Bayesian sample size determination in basket trials borrowing information between subsets.

Basket trials are increasingly used for the simultaneous evaluation of a new treatment in various patient subgroups under one overarching protocol. We propose a Bayesian approach to sample size determination in basket trials that permit borrowing of information between commensurate subsets. Specifically, we consider a randomized basket trial design where patients are randomly assigned to the new treatment or control within each trial subset ("subtrial" for short). Closed-form sample size formulae are derived to ensure that each subtrial has a specified chance of correctly deciding whether the new treatment is superior to or not better than the control by some clinically relevant difference. Given prespecified levels of pairwise (in)commensurability, the subtrial sample sizes are solved simultaneously. The proposed Bayesian approach resembles the frequentist formulation of the problem in yielding comparable sample sizes for circumstances of no borrowing. When borrowing is enabled between commensurate subtrials, a considerably smaller trial sample size is required compared to the widely implemented approach of no borrowing. We illustrate the use of our sample size formulae with two examples based on real basket trials. A comprehensive simulation study further shows that the proposed methodology can maintain the true positive and false positive rates at desired levels.

A multi-arm multistage platform design that allows preplanned addition of arms while still controlling the family-wise error.

There is growing interest in platform trials that allow for adding of new treatment arms as the trial progresses as well as being able to stop treatments part way through the trial for either lack of benefit/futility or for superiority. In some situations, platform trials need to guarantee that error rates are controlled. This paper presents a multistage design, that allows additional arms to be added in a platform trial in a preplanned fashion, while still controlling the family-wise error rate, under the assumption of known number and timing of treatments to be added, and no time trends. A method is given to compute the sample size required to achieve a desired level of power and we show how the distribution of the sample size and the expected sample size can be found. We focus on power under the least favorable configuration which is the power of finding the treatment with a clinically relevant effect out of a set of treatments while the rest have an uninteresting treatment effect. A motivating trial is presented which focuses on two settings, with the first being a set number of stages per active treatment arm and the second being a set total number of stages, with treatments that are added later getting fewer stages. Compared to Bonferroni, the savings in the total maximum sample size are modest in a trial with three arms, <1% of the total sample size. However, the savings are more substantial in trials with more arms.

A benchmark for dose-finding studies with unknown ordering.

An important tool to evaluate the performance of a dose-finding design is the nonparametric optimal benchmark that provides an upper bound on the performance of a design under a given scenario. A fundamental assumption of the benchmark is that the investigator can arrange doses in a monotonically increasing toxicity order. While the benchmark can be still applied to combination studies in which not all dose combinations can be ordered, it does not account for the uncertainty in the ordering. In this article, we propose a generalization of the benchmark that accounts for this uncertainty and, as a result, provides a sharper upper bound on the performance. The benchmark assesses how probable the occurrence of each ordering is, given the complete information about each patient. The proposed approach can be applied to trials with an arbitrary number of endpoints with discrete or continuous distributions. We illustrate the utility of the benchmark using recently proposed dose-finding designs for Phase I combination trials with a binary toxicity endpoint and Phase I/II combination trials with binary toxicity and continuous efficacy.

A Bayesian multi-arm multi-stage clinical trial design incorporating information about treatment ordering.

Multi-Arm Multi-Stage (MAMS) designs can notably improve efficiency in later stages of drug development, but they can be suboptimal when an order in the effects of the arms can be assumed. In this work, we propose a Bayesian multi-arm multi-stage trial design that selects all promising treatments with high probability and can efficiently incorporate information about the order in the treatment effects as well as incorporate prior knowledge on the treatments. A distinguishing feature of the proposed design is that it allows taking into account the uncertainty of the treatment effect order assumption and does not assume any parametric arm-response model. The design can provide control of the family-wise error rate under specific values of the control mean and we illustrate its operating characteristics in a study of symptomatic asthma. Via simulations, we compare the novel Bayesian design with frequentist multi-arm multi-stage designs and a frequentist order restricted design that does not account for the order uncertainty and demonstrate the gains in the sample sizes the proposed design can provide. We also find that the proposed design is robust to violations of the assumptions on the order.

