentiously debated in the literature of phase II oncology trials. Recently, as a compromise, the single-to-double arm transition design was proposed, combining the two designs into one trial over two stages. Successful implementation of the two-stage transition design requires a suspension period at the end of the first stage to collect the response data of the already enrolled patients. When the evaluation of the primary efficacy endpoint is overly long, the between-stage suspension period may unfavorably prolong the trial duration and cause a delay in treating future eligible patients. To accelerate the trial, we propose a Bayesian single-to-double arm design with short-term endpoints (BSDS), where an intermediate short-term endpoint is used for making early termination decisions at the end of the single-arm stage, followed by an evaluation of the long-term endpoint at the end of the subsequent double-arm stage. Bayesian posterior probabilities are used as the primary decision-making tool at the end of the trial. Design calibration steps are proposed for this Bayesian monitoring process to control the frequentist operating characteristics and minimize the expected sample size. Extensive simulation studies have demonstrated that our design has comparable power and average sample size but a much shorter trial duration than conventional single-to-double arm design. Applications of the design are illustrated using two phase II oncology trials with binary endpoints.     

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.     

A two‐stage phase II clinical trial design with nested criteria for early stopping and efficacy

We propose a two‐stage design for a single arm clinical trial with an early stopping rule for futility. This design employs different endpoints to assess early stopping and efficacy. The early stopping rule is based on a criteria determined more quickly than that for efficacy. These separate criteria are also nested in the sense that efficacy is a special case of, but usually not identical to, the early stopping endpoint. The design readily allows for planning in terms of statistical significance, power, expected sample size, and expected duration. This method is illustrated with a phase II design comparing rates of disease progression in elderly patients treated for lung cancer to rates found using a historical control. In this example, the early stopping rule is based on the number of patients who exhibit progression‐free survival (PFS) at 2 months post treatment follow‐up. Efficacy is judged by the number of patients who have PFS at 6 months. We demonstrate our design has expected sample size and power comparable with the Simon two‐stage design but exhibits shorter expected duration under a range of useful parameter values.     

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.     

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.     

Bayesian single-arm phase II trial designs with time-to-event endpoints

For the cancer clinical trials with immunotherapy and molecularly targeted therapy, time-to-event endpoint is often a desired endpoint. In this paper, we present an event-driven approach for Bayesian one-stage and two-stage single-arm phase II trial designs. Two versions of Bayesian one-stage designs were proposed with executable algorithms and meanwhile, we also develop theoretical relationships between the frequentist and Bayesian designs. These findings help investigators who want to design a trial using Bayesian approach have an explicit understanding of how the frequentist properties can be achieved. Moreover, the proposed Bayesian designs using the exact posterior distributions accommodate the single-arm phase II trials with small sample sizes. We also proposed an optimal two-stage approach, which can be regarded as an extension of Simon's two-stage design with the time-to-event endpoint. Comprehensive simulations were conducted to explore the frequentist properties of the proposed Bayesian designs and an R package BayesDesign can be assessed via R CRAN for convenient use of the proposed methods.     

Adaptive designs for single‐arm phase II trials in oncology

Clinical phase II trials in oncology are conducted to determine whether the activity of a new anticancer treatment is promising enough to merit further investigation. Two‐stage designs are commonly used for this situation to allow for early termination. Designs proposed in the literature so far have the common drawback that the sample sizes for the two stages have to be specified in the protocol and have to be adhered to strictly during the course of the trial. As a consequence, designs that allow a higher extent of flexibility are desirable. In this article, we propose a new adaptive method that allows an arbitrary modification of the sample size of the second stage using the results of the interim analysis or external information while controlling the type I error rate. If the sample size is not changed during the trial, the proposed design shows very similar characteristics to the optimal two‐stage design proposed by Chang et al. (Biometrics 1987; 43:865–874). However, the new design allows the use of mid‐course information for the planning of the second stage, thus meeting practical requirements when performing clinical phase II trials in oncology. Copyright © 2012 John Wiley & Sons, Ltd.     

