Propensity score matched augmented controls in randomized clinical trials: A case study

Existing statutes in the United States and Europe require manufacturers to demonstrate evidence of effectiveness through the conduct of adequate and well‐controlled studies to obtain marketing approval of a therapeutic product. What constitutes adequate and well‐controlled studies is usually interpreted as randomized controlled trials (RCTs). However, these trials are sometimes unfeasible because of their size, duration, cost, patient preference, or in some cases, ethical concerns. For example, RCTs may not be fully powered in rare diseases or in infections caused by multidrug resistant pathogens because of the low number of enrollable patients. In this case, data available from external controls (including historical controls and observational studies or data registries) can complement information provided by RCT. Propensity score matching methods can be used to select or “borrow” additional patients from the external controls, for maintaining a one‐to‐one randomization between the treatment arm and active control, by matching the new treatment and control units based on a set of measured covariates, ie, model‐based pairing of treatment and control units that are similar in terms of their observable pretreatment characteristics. To this end, 2 matching schemes based on propensity scores are explored and applied to a real clinical data example with the objective of using historical or external observations to augment data in a trial where the randomization is disproportionate or asymmetric.     

Sample size re‐estimation incorporating prior information on a nuisance parameter

Prior information is often incorporated informally when planning a clinical trial. Here, we present an approach on how to incorporate prior information, such as data from historical clinical trials, into the nuisance parameter–based sample size re‐estimation in a design with an internal pilot study. We focus on trials with continuous endpoints in which the outcome variance is the nuisance parameter. For planning and analyzing the trial, frequentist methods are considered. Moreover, the external information on the variance is summarized by the Bayesian meta‐analytic‐predictive approach. To incorporate external information into the sample size re‐estimation, we propose to update the meta‐analytic‐predictive prior based on the results of the internal pilot study and to re‐estimate the sample size using an estimator from the posterior. By means of a simulation study, we compare the operating characteristics such as power and sample size distribution of the proposed procedure with the traditional sample size re‐estimation approach that uses the pooled variance estimator. The simulation study shows that, if no prior‐data conflict is present, incorporating external information into the sample size re‐estimation improves the operating characteristics compared to the traditional approach. In the case of a prior‐data conflict, that is, when the variance of the ongoing clinical trial is unequal to the prior location, the performance of the traditional sample size re‐estimation procedure is in general superior, even when the prior information is robustified. When considering to include prior information in sample size re‐estimation, the potential gains should be balanced against the risks.     

Covariate handling approaches in combination with dynamic borrowing for hybrid control studies

Borrowing data from external control has been an appealing strategy for evidence synthesis when conducting randomized controlled trials (RCTs). Often named hybrid control trials, they leverage existing control data from clinical trials or potentially real-world data (RWD), enable trial designs to allocate more patients to the novel intervention arm, and improve the efficiency or lower the cost of the primary RCT. Several methods have been established and developed to borrow external control data, among which the propensity score methods and Bayesian dynamic borrowing framework play essential roles. Noticing the unique strengths of propensity score methods and Bayesian hierarchical models, we utilize both methods in a complementary manner to analyze hybrid control studies. In this article, we review methods including covariate adjustments, propensity score matching and weighting in combination with dynamic borrowing and compare the performance of these methods through comprehensive simulations. Different degrees of covariate imbalance and confounding are examined. Our findings suggested that the conventional covariate adjustment in combination with the Bayesian commensurate prior model provides the highest power with good type I error control under the investigated settings. It has desired performance especially under scenarios of different degrees of confounding. To estimate efficacy signals in the exploratory setting, the covariate adjustment method in combination with the Bayesian commensurate prior is recommended.     

Non‐inferiority and networks: inferring efficacy from a web of data

In the absence of placebo‐controlled trials, the efficacy of a test treatment can be alternatively examined by showing its non‐inferiority to an active control; that is, the test treatment is not worse than the active control by a pre‐specified margin. The margin is based on the effect of the active control over placebo in historical studies. In other words, the non‐inferiority setup involves a network of direct and indirect comparisons between test treatment, active controls, and placebo. Given this framework, we consider a Bayesian network meta‐analysis that models the uncertainty and heterogeneity of the historical trials into the non‐inferiority trial in a data‐driven manner through the use of the Dirichlet process and power priors. Depending on whether placebo was present in the historical trials, two cases of non‐inferiority testing are discussed that are analogs of the synthesis and fixed‐margin approach. In each of these cases, the model provides a more reliable estimate of the control given its effect in other trials in the network, and, in the case where placebo was only present in the historical trials, the model can predict the effect of the test treatment over placebo as if placebo had been present in the non‐inferiority trial. It can further answer other questions of interest, such as comparative effectiveness of the test treatment among its comparators. More importantly, the model provides an opportunity for disproportionate randomization or the use of small sample sizes by allowing borrowing of information from a network of trials to draw explicit conclusions on non‐inferiority. Copyright © 2015 John Wiley & Sons, Ltd.     

