Sequential designs for ordinal phase I clinical trials

Sequential designs for phase I clinical trials which incorporate maximum likelihood estimates (MLE) as data accrue are inherently problematic because of limited data for estimation early on. We address this problem for small phase I clinical trials with ordinal responses. In particular, we explore the problem of the nonexistence of the MLE of the logistic parameters under a proportional odds model with one predictor. We incorporate the probability of an undetermined MLE as a restriction, as well as ethical considerations, into a proposed sequential optimal approach, which consists of a start‐up design, a follow‐on design and a sequential dose‐finding design. Comparisons with nonparametric sequential designs are also performed based on simulation studies with parameters drawn from a real data set.     

Sequential designs for phase I clinical trials with late-onset toxicities

Traditional designs for phase I clinical trials require each patient (or small group of patients) to be completely followed before the next patient or group is assigned. In situations such as when evaluating late-onset effects of radiation or toxicities from chemopreventive agents, this may result in trials of impractically long duration. We propose a new method, called the time-to-event continual reassessment method (TITE-CRM), that allows patients to be entered in a staggered fashion. It is an extension of the continual reassessment method (CRM; O'Quigley, Pepe, and Fisher, 1990, Biometrics 46, 33-48). We also note that this time-to-toxicity approach can be applied to extend other designs for studies of short-term toxicities. We prove that the recommended dose given by the TITE-CRM converges to the correct level under certain conditions. A simulation study shows our method's accuracy and safety are comparable with CRM's while the former takes a much shorter trial duration: a trial that would take up to 12 years to complete by the CRM could be reduced to 2-4 years by our method.     

Statistical properties of the traditional algorithm-based designs for phase I cancer clinical trials

Although there are several new designs for phase I cancer clinical trials including the continual reassessment method and accelerated titration design, the traditional algorithm-based designs, like the '3 + 3' design, are still widely used because of their practical simplicity. In this paper, we study some key statistical properties of the traditional algorithm-based designs in a general framework and derive the exact formulae for the corresponding statistical quantities. These quantities are important for the investigator to gain insights regarding the design of the trial, and are (i) the probability of a dose being chosen as the maximum tolerated dose (MTD); (ii) the expected number of patients treated at each dose level; (iii) target toxicity level (i.e. the expected dose-limiting toxicity (DLT) incidences at the MTD); (iv) expected DLT incidences at each dose level and (v) expected overall DLT incidences in the trial. Real examples of clinical trials are given, and a computer program to do the calculation can be found at the authors' website approximately linyo" locator-type="url">http://www2.umdnj.edu/ approximately linyo.     

Bayesian optimal designs for Phase I clinical trials

A broad approach to the design of Phase I clinical trials for the efficient estimation of the maximum tolerated dose is presented. The method is rooted in formal optimal design theory and involves the construction of constrained Bayesian c- and D-optimal designs. The imposed constraint incorporates the optimal design points and their weights and ensures that the probability that an administered dose exceeds the maximum acceptable dose is low. Results relating to these constrained designs for log doses on the real line are described and the associated equivalence theorem is given. The ideas are extended to more practical situations, specifically to those involving discrete doses. In particular, a Bayesian sequential optimal design scheme comprising a pilot study on a small number of patients followed by the allocation of patients to doses one at a time is developed and its properties explored by simulation.     

Adaptive two-stage designs for single-arm phase IIA cancer clinical trials

The main purpose of a phase IIA trial of a new anticancer therapy is to determine whether the therapy has sufficient promise against a specific type of tumor to warrant its further development. The therapy will be rejected for further investigation if the true response rate is less than some uninteresting level and the test of hypothesis is powered at a specific target response rate. Two-stage designs are commonly used for this situation. However, in many situations investigators often express concern about uncertainty in targeting the alternative hypothesis to study power at the planning stage. In this article, motivated by a real example, we propose a strategy for adaptive two-stage designs that will use the information at the first stage of the study to either reject the therapy or continue testing with either an optimistic or a skeptic target response rate, while the type I error rate is controlled. We also introduce new optimal criteria to reduce the expected total sample size.     

