A multiple imputation strategy for sequential multiple assignment randomized trials

Sequential multiple assignment randomized trials (SMARTs) are increasingly being used to inform clinical and intervention science. In a SMART, each patient is repeatedly randomized over time. Each randomization occurs at a critical decision point in the treatment course. These critical decision points often correspond to milestones in the disease process or other changes in a patient's health status. Thus, the timing and number of randomizations may vary across patients and depend on evolving patient‐specific information. This presents unique challenges when analyzing data from a SMART in the presence of missing data. This paper presents the first comprehensive discussion of missing data issues typical of SMART studies: we describe five specific challenges and propose a flexible imputation strategy to facilitate valid statistical estimation and inference using incomplete data from a SMART. To illustrate these contributions, we consider data from the Clinical Antipsychotic Trial of Intervention and Effectiveness, one of the most well‐known SMARTs to date. Copyright © 2014 John Wiley & Sons, Ltd.     

A Bayesian design for phase II clinical trials with delayed responses based on multiple imputation

Interim monitoring is routinely conducted in phase II clinical trials to terminate the trial early if the experimental treatment is futile. Interim monitoring requires that patients’ responses be ascertained shortly after the initiation of treatment so that the outcomes are known by the time the interim decision must be made. However, in some cases, response outcomes require a long time to be assessed, which causes difficulties for interim monitoring. To address this issue, we propose a Bayesian trial design to allow for continuously monitoring phase II clinical trials in the presence of delayed responses. We treat the delayed responses as missing data and handle them using a multiple imputation approach. Extensive simulations show that the proposed design yields desirable operating characteristics under various settings and dramatically reduces the trial duration. Copyright © 2014 John Wiley & Sons, Ltd.     

Issues in designing flexible trials

We outline the general framework of adaptive combination tests and discuss their relationship to flexible group sequential designs. An important field of applications is sample size reassessment. We discuss reassessment rules based on conditional power arguments using either the observed or the prefixed effect size. These rules tend to lead to large expected sample sizes for small actual effects. However, the application of a maximal bound for the second stage sample size leads to more favourable properties. Additionally, we consider an optimized reassessment rule in terms of expected sample sizes. Since the adaptive design does not use the classical test statistics for some types of sample size reassessments, the adaptive test may reject the null hypothesis while the classical one-sample test does not. We characterize sample size reassessment rules, where such inconsistencies are avoided. Finally, the extension of flexibility to the number of stages is explored. In the first interim analysis a second interim analysis is only planned if the chance to achieve a decision there is high. This leads to savings in the average number of interim analysis performed, without paying a noticeable price in terms of expected sample size.     

A group-sequential design for clinical trials with treatment selection

A group-sequential design for clinical trials that involve treatment selection was proposed by Stallard and Todd (Statist. Med. 2003; 22:689-703). In this design, the best among a number of experimental treatments is selected on the basis of data observed at the first of a series of interim analyses. This experimental treatment then continues together with the control treatment to be assessed in one or more further analyses. The method was extended by Kelly et al. (J. Biopharm. Statist. 2005; 15:641-658) to allow more than one experimental treatment to continue beyond the first interim analysis. This design controls the familywise type I error rate under the global null hypothesis, that is in the weak sense, but may not strongly control the error rate, particularly if the treatments selected are not the best-performing ones. In some cases, for example when additional safety data are available, the restriction that the best-performing treatments continue may be unreasonable. This paper describes an extension of the approach of Stallard and Todd that enables construction of a group-sequential design for comparison of several experimental treatments with a control treatment. The new method controls the type I error rate in the strong sense if the number of treatments included at each stage is specified in advance, and is indicated by simulation studies to be conservative when the number of treatments is chosen based on the observed data in a practically relevant way.     

A frequentist design for basket trials using adaptive lasso

A basket trial aims to expedite the drug development process by evaluating a new therapy in multiple populations within the same clinical trial. Each population, referred to as a “basket”, can be defined by disease type, biomarkers, or other patient characteristics. The objective of a basket trial is to identify the subset of baskets for which the new therapy shows promise. The conventional approach would be to analyze each of the baskets independently. Alternatively, several Bayesian dynamic borrowing methods have been proposed that share data across baskets when responses appear similar. These methods can achieve higher power than independent testing in exchange for a risk of some inflation in the type 1 error rate. In this paper we propose a frequentist approach to dynamic borrowing for basket trials using adaptive lasso. Through simulation studies we demonstrate adaptive lasso can achieve similar power and type 1 error to the existing Bayesian methods. The proposed approach has the benefit of being easier to implement and faster than existing methods. In addition, the adaptive lasso approach is very flexible: it can be extended to basket trials with any number of treatment arms and any type of endpoint.     

