Adaptive decision making in a lymphocyte infusion trial

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

The main goals of Phase II trials are to identify the therapeutic efficacy of new treatments and continue monitoring all the possible adverse effects. In Phase II trials, it is important to develop an adaptive randomization (AR) procedure that takes into account both the efficacy and toxicity. In most existing articles, toxicity is modeled as a binary endpoint through an unobservable random effect (frailty) to link the efficacy and toxicity. However, this approach does not capture toxicity profiles that evolve over time. In this article, we propose a new Bayesian adaptive randomization (BAR) procedure using the covariate-adjusted efficacy-toxicity ratio (ETR) index, where efficacy and toxicity are jointly modelled as time-to-event (TTE) outcomes. Furthermore, we also propose early stopping rules for toxicity and futility such that inferior treatments can be dropped at earlier time of trial. Simulation results show that compared to the BAR procedures based solely on the efficacy and that based on TTE efficacy and binary toxicity outcomes, the proposed BAR procedure can better identify the difference in treatment toxicity such that it can assign more patients to the superior treatment arm under some scenarios.

The Bayesian Design of Adaptive Clinical Trials

This paper presents a brief overview of the recent literature on adaptive design of clinical trials from a Bayesian perspective for statistically not so sophisticated readers. Adaptive designs are attracting a keen interest in several disciplines, from a theoretical viewpoint and also—potentially—from a practical one, and Bayesian adaptive designs, in particular, have raised high expectations in clinical trials. The main conceptual tools are highlighted here, with a mention of several trial designs proposed in the literature that use these methods, including some of the registered Bayesian adaptive trials to this date. This review aims at complementing the existing ones on this topic, pointing at further interesting reading material.

A response-adaptive design of initial therapy for emergency department patients with heart failure

Finding safe and effective treatments for acute heart failure syndrome (AHFS) is a high priority. More than 80% of patients with AHFS who present to emergency departments are treated identically with intravenous diuretics, despite recognition of the syndrome's heterogeneity. We hypothesize that matching patient profiles with "personalized" AHFS treatments will improve outcomes. Matching multiple heterogeneous clinical profiles with a number of potentially effective treatments requires an adaptive trial design that can adjust for these complexities. We propose a Bayesian response-adaptive randomization trial design for AHFS patients. Baseline information collected for each patient with AHFS prior to randomization includes blood pressure, renal function, and dyspnea severity. The primary outcome is discharge readiness within 23h of presentation and no unplanned emergency visits or admissions for acute heart failure within 7days of discharge. We use a Bayesian logistic regression model to characterize the association between primary outcome and patient profile. We adaptively randomize patients to one of five treatments, basing the randomization probability on the cumulative data from the ongoing trial and fitting results from the regression model. Simulations show high probability of selecting the best treatment corresponding to the patient's profile while allocating more patients to the efficacious treatments within the trial.

Molecularly targeted therapies for malignant gliomas: advances and challenges

The identification of molecular markers associated with tumor but not with normal tissue has allowed the development of highly specific, targeted therapies for the treatment of cancer. Over the last several years, tremendous advances in our understanding of the genetic and molecular changes involved in the progression of malignant gliomas have triggered a large effort in the development of targeted therapies to treat these tumors. However, to date only a modest clinical benefit, limited to subsets of patients, has been demonstrated. Furthermore, despite a high degree of target selectivity, the use of targeted therapies often has systemic toxicity. The reasons behind this limited clinical success are complex and include the intricacy of the signaling pathways in gliomas and the heterogeneity of the disease process, compounded by existing limitations in assessing the efficacy of these novel agents when conventional end points and clinical trial designs are utilized. However, despite these difficulties targeted therapies remain a very attractive avenue of treatment for malignant gliomas. Three basic approaches are needed to overcome the hurdles associated with targeted therapies: first, further development of genetic profiling techniques will help to better determine the genetic changes and molecular pathways involved in gliomas and will potentially allow the design of individualized therapies based on the genetic and molecular signature of each tumor. Second, there is a need for the development of better combination strategies (complementary targeted agents or targeted agents with chemotherapy drugs) directed towards disease heterogeneity. Third, we need to optimize the design of preclinical and clinical trials to obtain the maximum amount of information in the shortest period of time.

