Oncology phase II proof‐of‐concept studies with multiple targets: Randomized controlled trial or single arm?

For oncology drug development, phase II proof‐of‐concept studies have played a key role in determining whether or not to advance to a confirmatory phase III trial. With the increasing number of immunotherapies, efficient design strategies are crucial in moving successful drugs quickly to market. Our research examines drug development decision making under the framework of maximizing resource investment, characterized by benefit cost ratios (BCRs). In general, benefit represents the likelihood that a drug is successful, and cost is characterized by the risk adjusted total sample size of the phases II and III studies. Phase III studies often include a futility interim analysis; this sequential component can also be incorporated into BCRs. Under this framework, multiple scenarios can be considered. For example, for a given drug and cancer indication, BCRs can yield insights into whether to use a randomized control trial or a single‐arm study. Importantly, any uncertainty in historical control estimates that are used to benchmark single‐arm studies can be explicitly incorporated into BCRs. More complex scenarios, such as restricted resources or multiple potential cancer indications, can also be examined. Overall, BCR analyses indicate that single‐arm trials are favored for proof‐of‐concept trials when there is low uncertainty in historical control data and smaller phase III sample sizes. Otherwise, especially if the most likely to succeed tumor indication can be identified, randomized controlled trials may be a better option. While the findings are consistent with intuition, we provide a more objective approach.     

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.     

Bayesian phase II adaptive randomization by jointly modeling time-to-event efficacy and binary toxicity

In oncology, toxicity is typically observable shortly after a chemotherapy treatment, whereas efficacy, often characterized by tumor shrinkage, is observable after a relatively long period of time. In a phase II clinical trial design, we propose a Bayesian adaptive randomization procedure that accounts for both efficacy and toxicity outcomes. We model efficacy as a time-to-event endpoint and toxicity as a binary endpoint, sharing common random effects in order to induce dependence between the bivariate outcomes. More generally, we allow the randomization probability to depend on patients’ specific covariates, such as prognostic factors. Early stopping boundaries are constructed for toxicity and futility, and a superior treatment arm is recommended at the end of the trial. Following the setup of a recent renal cancer clinical trial at M. D. Anderson Cancer Center, we conduct extensive simulation studies under various scenarios to investigate the performance of the proposed method, and compare it with available Bayesian adaptive randomization procedures.     

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.     

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.     

Bayesian adaptive patient enrollment restriction to identify a sensitive subpopulation using a continuous biomarker in a randomized phase 2 trial

With the development of molecular targeted drugs, predictive biomarkers have played an increasingly important role in identifying patients who are likely to receive clinically meaningful benefits from experimental drugs (i.e., sensitive subpopulation) even in early clinical trials. For continuous biomarkers, such as mRNA levels, it is challenging to determine cutoff value for the sensitive subpopulation, and widely accepted study designs and statistical approaches are not currently available. In this paper, we propose the Bayesian adaptive patient enrollment restriction (BAPER) approach to identify the sensitive subpopulation while restricting enrollment of patients from the insensitive subpopulation based on the results of interim analyses, in a randomized phase 2 trial with time‐to‐endpoint outcome and a single biomarker. Applying a four‐parameter change‐point model to the relationship between the biomarker and hazard ratio, we calculate the posterior distribution of the cutoff value that exhibits the target hazard ratio and use it for the restriction of the enrollment and the identification of the sensitive subpopulation. We also consider interim monitoring rules for termination because of futility or efficacy. Extensive simulations demonstrated that our proposed approach reduced the number of enrolled patients from the insensitive subpopulation, relative to an approach with no enrollment restriction, without reducing the likelihood of a correct decision for next trial (no‐go, go with entire population, or go with sensitive subpopulation) or correct identification of the sensitive subpopulation. Additionally, the four‐parameter change‐point model had a better performance over a wide range of simulation scenarios than a commonly used dichotomization approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Stopping for efficacy in single-arm phase II clinical trials

