TITE‐BOIN‐ET: Time‐to‐event Bayesian optimal interval design to accelerate dose‐finding based on both efficacy and toxicity outcomes

One of the primary purposes of an oncology dose‐finding trial is to identify an optimal dose (OD) that is both tolerable and has an indication of therapeutic benefit for subjects in subsequent clinical trials. In addition, it is quite important to accelerate early stage trials to shorten the entire period of drug development. However, it is often challenging to make adaptive decisions of dose escalation and de‐escalation in a timely manner because of the fast accrual rate, the difference of outcome evaluation periods for efficacy and toxicity and the late‐onset outcomes. To solve these issues, we propose the time‐to‐event Bayesian optimal interval design to accelerate dose‐finding based on cumulative and pending data of both efficacy and toxicity. The new design, named “TITE‐BOIN‐ET” design, is nonparametric and a model‐assisted design. Thus, it is robust, much simpler, and easier to implement in actual oncology dose‐finding trials compared with the model‐based approaches. These characteristics are quite useful from a practical point of view. A simulation study shows that the TITE‐BOIN‐ET design has advantages compared with the model‐based approaches in both the percentage of correct OD selection and the average number of patients allocated to the ODs across a variety of realistic settings. In addition, the TITE‐BOIN‐ET design significantly shortens the trial duration compared with the designs without sequential enrollment and therefore has the potential to accelerate early stage dose‐finding trials.     

A Three-Stage Bayesian Adaptive Phase I/II Design and Simulation Studies

Instead of using traditional separate phase I and II trials, in this article, we propose using a parallel three-stage phase I/II design, incorporating a dose expansion approach to flexibly evaluate the safety and efficacy of dose levels, and to select the optimal dose. In the proposed design, both the toxicity and efficacy responses are binary endpoints. A 3+3-based procedure is used for initial period of dose escalation at stage 1; at this level, the dose can be expanded to stage 2 for exploratory efficacy studies of phase IIa, while simultaneously, the safety testing can advance to a higher dose level. A beta-binomial model is used to model the efficacy responses. There are two placebo-controlled randomization interim monitoring analyses at stage 2 to select the promising doses to be recommended to stage 3 for further efficacy studies of phase IIb. An adaptive randomization approach is used to assign more patients to doses with higher efficacy levels at stage 3. We examine the properties of the proposed design through extensive simulation studies by using R programming language, and also compare the new design with the conventional design and a competing adaptive Bayesian design. The simulation results show that our design can efficiently assign more patients to doses with higher efficacy levels and is superior to the two competing designs in terms of total sample size reduction.     

Optimizing trial design in pharmacogenetics research: comparing a fixed parallel group,group sequential,and adaptive selection design on sample size requirements

Two‐stage clinical trial designs may be efficient in pharmacogenetics research when there is some but inconclusive evidence of effect modification by a genomic marker. Two‐stage designs allow to stop early for efficacy or futility and can offer the additional opportunity to enrich the study population to a specific patient subgroup after an interim analysis. This study compared sample size requirements for fixed parallel group, group sequential, and adaptive selection designs with equal overall power and control of the family‐wise type I error rate. The designs were evaluated across scenarios that defined the effect sizes in the marker positive and marker negative subgroups and the prevalence of marker positive patients in the overall study population. Effect sizes were chosen to reflect realistic planning scenarios, where at least some effect is present in the marker negative subgroup. In addition, scenarios were considered in which the assumed ‘true’ subgroup effects (i.e., the postulated effects) differed from those hypothesized at the planning stage. As expected, both two‐stage designs generally required fewer patients than a fixed parallel group design, and the advantage increased as the difference between subgroups increased. The adaptive selection design added little further reduction in sample size, as compared with the group sequential design, when the postulated effect sizes were equal to those hypothesized at the planning stage. However, when the postulated effects deviated strongly in favor of enrichment, the comparative advantage of the adaptive selection design increased, which precisely reflects the adaptive nature of the design. Copyright © 2013 John Wiley & Sons, Ltd.     