A comparison of Bayesian information borrowing methods in basket trials and a novel proposal of modified exchangeability-nonexchangeability method.

Recent innovation in trial design to improve study efficiency has led to the development of basket trials in which a single therapeutic treatment is tested on several patient populations, each of which forms a basket. In a common setting, patients across all baskets share a genetic marker and as such, an assumption can be made that all patients may have a homogeneous response to treatments. Bayesian information borrowing procedures utilize this assumption to draw on information regarding the response in one basket when estimating the response rate in others. This can improve power and precision of estimates particularly in the presence of small sample sizes, however, can come at a cost of biased estimates and an inflation of error rates, bringing into question validity of trial conclusions. We review and compare the performance of several Bayesian borrowing methods, namely: the Bayesian hierarchical model (BHM), calibrated Bayesian hierarchical model (CBHM), exchangeability-nonexchangeability (EXNEX) model and a Bayesian model averaging procedure. A generalization of the CBHM is made to account for unequal sample sizes across baskets. We also propose a modification of the EXNEX model that allows for better control of a type I error. The proposed method uses a data-driven approach to account for the homogeneity of the response data, measured through Hellinger distances. Through an extensive simulation study motivated by a real basket trial, for both equal and unequal sample sizes across baskets, we show that in the presence of a basket with a heterogeneous response, unlike the other methods discussed, this model can control type I error rates to a nominal level whilst yielding improved power.

Determining the minimum duration of treatment in tuberculosis: An order restricted non-inferiority trial design.

Tuberculosis (TB) is one of the biggest killers among infectious diseases worldwide. Together with the identification of drugs that can provide benefits to patients, the challenge in TB is also the optimisation of the duration of these treatments. While conventional duration of treatment in TB is 6 months, there is evidence that shorter durations might be as effective but could be associated with fewer side effects and may be associated with better adherence. Based on a recent proposal of an adaptive order-restricted superiority design that employs the ordering assumptions within various duration of the same drug, we propose a non-inferiority (typically used in TB trials) adaptive design that effectively uses the order assumption. Together with the general construction of the hypothesis testing and expression for type I and type II errors, we focus on how the novel design was proposed for a TB trial concept. We consider a number of practical aspects such as choice of the design parameters, randomisation ratios, and timings of the interim analyses, and how these were discussed with the clinical team.

Response-adaptive randomization for multiarm clinical trials using context-dependent information measures.

Theoretical-information approach applied to the clinical trial designs appeared to bring several advantages when tackling a problem of finding a balance between power and expected number of successes (ENS). In particular, it was shown that the built-in parameter of the weight function allows finding the desired trade-off between the statistical power and number of treated patients in the context of small population Phase II clinical trials. However, in real clinical trials, randomized designs are more preferable. The goal of this research is to introduce randomization to a deterministic entropy-based sequential trial procedure generalized to multiarm setting. Several methods of randomization applied to an entropy-based design are investigated in terms of statistical power and ENS. Namely, the four design types are considered: (a) deterministic procedures, (b) naive randomization using the inverse of entropy criteria as weights, (c) block randomization, and (d) randomized penalty parameter. The randomized entropy-based designs are compared to randomized Gittins index (GI) and fixed randomization (FR). After the comprehensive simulation study, the following conclusion on block randomization is made: for both entropy-based and GI-based block randomization designs the degree of randomization induced by forward-looking procedures is insufficient to achieve a decent statistical power. Therefore, we propose an adjustment for the forward-looking procedure that improves power with almost no cost in terms of ENS. In addition, the properties of randomization procedures based on randomly drawn penalty parameter are also thoroughly investigated.

An order restricted multi-arm multi-stage clinical trial design.

