Implementation of group sequential logrank tests in a maximum duration trial

To control the Type I error probability in a group sequential procedure using the logrank test, it is important to know the information times (fractions) at the times of interim analyses conducted for purposes of data monitoring. For the logrank test, the information time at an interim analysis is the fraction of the total number of events to be accrued in the entire trial. In a maximum information trial design, the trial is concluded when a prespecified total number of events has been accrued. For such a design, therefore, the information time at each interim analysis is known. However, many trials are designed to accrue data over a fixed duration of follow-up on a specified number of patients. This is termed a maximum duration trial design. Under such a design, the total number of events to be accrued is unknown at the time of an interim analysis. For a maximum duration trial design, therefore, these information times need to be estimated. A common practice is to assume that a fixed fraction of information will be accrued between any two consecutive interim analyses, and then employ a Pocock or O'Brien-Fleming boundary. In this article, we describe an estimate of the information time based on the fraction of total patient exposure, which tends to be slightly negatively biased (i.e., conservative) if survival is exponentially distributed. We then present a numerical exploration of the robustness of this estimate when nonexponential survival applies. We also show that the Lan-DeMets (1983, Biometrika 70, 659-663) procedure for constructing group sequential boundaries with the desired level of Type I error control can be computed using the estimated information fraction, even though it may be biased. Finally, we discuss the implications of employing a biased estimate of study information for a group sequential procedure.     

An optimal Bayesian predictive probability design for phase II clinical trials with simple and complicated endpoints

Most existing phase II clinical trial designs focus on conventional chemotherapy with binary tumor response as the endpoint. The advent of novel therapies, such as molecularly targeted agents and immunotherapy, has made the endpoint of phase II trials more complicated, often involving ordinal, nested, and coprimary endpoints. We propose a simple and flexible Bayesian optimal phase II predictive probability (OPP) design that handles binary and complex endpoints in a unified way. The Dirichlet-multinomial model is employed to accommodate different types of endpoints. At each interim, given the observed interim data, we calculate the Bayesian predictive probability of success, should the trial continue to the maximum planned sample size, and use it to make the go/no-go decision. The OPP design controls the type I error rate, maximizes power or minimizes the expected sample size, and is easy to implement, because the go/no-go decision boundaries can be enumerated and included in the protocol before the onset of the trial. Simulation studies show that the OPP design has satisfactory operating characteristics.     

PA-CRM: A continuous reassessment method for pediatric phase I oncology trials with concurrent adult trials

Pediatric phase I trials are usually carried out after the adult trial testing the same agent has started, but not completed yet. As the pediatric trial progresses, in light of the accrued interim data from the concurrent adult trial, the pediatric protocol often is amended to modify the original pediatric dose escalation design. In practice, this is done frequently in an ad hoc way, interrupting patient accrual and slowing down the trial. We developed a pediatric-continuous reassessment method (PA-CRM) to streamline this process, providing a more efficient and rigorous method to find the maximum tolerated dose for pediatric phase I oncology trials. We use a discounted joint likelihood of the adult and pediatric data, with a discount parameter controlling information borrowing between pediatric and adult trials. According to the interim adult and pediatric data, the discount parameter is adaptively updated using the Bayesian model averaging method. Numerical study shows that the PA-CRM improves the efficiency and accuracy of the pediatric trial and is robust to various model assumptions.     

Statistical inference for self-designing clinical trials with a one-sided hypothesis

In the process of monitoring clinical trials, it seems appealing to use the interim findings to determine whether the sample size originally planned will provide adequate power when the alternative hypothesis is true, and to adjust the sample size if necessary. In the present paper, we propose a flexible sequential monitoring method following the work of Fisher (1998), in which the maximum sample size does not have to be specified in advance. The final test statistic is constructed based on a weighted average of the sequentially collected data, where the weight function at each stage is determined by the observed data prior to that stage. Such a weight function is used to maintain the integrity of the variance of the final test statistic so that the overall type I error rate is preserved. Moreover, the weight function plays an implicit role in termination of a trial when a treatment difference exists. Finally, the design allows the trial to be stopped early when the efficacy result is sufficiently negative. Simulation studies confirm the performance of the method.     