Phase II clinical trials investigate whether a new drug or treatment has sufficient evidence of effectiveness against the disease under study. Two-stage designs are popular for phase II since they can stop in the first stage if the drug is ineffective. Investigators often face difficulties in determining the target response rates, and adaptive designs can help to set the target response rate tested in the second stage based on the number of responses observed in the first stage. Popular adaptive designs consider two alternate response rates, and they generally minimise the expected sample size at the maximum uninterested response rate. Moreover, these designs consider only futility as the reason for early stopping and have high expected sample sizes if the provided drug is effective. Motivated by this problem, we propose an adaptive design that enables us to terminate the single-arm trial at the first stage for efficacy and conclude which alternate response rate to choose. Comparing the proposed design with a popular adaptive design from literature reveals that the expected sample size decreases notably if any of the two target response rates are correct. In contrast, the expected sample size remains almost the same under the null hypothesis.     

A flexible multi-stage design for phase II oncology trials

Phase II trials evaluate whether a new drug or a new therapy is worth further pursuing or certain treatments are feasible or not. A typical phase II is a single arm (open label) trial with a binary clinical endpoint (response to therapy). Although many oncology Phase II clinical trials are designed with a two-stage procedure, multi-stage design for phase II cancer clinical trials are now feasible due to increased capability of data capture. Such design adjusts for multiple analyses and variations in analysis time, and provides greater flexibility such as minimizing the number of patients treated on an ineffective therapy and identifying the minimum number of patients needed to evaluate whether the trial would warrant further development. In most of the NIH sponsored studies, the early stopping rule is determined so that the number of patients treated on an ineffective therapy is minimized. In pharmaceutical trials, it is also of importance to know as early as possible if the trial is highly promising and what is the likelihood the early conclusion can sustain. Although various methods are available to address these issues, practitioners often use disparate methods for addressing different issues and do not realize a single unified method exists. This article shows how to utilize a unified approach via a fully sequential procedure, the sequential conditional probability ratio test, to address the multiple needs of a phase II trial. We show the fully sequential program can be used to derive an optimized efficient multi-stage design for either a low activity or a high activity, to identify the minimum number of patients required to assess whether a new drug warrants further study and to adjust for unplanned interim analyses. In addition, we calculate a probability of discordance that the statistical test will conclude otherwise should the trial continue to the planned end that is usually at the sample size of a fixed sample design. This probability can be used to aid in decision making in a drug development program. All computations are based on exact binomial distribution.     

Early stopping in seamless phase I/II clinical trials

In recent years, seamless phase I/II clinical trials have drawn much attention, as they consider both toxicity and efficacy endpoints in finding an optimal dose (OD). Engaging an appropriate number of patients in a trial is a challenging task. This paper attempts a dynamic stopping rule to save resources in phase I/II trials. That is, the stopping rule aims to save patients from unnecessary toxic or subtherapeutic doses. We allow a trial to stop early when widths of the confidence intervals for the dose-response parameters become narrower or when the sample size is equal to a predefined size, whichever comes first. The simulation study of dose-response scenarios in various settings demonstrates that the proposed stopping rule can engage an appropriate number of patients. Therefore, we suggest its use in clinical trials.     

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.     

Response-adaptive trial designs with accelerated Thompson sampling

In a clinical trial, sometimes it is desirable to allocate as many patients as possible to the best treatment, in particular, when a trial for a rare disease may contain a considerable portion of the whole target population. The Gittins index rule is a powerful tool for sequentially allocating patients to the best treatment based on the responses of patients already treated. However, its application in clinical trials is limited due to technical complexity and lack of randomness. Thompson sampling is an appealing approach, since it makes a compromise between optimal treatment allocation and randomness with some desirable optimal properties in the machine learning context. However, in clinical trial settings, multiple simulation studies have shown disappointing results with Thompson samplers. We consider how to improve short-run performance of Thompson sampling and propose a novel acceleration approach. This approach can also be applied to situations when patients can only be allocated by batch and is very easy to implement without using complex algorithms. A simulation study showed that this approach could improve the performance of Thompson sampling in terms of average total response rate. An application to a redesign of a preference trial to maximize patient's satisfaction is also presented.     