One family of designs that can noticeably improve efficiency in later stages of drug development are multi-arm multi-stage (MAMS) designs. They allow several arms to be studied concurrently and gain efficiency by dropping poorly performing treatment arms during the trial as well as by allowing to stop early for benefit. Conventional MAMS designs were developed for the setting, in which treatment arms are independent and hence can be inefficient when an order in the effects of the arms can be assumed (eg, when considering different treatment durations or different doses). In this work, we extend the MAMS framework to incorporate the order of treatment effects when no parametric dose-response or duration-response model is assumed. The design can identify all promising treatments with high probability. We show that the design provides strong control of the family-wise error rate and illustrate the design in a study of symptomatic asthma. Via simulations we show that the inclusion of the ordering information leads to better decision-making compared to a fixed sample and a MAMS design. Specifically, in the considered settings, reductions in sample size of around 15% were achieved in comparison to a conventional MAMS design.

Practical implementation of the partial ordering continual reassessment method in a Phase I combination-schedule dose-finding trial.

There is a growing medical interest in combining several agents and optimizing their dosing schedules in a single trial in order to optimize the treatment for patients. Evaluating at doses of several drugs and their scheduling in a single Phase I trial simultaneously possess a number of statistical challenges, and specialized methods to tackle these have been proposed in the literature. However, the uptake of these methods is slow and implementation examples of such advanced methods are still sparse to date. In this work, we share our experience of proposing a model-based partial ordering continual reassessment method (POCRM) design for three-dimensional dose-finding in an oncology trial. In the trial, doses of two agents and the dosing schedule of one of them can be escalated/de-escalated. We provide a step-by-step summary on how the POCRM design was implemented and communicated to the trial team. We proposed an approach to specify toxicity orderings and their a-priori probabilities, and developed a number of visualization tools to communicate the statistical properties of the design. The design evaluation included both a comprehensive simulation study and considerations of the individual trial behavior. The study is now enrolling patients. We hope that sharing our experience of the successful implementation of an advanced design in practice that went through evaluations of several health authorities will facilitate a better uptake of more efficient methods in practice.

Practical recommendations for implementing a Bayesian adaptive phase I design during a pandemic.

BACKGROUND: Modern designs for dose-finding studies (e.g., model-based designs such as continual reassessment method) have been shown to substantially improve the ability to determine a suitable dose for efficacy testing when compared to traditional designs such as the 3 + 3 design. However, implementing such designs requires time and specialist knowledge. METHODS: We present a practical approach to developing a model-based design to help support uptake of these methods; in particular, we lay out how to derive the necessary parameters and who should input, and when, to these decisions. Designing a model-based, dose-finding trial is demonstrated using a treatment within the AGILE platform trial, a phase I/II adaptive design for novel COVID-19 treatments. RESULTS: We present discussion of the practical delivery of AGILE, covering what information was found to support principled decision making by the Safety Review Committee, and what could be contained within a statistical analysis plan. We also discuss additional challenges we encountered in the study and discuss more generally what (unplanned) adaptations may be acceptable (or not) in studies using model-based designs. CONCLUSIONS: This example demonstrates both how to design and deliver an adaptive dose-finding trial in order to support uptake of these methods.

What is the expected benefit of patient-centric clinical development in oncology?

The identification and quantification of predictive biomarkers characterize personalized medicine approaches and patient-centric clinical development. In practice, the sponsor needs evaluating whether biomarker-informed clinical development strategies are more likely to benefit current and future patients. To this end, a simple metric is proposed and assessed here quantifying the expected clinical benefit (ECB) of clinical development programmes. Using simulation scenarios and endpoints relevant to oncology, the ECB of a simple biomarker-informed strategy is shown to be specific and sensitive. Also, the ECB difference is shown to increase in the biomarker-driven incremental efficacy and with the population prevalence of biomarker-positive study participants.

A dose-finding design for dual-agent trials with patient-specific doses for one agent with application to an opiate detoxification trial.