Bayesian adaptive trial design for a newly validated surrogate endpoint

The evaluation of surrogate endpoints for primary use in future clinical trials is an increasingly important research area, due to demands for more efficient trials coupled with recent regulatory acceptance of some surrogates as 'valid.' However, little consideration has been given to how a trial that utilizes a newly validated surrogate endpoint as its primary endpoint might be appropriately designed. We propose a novel Bayesian adaptive trial design that allows the new surrogate endpoint to play a dominant role in assessing the effect of an intervention, while remaining realistically cautious about its use. By incorporating multitrial historical information on the validated relationship between the surrogate and clinical endpoints, then subsequently evaluating accumulating data against this relationship as the new trial progresses, we adaptively guard against an erroneous assessment of treatment based upon a truly invalid surrogate. When the joint outcomes in the new trial seem plausible given similar historical trials, we proceed with the surrogate endpoint as the primary endpoint, and do so adaptively-perhaps stopping the trial for early success or inferiority of the experimental treatment, or for futility. Otherwise, we discard the surrogate and switch adaptive determinations to the original primary endpoint. We use simulation to test the operating characteristics of this new design compared to a standard O'Brien-Fleming approach, as well as the ability of our design to discriminate trustworthy from untrustworthy surrogates in hypothetical future trials. Furthermore, we investigate possible benefits using patient-level data from 18 adjuvant therapy trials in colon cancer, where disease-free survival is considered a newly validated surrogate endpoint for overall survival.     

A Bayesian platform trial design to simultaneously evaluate multiple drugs in multiple indications with mixed endpoints

In the era of targeted therapies and immunotherapies, the traditional drug development paradigm of testing one drug at a time in one indication has become increasingly inefficient. Motivated by a real-world application, we propose a master-protocol–based Bayesian platform trial design with mixed endpoints (PDME) to simultaneously evaluate multiple drugs in multiple indications, where different subsets of efficacy measures (eg, objective response and landmark progression-free survival) may be used by different indications as single or multiple endpoints. We propose a Bayesian hierarchical model to accommodate mixed endpoints and reflect the trial structure of indications that are nested within treatments. We develop a two-stage approach that first clusters the indications into homogeneous subgroups and then applies the Bayesian hierarchical model to each subgroup to achieve precision information borrowing. Patients are enrolled in a group-sequential way and adaptively assigned to treatments according to their efficacy estimates. At each interim analysis, the posterior probabilities that the treatment effect exceeds prespecified clinically relevant thresholds are used to drop ineffective treatments and “graduate” effective treatments. Simulations show that the PDME design has desirable operating characteristics compared to existing method.     

Flexible designs by adaptive plans of generalized Pocock- and O'Brien-Fleming-type and by self-designing clinical trials

Flexible designs are provided by adaptive planning of sample sizes as well as by introducing the weighted inverse normal combining method and the generalized inverse chi-square combining method in the context of conducting trials consecutively step by step. These general combining methods allow quite different weighting of sequential study parts, also in a completely adaptive way, based on full information from unblinded data in previously performed stages. So, in reviewing some basic developments of flexible designing, we consider a generalizing approach to group sequentially performed clinical trials of Pocock-type, of O'Brien-Fleming-type, and of Self-designing-type. A clinical trial may be originally planned either to show non-inferiority or superiority. The proposed flexible designs, however, allow in each interim analysis to change the planning from showing non-inferiority to showing superiority and vice versa. Several examples of clinical trials with normal and binary outcomes are worked out in detail. We demonstrate the practicable performance of the discussed approaches, confirmed in an extensive simulation study. Our flexible designing is a useful tool, provided that a priori information about parameters involved in the trial is not available or subject to uncertainty.     

Approximate Bayesian evaluation of multiple treatment effects

We propose an approximate Bayesian method for comparing an experimental treatment to a control based on a randomized clinical trial with multivariate patient outcomes. Overall treatment effect is characterized by a vector of parameters corresponding to effects on the individual patient outcomes. We partition the parameter space into four sets where, respectively, the experimental treatment is superior to the control, the control is superior to the experimental, the two treatments are equivalent, and the treatment effects are discordant. We compute posterior probabilities of the parameter sets by treating an estimator of the parameter vector like a random variable in the Bayesian paradigm. The approximation may be used in any setting where a consistent, asymptotically normal estimator of the parameter vector is available. The method is illustrated by application to a breast cancer data set consisting of multiple time-to-event outcomes with covariates and to count data arising from a cross-classification of response, infection, and treatment in an acute leukemia trial.     

Some remarks about the analysis of active control studies

In an active-controlled trial, the experimental treatment can be declared to be non-inferior to the control if the confidence interval for the difference excludes a fixed pre-specified margin. Recently, some articles have discussed an alternative method where the data from the current study and placebo-controlled studies for the active control are combined together into a single test statistic to test whether a fixed fraction of the effect of the active control is preserved. It has been shown that, conditional on nuisance parameters from the active-controlled study, a fixed margin can be defined that will be operationally equivalent to this latter method. In this article, we will discuss statistical properties associated with these approaches. Specifically, the interim monitoring boundaries and level of evidence will be considered.     