Decision theoretic designs for phase II clinical trials with multiple outcomes

In many phase II clinical trials, it is essential to assess both efficacy and safety. Although several phase II designs that accommodate multiple outcomes have been proposed recently, none are derived using decision theory. This paper describes a Bayesian decision theoretic strategy for constructing phase II designs based on both efficacy and adverse events. The gain function includes utilities assigned to patient outcomes, a reward for declaring the new treatment promising, and costs associated with the conduct of the phase II trial and future phase III testing. A method for eliciting gain function parameters from medical collaborators and for evaluating the design's frequentist operating characteristics is described. The strategy is illustrated by application to a clinical trial of peripheral blood stem cell transplantation for multiple myeloma.     

Decision-theoretic designs for phase II clinical trials allowing for competing studies

This article describes an approach to optimal design of phase II clinical trials using Bayesian decision theory. The method proposed extends that suggested by Stallard (1998, Biometrics 54, 279-294) in which designs were obtained to maximize a gain function including the cost of drug development and the benefit from a successful therapy. Here, the approach is extended by the consideration of other potential therapies, the development of which is competing for the same limited resources. The resulting optimal designs are shown to have frequentist properties much more similar to those traditionally used in phase II trials.     

Design and analysis of phase I clinical trials

The Phase I clinical trial is a study intended to estimate the so-called maximum tolerable dose (MTD) of a new drug. Although there exists more or less a standard type of design for such trials, its development has been largely ad hoc. As usually implemented, the trial design has no intrinsic property that provides a generally satisfactory basis for estimation of the MTD. In this paper, the standard design and several simple alternatives are compared with regard to the conservativeness of the design and with regard to point and interval estimation of an MTD (33rd percentile) with small sample sizes. Using a Markov chain representation, we found several designs to be nearly as conservative as the standard design in terms of the proportion of patients entered at higher dose levels. In Monte Carlo simulations, two two-stage designs are found to provide reduced bias in maximum likelihood estimation of the MTD in less than ideal dose-response settings. Of the three methods considered for determining confidence intervals--the delta method, a method based on Fieller's theorem, and a likelihood ratio method--none was able to provide both usefully narrow intervals and coverage probabilities close to nominal.     

A curve-free method for phase I clinical trials

Consider the problem of finding the dose that is as high as possible subject to having a controlled rate of toxicity. The problem is commonplace in oncology Phase I clinical trials. Such a dose is often called the maximum tolerated dose (MTD) since it represents a necessary trade-off between efficacy and toxicity. The continual reassessment method (CRM) is an improvement over traditional up-and-down schemes for estimating the MTD. It is based on a Bayesian approach and on the assumption that the dose-toxicity relationship follows a specific response curve, e.g., the logistic or power curve. The purpose of this paper is to illustrate how the assumption of a specific curve used in the CRM is not necessary and can actually hinder the efficient use of prior inputs. An alternative curve-free method in which the probabilities of toxicity are modeled directly as an unknown multidimensional parameter is presented. To that purpose, a product-of-beta prior (PBP) is introduced and shown to bring about logical improvements. Practical improvements are illustrated by simulation results.     

Restricted randomization designs in clinical trials.

Though therapeutic clinical trials are often categorized as using either "randomization" or "historical controls" as a basis for treatment evaluation, pure random assignment of treatments is rarely employed. Instead various restricted randomization designs are used. The restrictions include the balancing of treatment assignments over time and the stratification of the assignment with regard to covariates that may affect response. Restricted randomization designs for clinical trials differ from those of other experimental areas because patients arrive sequentially and a balanced design cannot be ensured. The major restricted randomization designs and arguments concerning the proper role of stratification are reviewed here. The effect of randomization restrictions on the validity of significance tests is discussed.     

Manufacturing mesenchymal stromal cells for phase I clinical trials

Mesenchymal stromal cells (MSCs) are multipotent progenitor cells capable of differentiating into adipocytes, osteoblasts and chondroblasts as well as secreting a vast array of soluble mediators. This potentially makes MSCs important mediators of a variety of therapeutic applications. They are actively under evaluation for immunomodulatory purposes such as graft-versus-host disease and Crohn’s disease as well as regenerative applications such as stroke and congestive heart failure. We report our method of generating clinical-grade MSCs together with suggestions gathered from manufacturing experience in our Good Manufacturing Practices facility.     