There is a growing interest in early phase dose-finding clinical trials studying combinations of several treatments. While the majority of dose finding designs for such setting were proposed for oncology trials, the corresponding designs are also essential in other therapeutic areas. Furthermore, there is increased recognition of recommending the patient-specific doses/combinations, rather than a single target one that would be recommended to all patients in later phases regardless of their characteristics. In this paper, we propose a dose-finding design for a dual-agent combination trial motivated by an opiate detoxification trial. The distinguishing feature of the trial is that the (continuous) dose of one compound is defined externally by the clinicians and is individual for every patient. The objective of the trial is to define the dosing function that for each patient would recommend the optimal dosage of the second compound. Via a simulation study, we have found that the proposed design results in high accuracy of individual dose recommendation and is robust to the model misspecification and assumptions on the distribution of externally defined doses.

A benchmark for dose finding studies with continuous outcomes.

An important tool to evaluate the performance of any design is an optimal benchmark proposed by O'Quigley and others (2002. Non-parametric optimal design in dose finding studies. Biostatistics3, 51-56) that provides an upper bound on the performance of a design under a given scenario. The original benchmark can only be applied to dose finding studies with a binary endpoint. However, there is a growing interest in dose finding studies involving continuous outcomes, but no benchmark for such studies has been developed. We show that the original benchmark and its extension by Cheung (2014. Simple benchmark for complex dose finding studies. Biometrics70, 389-397), when looked at from a different perspective, can be generalized to various settings with several discrete and continuous outcomes. We illustrate and compare the benchmark's performance in the setting of a dose finding Phase I clinical trial with a continuous toxicity endpoint and a Phase I/II trial with binary toxicity and continuous efficacy endpoints. We show that the proposed benchmark provides an accurate upper bound in these contexts and serves as a powerful tool for evaluating designs.

Optimal dose and safety of molnupiravir in patients with early SARS-CoV-2: a Phase I, open-label, dose-escalating, randomized controlled study.

OBJECTIVES: AGILE is a Phase Ib/IIa platform for rapidly evaluating COVID-19 treatments. In this trial (NCT04746183) we evaluated the safety and optimal dose of molnupiravir in participants with early symptomatic infection. METHODS: We undertook a dose-escalating, open-label, randomized-controlled (standard-of-care) Bayesian adaptive Phase I trial at the Royal Liverpool and Broadgreen Clinical Research Facility. Participants (adult outpatients with PCR-confirmed SARS-CoV-2 infection within 5 days of symptom onset) were randomized 2:1 in groups of 6 participants to 300, 600 and 800 mg doses of molnupiravir orally, twice daily for 5 days or control. A dose was judged unsafe if the probability of 30% or greater dose-limiting toxicity (the primary outcome) over controls was 25% or greater. Secondary outcomes included safety, clinical progression, pharmacokinetics and virological responses. RESULTS: Of 103 participants screened, 18 participants were enrolled between 17 July and 30 October 2020. Molnupiravir was well tolerated at 300, 600 and 800 mg doses with no serious or severe adverse events. Overall, 4 of 4 (100%), 4 of 4 (100%) and 1 of 4 (25%) of the participants receiving 300, 600 and 800 mg molnupiravir, respectively, and 5 of 6 (83%) controls, had at least one adverse event, all of which were mild (≤grade 2). The probability of ≥30% excess toxicity over controls at 800 mg was estimated at 0.9%. CONCLUSIONS: Molnupiravir was safe and well tolerated; a dose of 800 mg twice daily for 5 days was recommended for Phase II evaluation.

Response adaptive designs for Phase II trials with binary endpoint based on context-dependent information measures.