Seamlessly expanding a randomized phase II trial to phase III

A sequential Bayesian phase II/III design is proposed for comparative clinical trials. The design is based on both survival time and discrete early events that may be related to survival and assumes a parametric mixture model. Phase II involves a small number of centers. Patients are randomized between treatments throughout, and sequential decisions are based on predictive probabilities of concluding superiority of the experimental treatment. Whether to stop early, continue, or shift into phase III is assessed repeatedly in phase II. Phase III begins when additional institutions are incorporated into the ongoing phase II trial. Simulation studies in the context of a non-small-cell lung cancer trial indicate that the proposed method maintains overall size and power while usually requiring substantially smaller sample size and shorter trial duration when compared with conventional group-sequential phase III designs.     

Re‐Formulating Non‐inferiority Trials as Superiority Trials: The Case of Binary Outcomes

Non‐inferiority trials are conducted for a variety of reasons including to show that a new treatment has a negligible reduction in efficacy or safety when compared to the current standard treatment, or a more complex setting of showing that a new treatment has a negligible reduction in efficacy when compared to the current standard yet is superior in terms of other treatment characteristics. The latter reason for conducting a non‐inferiority trial presents the challenge of deciding on a balance between a suitable reduction in efficacy, known as the non‐inferiority margin, in return for a gain in other important treatment characteristics/findings. It would be ideal to alleviate the dilemma on the choice of margin in this setting by reverting to a traditional superiority trial design where a single p ‐value for superiority of both the most important endpoint (efficacy) and the most important finding (treatment characteristic) is provided. We discuss how this can be done using the information‐preserving composite endpoint (IPCE) approach and consider binary outcome cases in which the combination of efficacy and treatment characteristics, but not one itself, paints a clear picture that the novel treatment is superior to the active control (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sequential monitoring of randomization tests: stratified randomization

In many clinical trials, it is desirable to establish a sequential monitoring plan, whereby the test statistic is computed at an interim point or points in the trial and a decision is made whether to stop early due to evidence of treatment efficacy. In this article, we will set up a sequential monitoring plan for randomization-based inference under the permuted block design, stratified block design, and stratified urn design. We will also propose a definition of information fraction in these settings and discuss its calculation under these different designs.     

Adaptive group sequential designs for clinical trials: combining the advantages of adaptive and of classical group sequential approaches

A general method is presented integrating the concept of adaptive interim analyses into classical group sequential testing. This allows the researcher to represent every group sequential plan as an adaptive trial design and to make design changes during the course of the trial after every interim analysis in the same way as with adaptive designs. The concept of adaptive trial designing is thereby generalized to a large variety of possible sequential plans.     

Bayesian design and analysis of active control clinical trials

We consider the design and analysis of active control clinical trials, i.e., clinical trials comparing an experimental treatment E to a control treatment C considered to be effective. Direct comparison of E to placebo P, or no treatment, is sometimes ethically unacceptable. Much discussion of the design and analysis of such clinical trials has focused on whether the comparison of E to C should be based on a test of the null hypothesis of equivalence, on a test of a nonnull hypothesis that the difference is of some minimally medically important size delta, or on one or two-sided confidence intervals. These approaches are essentially the same for study planning. They all suffer from arbitrariness in specifying the size of the difference delta that must be excluded. We propose an alternative Bayesian approach to the design and analysis of active control trials. We derive the posterior probability that E is superior to P or that E is at least k% as good as C and that C is more effective than P. We also derive approximations for use with logistic and proportional hazard models. Selection of prior distributions is discussed, and results are illustrated using data from an active control trial of a drug for the treatment of unstable angina.     

Simple sequential boundaries for treatment selection in multi-armed randomized clinical trials with a control

Summary .   In situations when many regimens are possible candidates for a large phase III study, but too few resources are available to evaluate each relative to the standard, conducting a multi-armed randomized selection trial is a useful strategy to remove inferior treatments from further consideration. When the study has a relatively quick endpoint such as an imaging-based lesion volume change in acute stroke patients, frequent interim monitoring of the trial is ethically and practically appealing to clinicians. In this article, I propose a class of sequential selection boundaries for multi-armed clinical trials, in which the objective is to select a treatment with a clinically significant improvement upon the control group, or to declare futility if no such treatment exists. The proposed boundaries are easy to implement in a blinded fashion, and can be applied on a flexible monitoring schedule in terms of calendar time. Design calibration with respect to prespecified levels of confidence is simple, and can be accomplished when the response rate of the control group is known only up to an interval. One of the proposed methods is applied to redesign a selection trial with an imaging endpoint in acute stroke patients, and is compared to an optimal two-stage design via simulations: The proposed method imposes smaller sample size on average than the two-stage design; this advantage is substantial when there is in fact a superior treatment to the control group.     