An alternative phase II/III design for continuous endpoints

The success rate of drug development has been declined dramatically in recent years and the current paradigm of drug development is no longer functioning. It requires a major undertaking on breakthrough strategies and methodology for designs to minimize sample sizes and to shorten duration of the development. We propose an alternative phase II/III design based on continuous efficacy endpoints, which consists of two stages: a selection stage and a confirmation stage. For the selection stage, a randomized parallel design with several doses with a placebo group is employed for selection of doses. After the best dose is chosen, the patients of the selected dose group and placebo group continue to enter the confirmation stage. New patients will also be recruited and randomized to receive the selected dose or placebo group. The final analysis is performed with the cumulative data of patients from both stages. With the pre‐specified probabilities of rejecting the drug at each stage, sample sizes and critical values for both stages can be determined. As it is a single trial with controlling overall type I and II error rates, the proposed phase II/III adaptive design may not only reduce the sample size but also improve the success rate. An example illustrates the applications of the proposed phase II/III adaptive design. Copyright © 2010 John Wiley & Sons, Ltd.     

A simple two-stage design for quantitative responses with application to a study in diabetic neuropathic pain

Two-stage designs offer substantial advantages for early phase II studies. The interim analysis following the first stage allows the study to be stopped for futility, or more positively, it might lead to early progression to the trials needed for late phase II and phase III. If the study is to continue to its second stage, then there is an opportunity for a revision of the total sample size. Two-stage designs have been implemented widely in oncology studies in which there is a single treatment arm and patient responses are binary. In this paper the case of two-arm comparative studies in which responses are quantitative is considered. This setting is common in therapeutic areas other than oncology. It will be assumed that observations are normally distributed, but that there is some doubt concerning their standard deviation, motivating the need for sample size review. The work reported has been motivated by a study in diabetic neuropathic pain, and the development of the design for that trial is described in detail.     

Strengthening the understanding of the relationship between survival designs and test statistics

In the planning of randomized survival trials, the role of follow‐up time of trial participants introduces a level of complexity not encountered in non‐survival trials. Of the two commonly used survival designs, one design fixes the follow‐up time whereas the other allows it to vary. When the follow‐up time is fixed the number of events varies. Conversely, when the number of events is fixed, the follow‐up time varies. These two designs influence test statistics in ways that have not been fully explored resulting in a misunderstanding of the design–test statistic relationship. We use examples from the literature to strengthen the understanding of this relationship. Group sequential trials are briefly discussed. When the number of events is fixed, we demonstrate why a two‐sample risk difference test statistic reduces to a one‐sample test statistic which is nearly equal to the risk ratio test statistic. Some aspects of fixed event designs that need further consideration are also discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Do single‐arm trials have a role in drug development plans incorporating randomised trials?

Often, single‐arm trials are used in phase II to gather the first evidence of an oncological drug's efficacy, with drug activity determined through tumour response using the RECIST criterion. Provided the null hypothesis of ‘insufficient drug activity’ is rejected, the next step could be a randomised two‐arm trial. However, single‐arm trials may provide a biased treatment effect because of patient selection, and thus, this development plan may not be an efficient use of resources. Therefore, we compare the performance of development plans consisting of single‐arm trials followed by randomised two‐arm trials with stand‐alone single‐stage or group sequential randomised two‐arm trials. Through this, we are able to investigate the utility of single‐arm trials and determine the most efficient drug development plans, setting our work in the context of a published single‐arm non‐small‐cell lung cancer trial. Reference priors, reflecting the opinions of ‘sceptical’ and ‘enthusiastic’ investigators, are used to quantify and guide the suitability of single‐arm trials in this setting. We observe that the explored development plans incorporating single‐arm trials are often non‐optimal. Moreover, even the most pessimistic reference priors have a considerable probability in favour of alternative plans. Analysis suggests expected sample size savings of up to 25% could have been made, and the issues associated with single‐arm trials avoided, for the non‐small‐cell lung cancer treatment through direct progression to a group sequential randomised two‐arm trial. Careful consideration should thus be given to the use of single‐arm trials in oncological drug development when a randomised trial will follow. Copyright © 2015 The Authors. Pharmaceutical Statistics published by JohnWiley & Sons Ltd.     