Model-Robust Design of Conjoint Choice Experiments

Within the context of choice experimental designs, most authors have proposed designs for the multinomial logit model under the assumption that only the main effects matter. Very little attention has been paid to designs for attribute interaction models. In this article, three types of Bayesian D-optimal designs for the multinomial logit model are studied: main-effects designs, interaction-effects designs, and composite designs. Simulation studies are used to show that in situations where a researcher is not sure whether or not attribute interaction effects are present, it is best to take into account interactions in the design stage. In particular, it is shown that a composite design constructed by including an interaction-effects model and a main-effects model in the design criterion is most robust against misspecification of the underlying model when it comes to making precise predictions.     

Generalized phase I-II designs to increase long term therapeutic success rate

Designs for early phase dose finding clinical trials typically are either phase I based on toxicity, or phase I-II based on toxicity and efficacy. These designs rely on the implicit assumption that the dose of an experimental agent chosen using these short-term outcomes will maximize the agent's long-term therapeutic success rate. In many clinical settings, this assumption is not true. A dose selected in an early phase oncology trial may give suboptimal progression-free survival or overall survival time, often due to a high rate of relapse following response. To address this problem, a new family of Bayesian generalized phase I-II designs is proposed. First, a conventional phase I-II design based on short-term outcomes is used to identify a set of candidate doses, rather than selecting one dose. Additional patients then are randomized among the candidates, patients are followed for a predefined longer time period, and a final dose is selected to maximize the long-term therapeutic success rate, defined in terms of duration of response. Dose-specific sample sizes in the randomization are determined adaptively to obtain a desired level of selection reliability. The design was motivated by a phase I-II trial to find an optimal dose of natural killer cells as targeted immunotherapy for recurrent or treatment-resistant B-cell hematologic malignancies. A simulation study shows that, under a range of scenarios in the context of this trial, the proposed design has much better performance than two conventional phase I-II designs.     

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.     

Measures of non orthogonality in block designs

Orthogonality is an important concept in block design. Necessary and sufficient condition for a connected block design to be orthogonal is well known. However, when a design is not orthogonal, it is not clear how much it deviates from orthogonality. In this paper, an attempt has been made to first define the measures of or indices to non orthogonality in block design and then to characterize designs possessing minimum non orthogonality indices. It is shown that a Balanced Incomplete Block Design (BIBD) and a Balanced Block Design (BBD), if exist, possess this property.     

Some sufficient conditions for the type 1 optimality of block designs

In this paper, we investigate the problem of determining block designs which are optimal under type 1 optimality criteria within various classes of designs having υ treatments arranged in b blocks of size k. The solutions to two optimization problems are given which are related to a general result obtained by Cheng (1978) and which are useful in this investigation. As one application of the solutions obtained, the definition of a regular graph design given in Mitchell and John (1977) is extended to that of a semi-regular graph design and some sufficient conditions are derived for the existence of a semi-regular graph design which is optimal under a given type 1 criterion. A result is also given which shows how the sufficient conditions derived can be used to establish the optimality under a specific type 1 criterion of some particular types of semi- regular graph designs having both equal and unequal numbers of replicates. Finally,some sufficient conditions are obtained for the dual of an A- or D-optimal design to be A- or D-optimal within an appropriate class of dual designs.     

Performance of phase-I dose finding designs with and without a run-in intra-patient dose escalation stage

Dose-finding designs for phase-I trials aim to determine the recommended phase-II dose (RP2D) for further phase-II drug development. If the trial includes patients for whom several lines of standard therapy failed or if the toxicity of the investigated agent does not necessarily increase with dose, optimal dose-finding designs should limit the frequency of treatment with suboptimal doses. We propose a two-stage design strategy with a run-in intra-patient dose escalation part followed by a more traditional dose-finding design. We conduct simulation studies to compare the 3 + 3 design, the Bayesian Optimal Interval Design (BOIN) and the Continual Reassessment Method (CRM) with and without intra-patient dose escalation. The endpoints are accuracy, sample size, safety, and therapeutic efficiency. For scenarios where the correct RP2D is the highest dose, inclusion of an intra-patient dose escalation stage generally increases accuracy and therapeutic efficiency. However, for scenarios where the correct RP2D is below the highest dose, intra-patient dose escalation designs lead to increased risk of overdosing and an overestimation of RP2D. The magnitude of the change in operating characteristics after including an intra-patient stage is largest for the 3 + 3 design, decreases for the BOIN and is smallest for the CRM.     