In many rare disease Phase II clinical trials, two objectives are of interest to an investigator: maximising the statistical power and maximising the number of patients responding to the treatment. These two objectives are competing, therefore, clinical trial designs offering a balance between them are needed. Recently, it was argued that response-adaptive designs such as families of multi-arm bandit (MAB) methods could provide the means for achieving this balance. Furthermore, response-adaptive designs based on a concept of context-dependent (weighted) information criteria were recently proposed with a focus on Shannon's differential entropy. The information-theoretic designs based on the weighted Renyi, Tsallis and Fisher informations are also proposed. Due to built-in parameters of these novel designs, the balance between the statistical power and the number of patients that respond to the treatment can be tuned explicitly. The asymptotic properties of these measures are studied in order to construct intuitive criteria for arm selection. A comprehensive simulation study shows that using the exact criteria over asymptotic ones or using information measures with more parameters, namely Renyi and Tsallis entropies, brings no sufficient gain in terms of the power or proportion of patients allocated to superior treatments. The proposed designs based on information-theoretical criteria are compared to several alternative approaches. For example, via tuning of the built-in parameter, one can find designs with power comparable to the fixed equal randomisation's but a greater number of patients responded in the trials.

Adding flexibility to clinical trial designs: an example-based guide to the practical use of adaptive designs.

Adaptive designs for clinical trials permit alterations to a study in response to accumulating data in order to make trials more flexible, ethical, and efficient. These benefits are achieved while preserving the integrity and validity of the trial, through the pre-specification and proper adjustment for the possible alterations during the course of the trial. Despite much research in the statistical literature highlighting the potential advantages of adaptive designs over traditional fixed designs, the uptake of such methods in clinical research has been slow. One major reason for this is that different adaptations to trial designs, as well as their advantages and limitations, remain unfamiliar to large parts of the clinical community. The aim of this paper is to clarify where adaptive designs can be used to address specific questions of scientific interest; we introduce the main features of adaptive designs and commonly used terminology, highlighting their utility and pitfalls, and illustrate their use through case studies of adaptive trials ranging from early-phase dose escalation to confirmatory phase III studies.

Improving safety of the continual reassessment method via a modified allocation rule.

This article proposes a novel criterion for the allocation of patients in phase I dose-escalation clinical trials, aiming to find the maximum tolerated dose (MTD). Conventionally, using a model-based approach, the next patient is allocated to the dose with the toxicity estimate closest (in terms of the absolute or squared distance) to the maximum acceptable toxicity. This approach, however, ignores the uncertainty in point estimates and ethical concerns of assigning a lot of patients to overly toxic doses. In fact, balancing the trade-off between how accurately the MTD can be estimated and how many patients would experience adverse events is one of the primary challenges in phase I studies. Motivated by recent discussions in the theory of estimation in restricted parameter spaces, we propose a criterion that allows to balance these explicitly. The criterion requires a specification of one additional parameter only that has a simple and intuitive interpretation. We incorporate the proposed criterion into the one-parameter Bayesian continual reassessment method and show, using simulations, that it can result in similar accuracy on average as the original design, but with fewer toxic responses on average. A comparison with other model-based dose-escalation designs, such as escalation with overdose control and its modifications, demonstrates that the proposed design can result in either the same mean accuracy as alternatives but fewer toxic responses or in a higher mean accuracy but the same number of toxic responses. Therefore, the proposed design can provide a better trade-off between the accuracy and the number of patients experiencing adverse events, making the design a more ethical alternative over some of the existing methods for phase I trials.

A comparison of phase I dose-finding designs in clinical trials with monotonicity assumption violation.