A novel test to compare two treatments based on endpoints involving both nonfatal and fatal events

In a clinical trial comparing two treatment groups, one commonly‐used endpoint is time to death. Another is time until the first nonfatal event (if there is one) or until death (if not). Both endpoints have drawbacks. The wrong choice may adversely affect the value of the study by impairing power if deaths are too few (with the first endpoint) or by lessening the role of mortality if not (with the second endpoint). We propose a compromise that provides a simple test based on the time to death if the patient has died or time since randomization augmented by an increment otherwise. The test applies the ordinary two‐sample Wilcoxon statistic to these values. The formula for the increment (the same for experimental and control patients) must be specified before the trial starts. In the simplest (and perhaps most useful) case, the increment assumes only two values, according to whether or not the (surviving) patient had a nonfatal event. More generally, the increment depends on the time of the first nonfatal event, if any, and the time since randomization. The test has correct Type I error even though it does not handle censoring in a customary way. For conditions where investigators would face no easy (advance) choice between the two older tests, simulation results favor the new test. An example using a renal‐cancer trial is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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.     

An application of a multi‐stage strategy involving confidence intervals to evaluate whether a response rate is favourable or not

In early clinical development of new medicines, a single‐arm study with a limited number of patients is often used to provide a preliminary assessment of a response rate. A multi‐stage design may be indicated, especially when the first stage should only include very few patients so as to enable rapid identification of an ineffective drug. We used decision rules based on several types of nominal confidence intervals to evaluate a three‐stage design for a study that includes at most 30 patients. For each decision rule, we used exact binomial calculations to determine the probability of continuing to further stages as well as to evaluate Type I and Type II error rates. Examples are provided to illustrate the methods for evaluating alternative decision rules and to provide guidance on how to extend the methods to situations with modifications to the number of stages or number of patients per stage in the study design. Copyright © 2004 John Wiley & Sons, Ltd.     

Testing multiple primary endpoints in clinical trials with sample size adaptation

In this paper, we propose a design that uses a short‐term endpoint for accelerated approval at interim analysis and a long‐term endpoint for full approval at final analysis with sample size adaptation based on the long‐term endpoint. Two sample size adaptation rules are compared: an adaptation rule to maintain the conditional power at a prespecified level and a step function type adaptation rule to better address the bias issue. Three testing procedures are proposed: alpha splitting between the two endpoints; alpha exhaustive between the endpoints; and alpha exhaustive with improved critical value based on correlation. Family‐wise error rate is proved to be strongly controlled for the two endpoints, sample size adaptation, and two analysis time points with the proposed designs. We show that using alpha exhaustive designs greatly improve the power when both endpoints are effective, and the power difference between the two adaptation rules is minimal. The proposed design can be extended to more general settings. Copyright © 2015 John Wiley & Sons, Ltd.     

Survival trial design and monitoring using historical controls

In this paper, we propose a multistage group sequential procedure to design survival trials using historical controls. The formula for the number of events required for historical control trial designs is derived. Furthermore, a transformed information time is proposed for trial monitoring. An example is given to illustrate the application of the proposed methods to survival trial designs using historical controls. Copyright © 2016 John Wiley & Sons, Ltd.     

Generalized optimal design for two‐arm,randomized phase II clinical trials with endpoints from the exponential dispersion family

For two‐arm randomized phase II clinical trials, previous literature proposed an optimal design that minimizes the total sample sizes subject to multiple constraints on the standard errors of the estimated event rates and their difference. The original design is limited to trials with dichotomous endpoints. This paper extends the original approach to be applicable to phase II clinical trials with endpoints from the exponential dispersion family distributions. The proposed optimal design minimizes the total sample sizes needed to provide estimates of population means of both arms and their difference with pre‐specified precision. Its applications on data from specific distribution families are discussed under multiple design considerations. Copyright © 2016 John Wiley & Sons, Ltd.