TSNP: A two-stage nonparametric phase I/II clinical trial design for immunotherapy

We develop a transparent and efficient two-stage nonparametric (TSNP) phase I/II clinical trial design to identify the optimal biological dose (OBD) of immunotherapy. We propose a nonparametric approach to derive the closed-form estimates of the joint toxicity–efficacy response probabilities under the monotonic increasing constraint for the toxicity outcomes. These estimates are then used to measure the immunotherapy's toxicity–efficacy profiles at each dose and guide the dose finding. The first stage of the design aims to explore the toxicity profile. The second stage aims to find the OBD, which can achieve the optimal therapeutic effect by considering both the toxicity and efficacy outcomes through a utility function. The closed-form estimates and concise dose-finding algorithm make the TSNP design appealing in practice. The simulation results show that the TSNP design yields superior operating characteristics than the existing Bayesian parametric designs. User-friendly computational software is freely available to facilitate the application of the proposed design to real trials. We provide comprehensive illustrations and examples about implementing the proposed design with associated software.     

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.     

Curtailed two-stage designs with two dependent binary endpoints

When phase I clinical trials were found to be unable to precisely estimate the frequency of toxicity, Brayan and Day proposed incorporating toxicity considerations into two-stage designs in phase II clinical trials. Conaway and Petroni further pointed out that it is important to evaluate the clinical activity and safety simultaneously in studying cancer treatments with more toxic chemotherapies in a phase II clinical trial. Therefore, they developed multi-stage designs with two dependent binary endpoints. However, the usual sample sizes in phase II trials make these designs difficult to control the type I error rate at a desired level over the entire null region and still have sufficient power against reasonable alternatives. Therefore, the curtailed sampling procedure summarized by Phatak and Bhatt will be applied to the two-stage designs with two dependent binary endpoints in this paper to reduce sample sizes and speed up the development process for drugs.     

Design and inference for 3‐stage bioequivalence testing with serial sampling data

A bioequivalence test is to compare bioavailability parameters, such as the maximum observed concentration (C_max) or the area under the concentration‐time curve, for a test drug and a reference drug. During the planning of a bioequivalence test, it requires an assumption about the variance of C_max or area under the concentration‐time curve for the estimation of sample size. Since the variance is unknown, current 2‐stage designs use variance estimated from stage 1 data to determine the sample size for stage 2. However, the estimation of variance with the stage 1 data is unstable and may result in too large or too small sample size for stage 2. This problem is magnified in bioequivalence tests with a serial sampling schedule, by which only one sample is collected from each individual and thus the correct assumption of variance becomes even more difficult. To solve this problem, we propose 3‐stage designs. Our designs increase sample sizes over stages gradually, so that extremely large sample sizes will not happen. With one more stage of data, the power is increased. Moreover, the variance estimated using data from both stages 1 and 2 is more stable than that using data from stage 1 only in a 2‐stage design. These features of the proposed designs are demonstrated by simulations. Testing significance levels are adjusted to control the overall type I errors at the same level for all the multistage designs.     

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.     

The Construction of Efficient Two-replicate Row–Column Designs for Use in Field Trials

Two-replicate row–column designs are often used for field trials in multisite tree or plant breeding programmes. With only two replicates for each trial, it is important to use designs with optimal or near optimal efficiency factors. This paper presents an algorithm for generating such designs. The method extends the contraction approach of Bailey and Patterson to any set of parameters and uses the factorial design construction algorithm of Williams and John to generate designs. Our experience with the algorithm is that it produces designs that are at least as good as, and often much better and more quickly generated than, those obtained by other recent computer algorithms.     