Group sequential methods for an ordinal logistic random-effects model under misspecification

Interim analyses in clinical trials are planned for ethical as well as economic reasons. General results have been published in the literature that allow the use of standard group sequential methodology if one uses an efficient test statistic, e.g., when Wald-type statistics are used in random-effects models for ordinal longitudinal data. These models often assume that the random effects are normally distributed. However, this is not always the case. We will show that, when the random-effects distribution is misspecified in ordinal regression models, the joint distribution of the test statistics over the different interim analyses is still a multivariate normal distribution, but a sandwich-type correction to the covariance matrix is needed in order to obtain the correct covariance matrix. The independent increment structure is also investigated. A bias in estimation will occur due to the misspecification. However, we will also show that the treatment effect estimate will be unbiased under the null hypothesis, thus maintaining the type I error. Extensive simulations based on a toenail dermatophyte onychomycosis trial are used to illustrate our results.     

Testing for differences in survival with delayed ascertainment

During the interim stages of most large-scale clinical trials, knowledge that a patient is alive or dead is usually not up-to-date. This is due to the pattern of patient visits to hospitals as well as the administrative set-up used by the study to obtain information on vital status. On a two-armed study, if the process of ascertaining vital status is not the same in both treatment groups, then the standard method of testing based on the logrank statistic may not be applicable. Instead, an ad hoc modification to the logrank test, which artificially truncates follow-up prior to the time of analysis, is often used. These approaches have not been formally addressed in the literature. In the early stages of a clinical trial, severe bias or loss of power may result. For this situation, we propose a class of test statistics that extends the usual class of U statistics. Asymptotic normality is derived by reformulating the statistics in terms of counting processes and employing the theory of U statistics along with martingale techniques. For early interim analyses, a numerical study indicates that the new tests can be more powerful than the current practice when differential ascertainment is present. To illustrate the potential loss of information when lagging follow-up to control for ascertainment delays, we reanalyze an AIDS clinical trial with the truncated logrank and the new statistics.     

Full and reduced models for yield trials

Summary Empirical results routinely demonstrate that the reduced Additive Main effects and Multiplicative Interaction (AMMI) model achieves better predictive accuracy for yield trials than does the full treatment means model. It may seem mysterious that treatment means are not the most accurate estimates, but rather that the AMMI model is often more accurate than its data. The statistical explanation involves the Stein effect, whereby a small sacrifice in bias can produce a large gain in accuracy. The corresponding agricultural explanation is somewhat complex, beginning with a yield trial's design and ending with its research purposes and applications. In essence, AMMI selectively recovers pattern related to the treatment design in its model, while selectively relegating noise related to the experimental design in its discarded residual. For estimating the yield of a particular genotype in a particular environment, the AMMI model uses the entire yield trial, rather than only the several replications of this particular trial, as in the treatment means model. This use of more information is the source of AMMI's gain in accuracy.This research was supported by the Rhizobotany Project of the USDA-ARS     

Bayesian Adaptive Randomization and Trial Monitoring with Predictive Probability for Time-to-Event Endpoint

There has been much development in Bayesian adaptive designs in clinical trials. In the Bayesian paradigm, the posterior predictive distribution characterizes the future possible outcomes given the currently observed data. Based on the interim time-to-event data, we develop a new phase II trial design by combining the strength of both Bayesian adaptive randomization and the predictive probability. By comparing the mean survival times between patients assigned to two treatment arms, more patients are assigned to the better treatment on the basis of adaptive randomization. We continuously monitor the trial using the predictive probability for early termination in the case of superiority or futility. We conduct extensive simulation studies to examine the operating characteristics of four designs: the proposed predictive probability adaptive randomization design, the predictive probability equal randomization design, the posterior probability adaptive randomization design, and the group sequential design. Adaptive randomization designs using predictive probability and posterior probability yield a longer overall median survival time than the group sequential design, but at the cost of a slightly larger sample size. The average sample size using the predictive probability method is generally smaller than that of the posterior probability design.     

Interim monitoring in sequential multiple assignment randomized trials

A sequential multiple assignment randomized trial (SMART) facilitates the comparison of multiple adaptive treatment strategies (ATSs) simultaneously. Previous studies have established a framework to test the homogeneity of multiple ATSs by a global Wald test through inverse probability weighting. SMARTs are generally lengthier than classical clinical trials due to the sequential nature of treatment randomization in multiple stages. Thus, it would be beneficial to add interim analyses allowing for an early stop if overwhelming efficacy is observed. We introduce group sequential methods to SMARTs to facilitate interim monitoring based on the multivariate chi-square distribution. Simulation studies demonstrate that the proposed interim monitoring in SMART (IM-SMART) maintains the desired type I error and power with reduced expected sample size compared to the classical SMART. Finally, we illustrate our method by reanalyzing a SMART assessing the effects of cognitive behavioral and physical therapies in patients with knee osteoarthritis and comorbid subsyndromal depressive symptoms.