Coherence principles in interval‐based dose finding

This paper studies the notion of coherence in interval‐based dose‐finding methods. An incoherent decision is either (a) a recommendation to escalate the dose following an observed dose‐limiting toxicity or (b) a recommendation to deescalate the dose following a non–dose‐limiting toxicity. In a simulated example, we illustrate that the Bayesian optimal interval method and the Keyboard method are not coherent. We generated dose‐limiting toxicity outcomes under an assumed set of true probabilities for a trial of n=36 patients in cohorts of size 1, and we counted the number of incoherent dosing decisions that were made throughout this simulated trial. Each of the methods studied resulted in 13/36 (36%) incoherent decisions in the simulated trial. Additionally, for two different target dose‐limiting toxicity rates, 20% and 30%, and a sample size of n=30 patients, we randomly generated 100 dose‐toxicity curves and tabulated the number of incoherent decisions made by each method in 1000 simulated trials under each curve. For each method studied, the probability of incurring at least one incoherent decision during the conduct of a single trial is greater than 75%. Coherency is an important principle in the conduct of dose‐finding trials. Interval‐based methods violate this principle for cohorts of size 1 and require additional modifications to overcome this shortcoming. Researchers need to take a closer look at the dose assignment behavior of interval‐based methods when using them to plan dose‐finding studies.     

Incorporating historical two‐arm data in clinical trials with binary outcome: A practical approach

The feasibility of a new clinical trial may be increased by incorporating historical data of previous trials. In the particular case where only data from a single historical trial are available, there exists no clear recommendation in the literature regarding the most favorable approach. A main problem of the incorporation of historical data is the possible inflation of the type I error rate. A way to control this type of error is the so‐called power prior approach. This Bayesian method does not “borrow” the full historical information but uses a parameter 0 ≤ δ ≤ 1 to determine the amount of borrowed data. Based on the methodology of the power prior, we propose a frequentist framework that allows incorporation of historical data from both arms of two‐armed trials with binary outcome, while simultaneously controlling the type I error rate. It is shown that for any specific trial scenario a value δ > 0 can be determined such that the type I error rate falls below the prespecified significance level. The magnitude of this value of δ depends on the characteristics of the data observed in the historical trial. Conditionally on these characteristics, an increase in power as compared to a trial without borrowing may result. Similarly, we propose methods how the required sample size can be reduced. The results are discussed and compared to those obtained in a Bayesian framework. Application is illustrated by a clinical trial example.     

Structured approach to the elicitation of expert beliefs for a Bayesian‐designed clinical trial: a case study

To quantify uncertainty in a formal manner, statisticians play a vital role in identifying a prior distribution for a Bayesian‐designed clinical trial. However, when expert beliefs are to be used to form the prior, the literature is sparse on how feasible and how reliable it is to elicit beliefs from experts. For late‐stage clinical trials, high importance is placed on reliability; however, feasibility may be equally important in early‐stage trials. This article describes a case study to assess how feasible it is to conduct an elicitation session in a structured manner and to form a probability distribution that would be used in a hypothetical early‐stage trial. The case study revealed that by using a structured approach to planning, training and conduct, it is feasible to elicit expert beliefs and form a probability distribution in a timely manner. We argue that by further increasing the published accounts of elicitation of expert beliefs in drug development, there will be increased confidence in the feasibility of conducting elicitation sessions. Furthermore, this will lead to wider dissemination of the pertinent issues on how to quantify uncertainty to both practicing statisticians and others involved with designing trials in a Bayesian manner. Copyright © 2013 John Wiley & Sons, Ltd.     

A review and re‐interpretation of a group‐sequential approach to sample size re‐estimation in two‐stage trials

In this paper, we review the adaptive design methodology of Li et al. (Biostatistics 3 :277–287) for two‐stage trials with mid‐trial sample size adjustment. We argue that it is closer in principle to a group sequential design, in spite of its obvious adaptive element. Several extensions are proposed that aim to make it even more attractive and transparent alternative to a standard (fixed sample size) trial for funding bodies to consider. These enable a cap to be put on the maximum sample size and for the trial data to be analysed using standard methods at its conclusion. The regulatory view of trials incorporating unblinded sample size re‐estimation is also discussed. © 2014 The Authors. Pharmaceutical Statistics published by John Wiley & Sons, Ltd.     