BACKGROUND/AIMS: In oncology, new combined treatments make it difficult to order dose levels according to monotonically increasing toxicity. New flexible dose-finding designs that take into account uncertainty in dose levels ordering were compared with classical designs through simulations in the setting of the monotonicity assumption violation. We give recommendations for the choice of dose-finding design. METHODS: Motivated by a clinical trial for patients with high-risk neuroblastoma, we considered designs that require a monotonicity assumption, the Bayesian Continual Reassessment Method, the modified Toxicity Probability Interval, the Bayesian Optimal Interval design, and designs that relax monotonicity assumption, the Bayesian Partial Ordering Continual Reassessment Method and the No Monotonicity Assumption design. We considered 15 scenarios including monotonic and non-monotonic dose-toxicity relationships among six dose levels. RESULTS: The No Monotonicity Assumption and Partial Ordering Continual Reassessment Method designs were robust to the violation of the monotonicity assumption. Under non-monotonic scenarios, the No Monotonicity Assumption design selected the correct dose level more often than alternative methods on average. Under the majority of monotonic scenarios, the Partial Ordering Continual Reassessment Method selected the correct dose level more often than the No Monotonicity Assumption design. Other designs were impacted by the violation of the monotonicity assumption with a proportion of correct selections below 20% in most scenarios. Under monotonic scenarios, the highest proportions of correct selections were achieved using the Continual Reassessment Method and the Bayesian Optimal Interval design (between 52.8% and 73.1%). The costs of relaxing the monotonicity assumption by the No Monotonicity Assumption design and Partial Ordering Continual Reassessment Method were decreases in the proportions of correct selections under monotonic scenarios ranging from 5.3% to 20.7% and from 1.4% to 16.1%, respectively, compared with the best performing design and were higher proportions of patients allocated to toxic dose levels during the trial. CONCLUSIONS: Innovative oncology treatments may no longer follow monotonic dose levels ordering which makes standard phase I methods fail. In such a setting, appropriate designs, as the No Monotonicity Assumption or Partial Ordering Continual Reassessment Method designs, should be used to safely determine recommended for phase II dose.

Using a dose-finding benchmark to quantify the loss incurred by dichotomization in Phase II dose-ranging studies.

While there is recognition that more informative clinical endpoints can support better decision-making in clinical trials, it remains a common practice to categorize endpoints originally measured on a continuous scale. The primary motivation for this categorization (and most commonly dichotomization) is the simplicity of the analysis. There is, however, a long argument that this simplicity can come at a high cost. Specifically, larger sample sizes are needed to achieve the same level of accuracy when using a dichotomized outcome instead of the original continuous endpoint. The degree of "loss of information" has been studied in the contexts of parallel-group designs and two-stage Phase II trials. Limited attention, however, has been given to the quantification of the associated losses in dose-ranging trials. In this work, we propose an approach to estimate the associated losses in Phase II dose-ranging trials that is free of the actual dose-ranging design used and depends on the clinical setting only. The approach uses the notion of a nonparametric optimal benchmark for dose-finding trials, an evaluation tool that facilitates the assessment of a dose-finding design by providing an upper bound on its performance under a given scenario in terms of the probability of the target dose selection. After demonstrating how the benchmark can be applied to Phase II dose-ranging trials, we use it to quantify the dichotomization losses. Using parameters from real clinical trials in various therapeutic areas, it is found that the ratio of sample sizes needed to obtain the same precision using continuous and binary (dichotomized) endpoints varies between 70% and 75% under the majority of scenarios but can drop to 50% in some cases.

Randomized dose-escalation designs for drug combination cancer trials with immunotherapy.

This work considers Phase I cancer dual-agent dose-escalation clinical trials in which one of the compounds is an immunotherapy. The distinguishing feature of trials considered is that the dose of one agent, referred to as a standard of care, is fixed and another agent is dose-escalated. Conventionally, the goal of a Phase I trial is to find the maximum tolerated combination (MTC). However, in trials involving an immunotherapy, it is also essential to test whether a difference in toxicities associated with the MTC and the standard of care alone is present. This information can give useful insights about the interaction of the compounds and can provide a quantification of the additional toxicity burden and therapeutic index. We show that both, testing for difference between toxicity risks and selecting MTC can be achieved using a Bayesian model-based dose-escalation design with two modifications. Firstly, the standard of care administrated alone is included in the trial as a control arm and each patient is randomized between the control arm and one of the combinations selected by a model-based design. Secondly, a flexible model is used to allow for toxicities at the MTC and the control arm to be modeled directly. We compare the performance of two-parameter and four-parameter logistic models with and without randomization to a current standard of such trials: a one-parameter model. It is found that at the cost of a small reduction in the proportion of correct selections in some scenarios, randomization provides a significant improvement in the ability to test for a difference in the toxicity risks. It also allows a better fitting of the combination-toxicity curve that leads to more reliable recommendations of the combination(s) to be studied in subsequent phases.