A Phase I/II trial design when response is unobserved in subjects with dose-limiting toxicity

We propose a Phase I/II trial design in which subjects with dose-limiting toxicity are not followed for response, leading to three possible outcomes for each subject: dose-limiting toxicity, absence of therapeutic response without dose-limiting toxicity, and presence of therapeutic response without dose-limiting toxicity. We define the latter outcome as a 'success,' and the goal of the trial is to identify the dose with the largest probability of success. This dose is commonly referred to as the most successful dose. We propose a design that accumulates information on subjects with regard to both dose-limiting toxicity and response conditional on no dose-limiting toxicity. Bayesian methods are used to update the estimates of dose-limiting toxicity and response probabilities when each subject is enrolled, and we use these methods to determine the dose level assigned to each subject. Due to the need to explore doses more fully, each subject is not necessarily assigned the current estimate of the most successful dose; our algorithm may instead assign a dose that is in a neighborhood of the current most successful dose. We examine the ability of our design to correctly identify the most successful dose in a variety of settings via simulation and compare the performance of our design to that of competing approaches.

Two-stage designs for Phase 2 dose-finding trials

We propose a Bayesian adaptive two-stage design for the efficient estimation of the maximum dose or the minimum effective dose in a dose-finding trial. The new design allocates subjects in stage two according to the posterior distribution of the target dose location. Simulations show that the proposed two-stage design is superior to equal allocation and to a two-stage strategy where only one dose is left in the second stage.

Bayesian adaptive clinical trials: a dream for statisticians only?

Adaptive or 'flexible' designs have emerged, mostly within frequentist frameworks, as an effective way to speed up the therapeutic evaluation process. Because of their flexibility, Bayesian methods have also been proposed for Phase I through Phase III adaptive trials; however, it has been reported that they are poorly used in practice. We aim to describe the international scientific production of Bayesian clinical trials by investigating the actual development and use of Bayesian 'adaptive' methods in the setting of clinical trials. A bibliometric study was conducted using the PubMed and Science Citation Index-Expanded databases. Most of the references found were biostatistical papers from various teams around the world. Most of the authors were from the US, and a large proportion was from the MD Anderson Cancer Center (University of Texas, Houston, TX). The spread and use of these articles depended heavily on their topic, with 3.1% of the biostatistical articles accumulating at least 25 citations within 5 years of their publication compared with 15% of the reviews and 32% of the clinical articles. We also examined the reasons for the limited use of Bayesian adaptive design methods in clinical trials and the areas of current and future research to address these challenges. Efforts to promote Bayesian approaches among statisticians and clinicians appear necessary.

A case study of model-based Bayesian dose response estimation

A Bayesian nonlinear longitudinal Emax model for a binary endpoint was used to characterize the dose-response relationship for a new treatment of rheumatoid arthritis. The model includes prespecified parametric functions for the dependence of response on dose level and time. It was selected based on pharmacometric input about likely dose and time trends. The longitudinal model was useful for combining data collected at different doses and times from two different studies. The example illustrates the utility of more substantive parametric models to guide selection of doses outside the initial dosing range when designing an additional phase 2 study and for extrapolating shorter-term phase 2 dose response to longer-term phase 3 studies, as is often required for dosing decisions in drug development for chronic diseases. Comparison of the estimated dose response from the longitudinal model with a corresponding logistic regression model applied at a single time point also demonstrated improved precision. Specification of an informative prior distribution based on numerous sources of prior information is described. This was the most difficult step in the analysis and one that has limited the use of Bayesian methods in similar applications. Model fit was evaluated and the potential impact of some model deficiencies on the dosing decision was assessed. Analyses of the combined studies identified doses likely to achieve a targeted effect in larger and longer confirmatory trials.