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.     

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.     

When is a seamless study desirable? Case studies from different pharmaceutical sponsors

Background: Inferentially seamless studies are one of the best‐known adaptive trial designs. Statistical inference for these studies is a well‐studied problem. Regulatory guidance suggests that statistical issues associated with study conduct are not as well understood. Some of these issues are caused by the need for early pre‐specification of the phase III design and the absence of sponsor access to unblinded data. Before statisticians decide to choose a seamless IIb/III design for their programme, they should consider whether these pitfalls will be an issue for their programme. Methods: We consider four case studies. Each design met with varying degrees of success. We explore the reasons for this variation to identify characteristics of drug development programmes that lend themselves well to inferentially seamless trials and other characteristics that warn of difficulties. Results: Seamless studies require increased upfront investment and planning to enable the phase III design to be specified at the outset of phase II. Pivotal, inferentially seamless studies are unlikely to allow meaningful sponsor access to unblinded data before study completion. This limits a sponsor's ability to reflect new information in the phase III portion. Conclusions: When few clinical data have been gathered about a drug, phase II data will answer many unresolved questions. Committing to phase III plans and study designs before phase II begins introduces extra risk to drug development. However, seamless pivotal studies may be an attractive option when the clinical setting and development programme allow, for example, when revisiting dose selection. Copyright © 2014 John Wiley & Sons, Ltd.     

A comparison of subgroup identification methods in clinical drug development: Simulation study and regulatory considerations

With advancement of technologies such as genomic sequencing, predictive biomarkers have become a useful tool for the development of personalized medicine. Predictive biomarkers can be used to select subsets of patients, which are most likely to benefit from a treatment. A number of approaches for subgroup identification were proposed over the last years. Although overviews of subgroup identification methods are available, systematic comparisons of their performance in simulation studies are rare. Interaction trees (IT), model‐based recursive partitioning, subgroup identification based on differential effect, simultaneous threshold interaction modeling algorithm (STIMA), and adaptive refinement by directed peeling were proposed for subgroup identification. We compared these methods in a simulation study using a structured approach. In order to identify a target population for subsequent trials, a selection of the identified subgroups is needed. Therefore, we propose a subgroup criterion leading to a target subgroup consisting of the identified subgroups with an estimated treatment difference no less than a pre‐specified threshold. In our simulation study, we evaluated these methods by considering measures for binary classification, like sensitivity and specificity. In settings with large effects or huge sample sizes, most methods perform well. For more realistic settings in drug development involving data from a single trial only, however, none of the methods seems suitable for selecting a target population. Using the subgroup criterion as alternative to the proposed pruning procedures, STIMA and IT can improve their performance in some settings. The methods and the subgroup criterion are illustrated by an application in amyotrophic lateral sclerosis.     

Robustness and Corrections for Sample Size Adaptation Strategies Based on Effect Size Estimation

A study on the robustness of the adaptation of the sample size for a phase III trial on the basis of existing phase II data is presented—when phase III is lower than phase II effect size. A criterion of clinical relevance for phase II results is applied in order to launch phase III, where data from phase II cannot be included in statistical analysis. The adaptation consists in adopting the conservative approach to sample size estimation, which takes into account the variability of phase II data. Some conservative sample size estimation strategies, Bayesian and frequentist, are compared with the calibrated optimal γ conservative strategy (viz. COS) which is the best performer when phase II and phase III effect sizes are equal. The Overall Power (OP) of these strategies and the mean square error (MSE) of their sample size estimators are computed under different scenarios, in the presence of the structural bias due to lower phase III effect size, for evaluating the robustness of the strategies. When the structural bias is quite small (i.e., the ratio of phase III to phase II effect size is greater than 0.8), and when some operating conditions for applying sample size estimation hold, COS can still provide acceptable results for planning phase III trials, even if in bias absence the OP was higher.