A three-outcome design for randomized comparative phase II clinical trials

Randomized designs have been increasingly called for use in phase II oncology clinical trials to protect against potential patient selection bias. However, formal statistical comparison is rarely conducted due to the sample size restriction, despite its appeal. In this paper, we offer an approach to sample size reduction by extending the three-outcome design of Sargent et al. (Control Clin. Trials 2001; 22:117-125) for single-arm trials to randomized comparative trials. In addition to the usual two outcomes of a hypothesis testing (rejecting the null hypothesis or rejecting the alternative hypothesis), the three-outcome comparative design allows a third outcome of rejecting neither hypotheses when the testing result is in some 'grey area' and leaves the decision to the clinical judgment based on the overall evaluation of trial outcomes and other relevant factors. By allowing a reasonable region of uncertainty, the three-outcome design enables formal statistical comparison with considerably smaller sample size, compared to the standard two-outcome comparative design. Statistical formulation of the three-outcome comparative design is discussed for both the single-stage and two-stage trials. Sample sizes are tabulated for some common clinical scenarios.     

A Bayesian predictive two-stage design for phase II clinical trials

In this paper, we propose a Bayesian two-stage design for phase II clinical trials, which represents a predictive version of the single threshold design (STD) recently introduced by Tan and Machin. The STD two-stage sample sizes are determined specifying a minimum threshold for the posterior probability that the true response rate exceeds a pre-specified target value and assuming that the observed response rate is slightly higher than the target. Unlike the STD, we do not refer to a fixed experimental outcome, but take into account the uncertainty about future data. In both stages, the design aims to control the probability of getting a large posterior probability that the true response rate exceeds the target value. Such a probability is expressed in terms of prior predictive distributions of the data. The performance of the design is based on the distinction between analysis and design priors, recently introduced in the literature. The properties of the method are studied when all the design parameters vary.     

A Bayesian design for phase I cancer therapeutic vaccine trials

Phase I clinical trials are the first step in drug development to test a new drug or drug combination on humans. Typical designs of Phase I trials use toxicity as the primary endpoint and aim to find the maximum tolerable dosage. However, these designs are poorly applicable for the development of cancer therapeutic vaccines because the expected safety concerns for these vaccines are not as much as cytotoxic agents. The primary objectives of a cancer therapeutic vaccine phase I trial thus often include determining whether the vaccine shows biologic activity and the minimum dose necessary to achieve a full immune or even clinical response. In this paper, we propose a new Bayesian phase I trial design that allows simultaneous evaluation of safety and immunogenicity outcomes. We demonstrate the proposed clinical trial design by both a numeric study and a therapeutic human papillomavirus vaccine trial.     

A rank-based sample size method for multiple outcomes in clinical trials

O'Brien (Biometrics 1984; 40:1079-1087) introduced a rank-sum-type global statistical test to summarize treatment's effect on multiple outcomes and to determine whether a treatment is better than others. This paper presents a sample size computation method for clinical trial design with multiple primary outcomes, and O'Brien's test or its modified test (Biometrics 2005; 61:532-539) is used for the primary analysis. A new measure, the global treatment effect (GTE), is introduced to summarize treatment's efficacy from multiple primary outcomes. Computation of the GTE under various settings is provided. Sample size methods are presented based on prespecified GTE both when pilot data are available and when no pilot data are available. The optimal randomization ratio is given for both cases. We compare our sample size method with the Bonferroni adjustment for multiple tests. Since ranks are used in our derivation, sample size formulas derived here are invariant to any monotone transformation of the data and are robust to outliers and skewed distributions. When all outcomes are binary, we show how sample size is affected by the success probabilities of outcomes. Simulation shows that these sample size formulas provide good control of type I error and statistical power. An application to a Parkinson's disease clinical trial design is demonstrated. Splus codes to compute sample size and the test statistic are provided.     

A Bayesian dose finding design for dual endpoint phase I trials

We propose a dose-finding weighted design for an early clinical trial which aims to determine the optimal dose, selected on the basis of both efficacy and toxicity, to be used in patients entering subsequent studies in a drug development process. The goal is to identify the optimal dose, while using a minimal number of subjects. For each dose under test, a decision table is defined with a utility value attached to each possible decision. The relationship between the utility and the target probability for each outcome is shown. A Dirichlet prior is used and we illustrate the process of maximizing the expected utility under the resulting posterior distribution to find the optimal decision at each stage of the trial. We show how this affects the eventual choice of optimal dose in various scenarios. Properties of our design are discussed and compared with a current standard design.     

A multiple comparison procedure for three- and four-armed controlled clinical trials.