A Bayesian response-adaptive covariate-balanced randomization design with application to a leukemia clinical trial

We propose a Bayesian response-adaptive covariate-balanced (RC) randomization design for multiple-arm comparative clinical trials. The goal of the design is to skew the allocation probability to more efficacious treatment arms, while also balancing the distribution of the covariates across the arms. In particular, we first propose a new covariate-adaptive randomization (CA) method based on a prognostic score that naturally accommodates continuous and categorical prognostic factors and automatically assigns imbalance weights to covariates according to their importance in response prediction. We then incorporate this CA design into a group sequential response-adaptive randomization (RA) scheme. The resulting RC randomization design combines the advantages of both CA and RA randomizations and meets the design goal. We illustrate the proposed design through its application to a phase II leukemia clinical trial, and evaluate its operating characteristics through simulation studies.

Clofarabine ± fludarabine with once daily i.v. busulfan as pretransplant conditioning therapy for advanced myeloid leukemia and MDS

Although a combination of i.v. busulfan (Bu) and fludarabine (Flu) is a safe, reduced-toxicity conditioning program for acute myelogenous leukemia/myelodysplastic syndromes (AML/MDS), recurrent leukemia posttransplantation remains a problem. To enhance the conditioning regimen's antileukemic effect, we decided to supplant Flu with clofarabine (Clo), and assayed the interactions of these nucleoside analogs alone and in combination with Bu in Bu-resistant human cell lines in vitro. We found pronounced synergy between each nucleoside and the alkylator but even more enhanced cytotoxic synergy when the nucleoside analogs were combined prior to exposing the cells to Bu. We then designed a 4-arm clinical trial in patients with myeloid leukemia undergoing allogeneic stem cell transplantation (allo-SCT). Patients were adaptively randomized as follows: Arm I-Clo:Flu 10:30 mg/m(2), Arm II-20:20 mg/m(2), Arm III-30:10 mg/m(2), and Arm IV-single-agent Clo at 40 mg/m(2). The nucleoside analog(s) were/was infused over 1 hour once daily for 4 days, followed on each day by Bu, infused over 3 hours to a pharmacokinetically targeted daily area under the curve (AUC) of 6000 μMol-min ± 10%. Fifty-one patients have been enrolled with a minimum follow-up exceeding 100 days. There were 32 males and 19 females, with a median age of 45 years (range: 6-59). Nine patients had chronic myeloid leukemia (CML) (BC: 2, second AP: 3, and tyrosine-kinase inhibitor refractory first chronic phase [CP]: 4). Forty-two patients had AML: 14 were induction failures, 8 in first chemotherapy-refractory relapse, 7 in untreated relapse, 3 in second or subsequent relapse, 4 were in second complete remission (CR), and 3 in second CR without platelet recovery (CRp), 2 were in high-risk CR1. Finally, 1 patient was in first CRp. Graft-versus-host disease (GVHD) prophylaxis was tacrolimus and mini-methorexate (MTX), and those who had an unrelated or 1 antigen-mismatched donor received low-dose rabbit-ATG (Thymoglobulin™). All patients engrafted. Forty-one patients had active leukemia at the time of transplant, and 35 achieved CR (85%). Twenty of the 42 AML patients and 5 of 9 CML patients are alive with a projected median overall survival (OS) of 23 months. Marrow and blood (T cell) chimerism studies at day +100 revealed that both in the lower-dose Clo groups (groups 1+2) and the higher-dose Clo groups (groups 3+4), the patients had a median of 100% donor (T cell)-derived DNA. There has been no secondary graft failure. In the first 100 days, 1 patient died of pneumonia, and 1 of liver GVHD. We conclude that (1) Clo ± Flu with i.v. Bu as pretransplant conditioning is safe in high-risk myeloid leukemia patients; (2) clofarabine is sufficiently immunosuppressive to support allo-SCT in myeloid leukemia; and (3) the median OS of 23 months in this high-risk patient population is encouraging. Additional studies to evaluate the antileukemic efficacy of Clo ± Flu with i.v. Bu as pretransplant conditioning therapy are warranted.