Main results concern the introduction of a correction, which affects just sample size estimates and not launch probabilities, for balancing the structural bias. In particular, the correction is based on a postulation of the structural bias; hence, it is more intuitive and easier to use than those based on the modification of Type I or/and Type II errors. A comparison of corrected conservative sample size estimation strategies is performed in the presence of a quite small bias. When the postulated correction is right, COS provides good OP and the lowest MSE. Moreover, the OPs of COS are even higher than those observed without bias, thanks to higher launch probability and a similar estimation performance. The structural bias can therefore be exploited for improving sample size estimation performances. When the postulated correction is smaller than necessary, COS is still the best performer, and it also works well. A higher than necessary correction should be avoided.     

Discounting phase 2 results when planning phase 3 clinical trials

Sample size planning is an important design consideration for a phase 3 trial. In this paper, we consider how to improve this planning when using data from phase 2 trials. We use an approach based on the concept of assurance. We consider adjusting phase 2 results because of two possible sources of bias. The first source arises from selecting compounds with pre‐specified favourable phase 2 results and using these favourable results as the basis of treatment effect for phase 3 sample size planning. The next source arises from projecting phase 2 treatment effect to the phase 3 population when this projection is optimistic because of a generally more heterogeneous patient population at the confirmatory stage. In an attempt to reduce the impact of these two sources of bias, we adjust (discount) the phase 2 estimate of treatment effect. We consider multiplicative and additive adjustment. Following a previously proposed concept, we consider the properties of several criteria, termed launch criteria, for deciding whether or not to progress development to phase 3. We use simulations to investigate launch criteria with or without bias adjustment for the sample size calculation under various scenarios. The simulation results are supplemented with empirical evidence to support the need to discount phase 2 results when the latter are used in phase 3 planning. Finally, we offer some recommendations based on both the simulations and the empirical investigations. Copyright © 2012 John Wiley & Sons, Ltd.     

Blinded sample size re‐estimation in crossover bioequivalence trials

In drug development, bioequivalence studies are used to indirectly demonstrate clinical equivalence of a test formulation and a reference formulation of a specific drug by establishing their equivalence in bioavailability. These studies are typically run as crossover studies. In the planning phase of such trials, investigators and sponsors are often faced with a high variability in the coefficients of variation of the typical pharmacokinetic endpoints such as the area under the concentration curve or the maximum plasma concentration. Adaptive designs have recently been considered to deal with this uncertainty by adjusting the sample size based on the accumulating data. Because regulators generally favor sample size re‐estimation procedures that maintain the blinding of the treatment allocations throughout the trial, we propose in this paper a blinded sample size re‐estimation strategy and investigate its error rates. We show that the procedure, although blinded, can lead to some inflation of the type I error rate. In the context of an example, we demonstrate how this inflation of the significance level can be adjusted for to achieve control of the type I error rate at a pre‐specified level. Furthermore, some refinements of the re‐estimation procedure are proposed to improve the power properties, in particular in scenarios with small sample sizes. Copyright © 2014 John Wiley & Sons, Ltd.     

Bayesian optimal phase II designs with dual-criterion decision making

The conventional phase II trial design paradigm is to make the go/no-go decision based on the hypothesis testing framework. Statistical significance itself alone, however, may not be sufficient to establish that the drug is clinically effective enough to warrant confirmatory phase III trials. We propose the Bayesian optimal phase II trial design with dual-criterion decision making (BOP2-DC), which incorporates both statistical significance and clinical relevance into decision making. Based on the posterior probability that the treatment effect reaches the lower reference value (statistical significance) and the clinically meaningful value (clinical significance), BOP2-DC allows for go/consider/no-go decisions, rather than a binary go/no-go decision. BOP2-DC is highly flexible and accommodates various types of endpoints, including binary, continuous, time-to-event, multiple, and coprimary endpoints, in single-arm and randomized trials. The decision rule of BOP2-DC is optimized to maximize the probability of a go decision when the treatment is effective or minimize the expected sample size when the treatment is futile. Simulation studies show that the BOP2-DC design yields desirable operating characteristics. The software to implement BOP2-DC is freely available at www.trialdesign.org .