Multi-armed controlled trials are becoming increasingly popular. With them comes the issue of how to deal with the possibility of multiple Type I errors. This paper recommends a simple and appealing method for three- and four-armed trials in which one is a control. This article is a US Government work and is in the public domain in the United States.     

A multiple imputation strategy for clinical trials with truncation of patient data

Clinical trials of drug treatments for psychiatric disorders commonly employ the parallel groups, placebo-controlled, repeated measure randomized comparison. When patients stop adhering to their originally assigned treatment, investigators often abandon data collection. Thus, non-adherence produces a monotone pattern of unit-level missing data, disabling the analysis by intent-to-treat. We propose an approach based on multiple imputation of the missing responses, using the approximate Bayesian bootstrap to draw ignorable repeated imputations from the postrior predictive distribution of the missing data, stratifying by a balancing score for the observed responses prior to withdrawal. We apply the method and some variations to data from a large randomized trial of treatments for panic disorder, and compare the results to those obtained by the original analysis that used the standard (endpoint) method.     

The randomized placebo-phase design for clinical trials

Randomized controlled trials are the criterion standard method for evaluating the effectiveness of medical treatments. There are situations, however, where the possibility of being in the control group in a randomized controlled trial is unacceptable to potential subjects or their physicians. This lack of acceptance is a reason for poor accrual. We developed and validated a new clinical trial design for survival data that may allay concerns about not receiving an investigational product and should be more acceptable. Called the randomized placebo-phase design, this new design asks whether, on average, those subjects who begin active treatment sooner respond sooner than those who begin it later. Using Monte Carlo computer simulations, we demonstrated that the design is valid and may offer advantages over traditional randomized controlled trials in some situations. The randomized placebo-phase design may be especially useful when highly potent therapies for rare diseases are tested or when accrual may be otherwise difficult.     

Reinforcement learning design for cancer clinical trials

We develop reinforcement learning trials for discovering individualized treatment regimens for life‐threatening diseases such as cancer. A temporal‐difference learning method called Q‐learning is utilized that involves learning an optimal policy from a single training set of finite longitudinal patient trajectories. Approximating the Q‐function with time‐indexed parameters can be achieved by using support vector regression or extremely randomized trees. Within this framework, we demonstrate that the procedure can extract optimal strategies directly from clinical data without relying on the identification of any accurate mathematical models, unlike approaches based on adaptive design. We show that reinforcement learning has tremendous potential in clinical research because it can select actions that improve outcomes by taking into account delayed effects even when the relationship between actions and outcomes is not fully known. To support our claims, the methodology's practical utility is illustrated in a simulation analysis. In the immediate future, we will apply this general strategy to studying and identifying new treatments for advanced metastatic stage IIIB/IV non‐small cell lung cancer, which usually includes multiple lines of chemotherapy treatment. Moreover, there is significant potential of the proposed methodology for developing personalized treatment strategies in other cancers, in cystic fibrosis, and in other life‐threatening diseases. Copyright © 2009 John Wiley & Sons, Ltd.     

Mid-trial design reviews for sequential clinical trials

When sequential clinical trials are conducted by plotting a statistic measuring treatment difference against another measuring information, power is guaranteed regardless of nuisance parameters. However, values need to be assigned to nuisance parameters in order to gain an impression of the sample size distribution. Each interim analysis provides an opportunity to re-evaluate the relationship between sample size and information. In this paper we discuss such mid-trial design reviews. In the special cases of trials with a relatively short recruitment phase followed by a longer period of follow-up, and of normally distributed responses, mid-trial design reviews are particularly important. Examples are given of the various situations considered, and extensive simulations are reported demonstrating the validity of the review procedure in the case of normally distributed responses.     

Stopping guidelines for clinical trials with multiple treatments

Stopping guidelines are widely used in long-term clinical trials involving two treatments. These allow planned interim analyses of the accumulating data to be undertaken whilst preserving the type I error rate for the treatment comparison. Their philosophy is extended to the case of trials with multiple treatments so that at any interim analysis, treatments may be considered for dropping from the trial if they are significantly inferior to all treatments that will remain. The proposed guidelines are designed to preserve the error rate in determining that treatment or group of treatments which is, in reality, best. Using simulation studies, stopping guidelines developed for two-arm trials are shown to be directly usable in multiple-arm studies when the treatments studied are all experimental and so in direct competition. When one treatment is the standard of care, a modification gives a better ethical perspective by also permitting treatments to be dropped when they are deemed inferior to the standard. Results are presented for normally distributed responses in trials involving three or four treatments and using stopping boundaries of the form proposed by O'Brien and Fleming. In conclusion, I discuss some of the additional considerations that are important in employing stopping guidelines in trials with multiple treatments.