Optimal adaptive two‐stage designs for phase II cancer clinical trials

In oncology, single‐arm two‐stage designs with binary endpoint are widely applied in phase II for the development of cytotoxic cancer therapies. Simon's optimal design with prefixed sample sizes in both stages minimizes the expected sample size under the null hypothesis and is one of the most popular designs. The search algorithms that are currently used to identify phase II designs showing prespecified characteristics are computationally intensive. For this reason, most authors impose restrictions on their search procedure. However, it remains unclear to what extent this approach influences the optimality of the resulting designs. This article describes an extension to fixed sample size phase II designs by allowing the sample size of stage two to depend on the number of responses observed in the first stage. Furthermore, we present a more efficient numerical algorithm that allows for an exhaustive search of designs. Comparisons between designs presented in the literature and the proposed optimal adaptive designs show that while the improvements are generally moderate, notable reductions in the average sample size can be achieved for specific parameter constellations when applying the new method and search strategy.     

Optimal adaptive randomized designs for clinical trials

Optimal decision-analytic designs are deterministic. Such designsare appropriately criticized in the context of clinical trialsbecause they are subject to assignment bias. On the other hand,balanced randomized designs may assign an excessive number ofpatients to a treatment arm that is performing relatively poorly.We propose a compromise between these two extremes, one thatachieves some of the good characteristics of both. We introducea constrained optimal adaptive design for a fully sequentialrandomized clinical trial with k arms and n patients. An r-designis one for which, at each allocation, each arm has probabilityat least r of being chosen, 0 r 1/k. An optimal design amongall r-designs is called r-optimal. An r₁-design is also an r₂-designif r₁ r₂. A design without constraint is the special case r = 0and a balanced randomized design is the special case r = 1/k.The optimization criterion is to maximize the expected overallutility in a Bayesian decision-analytic approach, where utilityis the sum over the utilities for individual patients over a‘patient horizon’ N. We prove analytically thatthere exists an r-optimal design such that each patient is assignedto a particular one of the arms with probability 1 – (k – 1)r,and to the remaining arms with probability r. We also show thatthe balanced design is asymptotically r-optimal for any givenr, 0 r < 1/k, as N/n  . This implies that everyr-optimal design is asymptotically optimal without constraint.Numerical computations using backward induction for k = 2arms show that, in general, this asymptotic optimality featurefor r-optimal designs can be accomplished with moderate trialsize n if the patient horizon N is large relative to n. We alsoshow that, in a trial with an r-optimal design, r < 1/2,fewer patients are assigned to an inferior arm than when followinga balanced design, even for r-optimal designs having the samestatistical power as a balanced design. We discuss extensionsto various clinical trial settings.     

Challenges in implementing adaptive designs: comments on the viewpoints expressed by regulatory statisticians

This is a discussion of the following three papers appearing in this special issue on adaptive designs: 'FDA's critical path initiative: A perspective on contributions of biostatistics' by Robert T. O'Neill; 'A regulatory view on adaptive/flexible clinical trial design' by H. M. James Hung, Robert T. O'Neill, Sue-Jane Wang and John Lawrence; and 'Confirmatory clinical trials with an adaptive design' by Armin Koch.     

Optimal response-adaptive designs for continuous responses in phase III trials

Optimal response-adaptive designs in phase III clinical trial set up are gaining more interest. Most of the available designs are not based on any optimal consideration. An optimal design for binary responses is given by Rosenberger et al. (2001) and one for continuous responses is provided by Biswas and Mandal (2004). Recently, Zhang and Rosenberger (2006) proposed another design for normal responses. This paper illustrates that the Zhang and Rosenberger (2006) design is not suitable for normally distributed responses, in general. The approach cannot be extended for other continuous response cases, such as exponential or gamma. In this paper, we first describe when the optimal design of Zhang and Rosenberger (2006) fails. We then suggest the appropriate adjustments for designs in different continuous distributions. A unified framework to find optimal response-adaptive designs for two competing treatments is proposed. The proposed methods are illustrated using some real data.     

Randomized response‐adaptive designs in clinical trials

EDITOR: TAESUNG PARK Randomized Response‐Adaptive Designs in Clinical Trials

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