Response-adaptive randomization for clinical trials with adjustment for covariate imbalance

In clinical trials with a small sample size, the characteristics (covariates) of patients assigned to different treatment arms may not be well balanced. This may lead to an inflated type I error rate. This problem can be more severe in trials that use response-adaptive randomization rather than equal randomization because the former may result in smaller sample sizes for some treatment arms. We have developed a patient allocation scheme for trials with binary outcomes to adjust the covariate imbalance during response-adaptive randomization. We used simulation studies to evaluate the performance of the proposed design. The proposed design keeps the important advantage of a standard response-adaptive design, that is to assign more patients to the better treatment arms, and thus it is ethically appealing. On the other hand, the proposed design improves over the standard response-adaptive design by controlling covariate imbalance between treatment arms, maintaining the nominal type I error rate, and offering greater power.

An adaptive design for identifying the dose with the best efficacy/tolerability profile with application to a crossover dose-finding study

Proof-of-concept in clinical trials has traditionally focused on the identification of a maximum tolerated dose with the assumption that the higher doses provide better efficacy. However, adverse events associated with a maximum tolerated dose may have a negative effect on efficacy. We present an efficient adaptive dose-finding strategy that concentrates patient assignments at and around the dose which has the best efficacy/tolerability profile based on a utility function. The strategy is applied within the setting of a crossover design. While the strategy may also be applied to parallel studies, a crossover design provides more power for a given sample size for comparisons between the optimal dose versus placebo and/or active control when it is reasonable to assume no carryover effects.

Practical Bayesian adaptive randomisation in clinical trials

While randomisation is the established method for obtaining scientifically valid treatment comparisons in clinical trials, it sometimes is at odds with what physicians feel is good medical practice. If a physician favours one treatment over another based on personal experience or published data, it may be more appropriate ethically for that physician to use the favoured treatment, rather than enrolling patients on a randomised trial. Still, the randomised trial may later show the physician's favoured treatment to be inferior. This paper reviews a statistical method, Bayesian adaptive randomisation, that provides a practical compromise between the scientific ideal of conventional randomisation and choosing each patient's treatment based on a personal preference that may prove to be incorrect. The method will first be illustrated by a simple hypothetical example, then by a recent trial in which patients with unresectable soft tissue sarcoma were adaptively randomised between two chemotherapy regimens.

How practical are adaptive designs likely to be for confirmatory trials?

This is a discussion of the following papers appearing in this special issue on adaptive designs: 'Confirmatory Seamless Phase II/III Clinical trials with Hypotheses Selection at Interim: General Concepts' by Frank Bretz, Heinz Schmidli, Franz König, Amy Racine and Willi Maurer; and 'Confirmatory Seamless Phase II/III Clinical Trials with Hypotheses Selection at Interim: Applications and Practical Considerations' by Heinz Schmidli, Frank Bretz, Amy Racine and Willi Maurer.

Stochastic Inequality Probabilities for Adaptively Randomized Clinical Trials

We examine stochastic inequality probabilities of the form P (X > Y) and P (X > max (Y, Z)) where X, Y, and Z are random variables with beta, gamma, or inverse gamma distributions. We discuss the applications of such inequality probabilities to adaptively randomized clinical trials as well as methods for calculating their values.