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

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

Bayesian optimization design for dose-finding based on toxicity and efficacy outcomes in phase I/II clinical trials

In phase I trials, the main goal is to identify a maximum tolerated dose under an assumption of monotonicity in dose–response relationships. On the other hand, such monotonicity is no longer applied to biologic agents because a different mode of action from that of cytotoxic agents potentially draws unimodal or flat dose–efficacy curves. Therefore, biologic agents require an optimal dose that provides a sufficient efficacy rate under an acceptable toxicity rate instead of a maximum tolerated dose. Many trials incorporate both toxicity and efficacy data, and drugs with a variety of modes of actions are increasingly being developed; thus, optimal dose estimation designs have been receiving increased attention. Although numerous authors have introduced parametric model-based designs, it is not always appropriate to apply strong assumptions in dose–response relationships. We propose a new design based on a Bayesian optimization framework for identifying optimal doses for biologic agents in phase I/II trials. Our proposed design models dose–response relationships via nonparametric models utilizing a Gaussian process prior, and the uncertainty of estimates is considered in the dose selection process. We compared the operating characteristics of our proposed design against those of three other designs through simulation studies. These include an expansion of Bayesian optimal interval design, the parametric model-based EffTox design, and the isotonic design. In simulations, our proposed design performed well and provided results that were more stable than those from the other designs, in terms of the accuracy of optimal dose estimations and the percentage of correct recommendations.     

AIDE: Adaptive intrapatient dose escalation designs to accelerate Phase I clinical trials

Designing Phase I clinical trials is challenging when accrual is slow or sample size is limited. The corresponding key question is: how to efficiently and reliably identify the maximum tolerated dose (MTD) using a sample size as small as possible? We propose model-assisted and model-based designs with adaptive intrapatient dose escalation (AIDE) to address this challenge. AIDE is adaptive in that the decision of conducting intrapatient dose escalation depends on both the patient's individual safety data, as well as other enrolled patient's safety data. When both data indicate reasonable safety, a patient may perform intrapatient dose escalation, generating toxicity data at more than one dose. This strategy not only provides patients the opportunity to receive higher potentially more effective doses, but also enables efficient statistical learning of the dose-toxicity profile of the treatment, which dramatically reduces the required sample size. Simulation studies show that the proposed designs are safe, robust, and efficient to identify the MTD with a sample size that is substantially smaller than conventional interpatient dose escalation designs. Practical considerations are provided and R code for implementing AIDE is available upon request.     

Cumulative cohort design for dose-finding

We introduce a new design for dose-finding in the context of toxicity studies for which it is assumed that toxicity increases with dose. The goal is to identify the maximum tolerated dose, which is taken to be the dose associated with a prespecified “target” toxicity rate. The decision to decrease, increase or repeat a dose for the next subject depends on how far an estimated toxicity rate at the current dose is from the target. The size of the window within which the current dose will be repeated is obtained based on the theory of Markov chains as applied to group up-and-down designs. But whereas the treatment allocation rule in Markovian group up-and-down designs is only based on information from the current cohort of subjects, the treatment allocation rule for the proposed design is based on the cumulative information at the current dose. We then consider an extension of this new design for clinical trials in which the subject's outcome is not known immediately. The new design is compared to the continual reassessment method.     

An adaptive seamless phase II/III design for oncology trials with subpopulation selection using correlated survival endpoints

Although the statistical methods enabling efficient adaptive seamless designs are increasingly well established, it is important to continue to use the endpoints and specifications that best suit the therapy area and stage of development concerned when conducting such a trial. Approaches exist that allow adaptive designs to continue seamlessly either in a subpopulation of patients or in the whole population on the basis of data obtained from the first stage of a phase II/III design: our proposed design adds extra flexibility by also allowing the trial to continue in all patients but with both the subgroup and the full population as co-primary populations. Further, methodology is presented which controls the Type-I error rate at less than 2.5% when the phase II and III endpoints are different but correlated time-to-event endpoints. The operating characteristics of the design are described along with a discussion of the practical aspects in an oncology setting.