Adaptive graph‐based multiple testing procedures

Multiple testing procedures defined by directed, weighted graphs have recently been proposed as an intuitive visual tool for constructing multiple testing strategies that reflect the often complex contextual relations between hypotheses in clinical trials. Many well‐known sequentially rejective tests, such as (parallel) gatekeeping tests or hierarchical testing procedures are special cases of the graph based tests. We generalize these graph‐based multiple testing procedures to adaptive trial designs with an interim analysis. These designs permit mid‐trial design modifications based on unblinded interim data as well as external information, while providing strong family wise error rate control. To maintain the familywise error rate, it is not required to prespecify the adaption rule in detail. Because the adaptive test does not require knowledge of the multivariate distribution of test statistics, it is applicable in a wide range of scenarios including trials with multiple treatment comparisons, endpoints or subgroups, or combinations thereof. Examples of adaptations are dropping of treatment arms, selection of subpopulations, and sample size reassessment. If, in the interim analysis, it is decided to continue the trial as planned, the adaptive test reduces to the originally planned multiple testing procedure. Only if adaptations are actually implemented, an adjusted test needs to be applied. The procedure is illustrated with a case study and its operating characteristics are investigated by simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Covariate‐adjusted borrowing of historical control data in randomized clinical trials

The borrowing of historical control data can be an efficient way to improve the treatment effect estimate of the current control group in a randomized clinical trial. When the historical and current control data are consistent, the borrowing of historical data can increase power and reduce Type I error rate. However, when these 2 sources of data are inconsistent, it may result in a combination of biased estimates, reduced power, and inflation of Type I error rate. In some situations, inconsistency between historical and current control data may be caused by a systematic variation in the measured baseline prognostic factors, which can be appropriately addressed through statistical modeling. In this paper, we propose a Bayesian hierarchical model that can incorporate patient‐level baseline covariates to enhance the appropriateness of the exchangeability assumption between current and historical control data. The performance of the proposed method is shown through simulation studies, and its application to a clinical trial design for amyotrophic lateral sclerosis is described. The proposed method is developed for scenarios involving multiple imbalanced prognostic factors and thus has meaningful implications for clinical trials evaluating new treatments for heterogeneous diseases such as amyotrophic lateral sclerosis.     

Nested combination tests with a time‐to‐event endpoint using a short‐term endpoint for design adaptations

Adaptive trial methodology for multiarmed trials and enrichment designs has been extensively discussed in the past. A general principle to construct test procedures that control the family‐wise Type I error rate in the strong sense is based on combination tests within a closed test. Using survival data, a problem arises when using information of patients for adaptive decision making, which are under risk at interim. With the currently available testing procedures, either no testing of hypotheses in interim analyses is possible or there are restrictions on the interim data that can be used in the adaptation decisions as, essentially, only the interim test statistics of the primary endpoint may be used. We propose a general adaptive testing procedure, covering multiarmed and enrichment designs, which does not have these restrictions. An important application are clinical trials, where short‐term surrogate endpoints are used as basis for trial adaptations, and we illustrate how such trials can be designed. We propose statistical models to assess the impact of effect sizes, the correlation structure between the short‐term and the primary endpoint, the sample size, the timing of interim analyses, and the selection rule on the operating characteristics.     

Bayesian sample size determination for phase IIA clinical trials using historical data and semi‐parametric prior's elicitation

The Simon's two‐stage design is the most commonly applied among multi‐stage designs in phase IIA clinical trials. It combines the sample sizes at the two stages in order to minimize either the expected or the maximum sample size. When the uncertainty about pre‐trial beliefs on the expected or desired response rate is high, a Bayesian alternative should be considered since it allows to deal with the entire distribution of the parameter of interest in a more natural way. In this setting, a crucial issue is how to construct a distribution from the available summaries to use as a clinical prior in a Bayesian design. In this work, we explore the Bayesian counterparts of the Simon's two‐stage design based on the predictive version of the single threshold design. This design requires specifying two prior distributions: the analysis prior, which is used to compute the posterior probabilities, and the design prior, which is employed to obtain the prior predictive distribution. While the usual approach is to build beta priors for carrying out a conjugate analysis, we derived both the analysis and the design distributions through linear combinations of B‐splines. The motivating example is the planning of the phase IIA two‐stage trial on anti‐HER2 DNA vaccine in breast cancer, where initial beliefs formed from elicited experts' opinions and historical data showed a high level of uncertainty. In a sample size determination problem, the impact of different priors is evaluated.     