Dose escalation trial designs based on a molecularly targeted endpoint

Traditional phase I dose-finding studies for chemotoxic agents base dose escalation on toxicity, with escalation continuing until unacceptable toxicity is observed. Recent development of molecularly targeted agents that have little or no toxicity in the therapeutic dose range has raised questions over the best study designs for phase I studies. Two types of designs are proposed and evaluated in this paper. In these designs, escalation is based on a binary response that indicates whether or not the agent has had the desired effect on the molecular target. One design is developed to ensure that if the true target response rate is low there will be a high probability of escalating and if the true target response rate is high there will be a low probability of escalating. The other design is developed to continue to escalate as long as the true response rate is increasing and to stop escalating when the response rate plateaus or decreases. A limited simulation study is performed and the designs are compared with respect to the dose level at the end of escalation and the number of patients treated on study.

Covariate-adjusted adaptive randomization in a sarcoma trial with multi-stage treatments

We present a Bayesian design for a multi-centre, randomized clinical trial of two chemotherapy regimens for advanced or metastatic unresectable soft tissue sarcoma. After randomization, each patient receives up to four stages of chemotherapy, with the patient's disease evaluated after each stage and categorized on a trinary scale of severity. Therapy is continued to the next stage if the patient's disease is stable, and is discontinued if either tumour response or treatment failure is observed. We assume a probability model that accounts for baseline covariates and the multi-stage treatment and disease evaluation structure. The design uses covariate-adjusted adaptive randomization based on a score that combines the patient's probabilities of overall treatment success or failure. The adaptive randomization procedure generalizes the method proposed by Thompson (1933) for two binomial distributions with beta priors. A simulation study of the design in the context of the sarcoma trial is presented.

Sequential urn designs with elimination for comparing K > or =3 treatments

A fully sequential procedure is proposed for comparing K > or =3 treatments with immediate binary responses. The procedure uses an adaptive urn design to randomize patients to the treatments and stopping rules are incorporated for eliminating less promising treatments. Simulation is used to assess the performance of the procedure for several adaptive urn designs, in terms of expected numbers of treatment failures and allocation proportions, and the effect on estimation at the end of the trial is also addressed. It is concluded that the drop-the-loser rule is more effective than equal allocation and all of the other designs considered. The practical benefits of the procedure are illustrated using the results of a three-treatment lung cancer study. It is then shown how the sequential elimination procedure may be used in dose-finding studies and its performance is compared with a recently proposed method. Several possible extensions to the work are briefly indicated.

Continuous Bayesian adaptive randomization based on event times with covariates

In comparative clinical trials, the randomization probabilities may be unbalanced adaptively by utilizing the interim data available at each patient's entry time to favour the treatment or treatments having comparatively superior outcomes. This is ethically appealing because, on average, more patients are assigned to the more successful treatments. Consequently, physicians are more likely to enroll patients onto trials where the randomization is outcome-adaptive rather than balanced in the conventional manner. Outcome-adaptive methods based on a binary variable may be applied by reducing an event time to the indicator of the event's occurrence within a predetermined time interval. This results in a loss of information, however, since it ignores the censoring times of patients who have not experienced the event but whose evaluation interval is not complete. This paper proposes and compares exact and approximate Bayesian outcome-adaptive randomization procedures based on time-to-event outcomes. The procedures account for baseline prognostic covariates, and they may be applied continuously over the course of the trial. We illustrate these methods by application to a phase II selection trial in acute leukaemia. A simulation study in the context of this trial is presented.

A new dose-finding design for bivariate outcomes

For some drugs, toxicity events lead to early termination of treatment before a therapeutic response is observed. That is, there are three possible outcomes: toxicity (therapeutic response unknown), therapeutic response without toxicity, and no response with no toxicity. The optimal dose is the dose that maximizes the probability of the joint event, response, and no toxicity. The optimal safe dose is the dose, from among the doses with toxicity rate less than the maximum tolerable level, that maximizes the probability of response and no toxicity. We present a new sequential design to maximize the number of subjects assigned in the neighborhood of the optimal safe dose in a dose-finding trial with two outcomes.