Study design of single‐arm phase II immunotherapy trials with long‐term survivors and random delayed treatment effect

In the traditional study design of a single‐arm phase II cancer clinical trial, the one‐sample log‐rank test has been frequently used. A common practice in sample size calculation is to assume that the event time in the new treatment follows exponential distribution. Such a study design may not be suitable for immunotherapy cancer trials, when both long‐term survivors (or even cured patients from the disease) and delayed treatment effect are present, because exponential distribution is not appropriate to describe such data and consequently could lead to severely underpowered trial. In this research, we proposed a piecewise proportional hazards cure rate model with random delayed treatment effect to design single‐arm phase II immunotherapy cancer trials. To improve test power, we proposed a new weighted one‐sample log‐rank test and provided a sample size calculation formula for designing trials. Our simulation study showed that the proposed log‐rank test performs well and is robust of misspecified weight and the sample size calculation formula also performs well.     

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.     

Subject‐level matching for imbalance in cluster randomized trials with a small number of clusters

In a cluster randomized controlled trial (RCT), the number of randomized units is typically considerably smaller than in trials where the unit of randomization is the patient. If the number of randomized clusters is small, there is a reasonable chance of baseline imbalance between the experimental and control groups. This imbalance threatens the validity of inferences regarding post‐treatment intervention effects unless an appropriate statistical adjustment is used. Here, we consider application of the propensity score adjustment for cluster RCTs. For the purpose of illustration, we apply the propensity adjustment to a cluster RCT that evaluated an intervention to reduce suicidal ideation and depression. This approach to adjusting imbalance had considerable bearing on the interpretation of results. A simulation study demonstrates that the propensity adjustment reduced well over 90% of the bias seen in unadjusted models for the specifications examined. Copyright © 2013 John Wiley & Sons, Ltd.     

Addressing potential prior‐data conflict when using informative priors in proof‐of‐concept studies

Bayesian methods are increasingly used in proof‐of‐concept studies. An important benefit of these methods is the potential to use informative priors, thereby reducing sample size. This is particularly relevant for treatment arms where there is a substantial amount of historical information such as placebo and active comparators. One issue with using an informative prior is the possibility of a mismatch between the informative prior and the observed data, referred to as prior‐data conflict. We focus on two methods for dealing with this: a testing approach and a mixture prior approach. The testing approach assesses prior‐data conflict by comparing the observed data to the prior predictive distribution and resorting to a non‐informative prior if prior‐data conflict is declared. The mixture prior approach uses a prior with a precise and diffuse component. We assess these approaches for the normal case via simulation and show they have some attractive features as compared with the standard one‐component informative prior. For example, when the discrepancy between the prior and the data is sufficiently marked, and intuitively, one feels less certain about the results, both the testing and mixture approaches typically yield wider posterior‐credible intervals than when there is no discrepancy. In contrast, when there is no discrepancy, the results of these approaches are typically similar to the standard approach. Whilst for any specific study, the operating characteristics of any selected approach should be assessed and agreed at the design stage; we believe these two approaches are each worthy of consideration. Copyright © 2015 John Wiley & Sons, Ltd.     

Applications of Bayesian analysis to proof‐of‐concept trial planning and decision making

Decision making is a critical component of a new drug development process. Based on results from an early clinical trial such as a proof of concept trial, the sponsor can decide whether to continue, stop, or defer the development of the drug. To simplify and harmonize the decision‐making process, decision criteria have been proposed in the literature. One of them is to exam the location of a confidence bar relative to the target value and lower reference value of the treatment effect. In this research, we modify an existing approach by moving some of the “stop” decision to “consider” decision so that the chance of directly terminating the development of a potentially valuable drug can be reduced. As Bayesian analysis has certain flexibilities and can borrow historical information through an inferential prior, we apply the Bayesian analysis to the trial planning and decision making. Via a design prior, we can also calculate the probabilities of various decision outcomes in relationship with the sample size and the other parameters to help the study design. An example and a series of computations are used to illustrate the applications, assess the operating characteristics, and compare the performances of different approaches.     

An exact test for comparing two predictive values in small‐size clinical trials

Positive and negative predictive values describe the performance of a diagnostic test. There are several methods to test the equality of predictive values in paired designs. However, these methods were premised on large sample theory, and they may not be suitable for small‐size clinical trials because of inflation of the type 1 error rate. In this study, we propose an exact test to control the type 1 error rate strictly for conducting a small‐size clinical trial that investigates the equality of predictive values in paired designs. In addition, we execute simulation studies to evaluate the performance of the proposed exact test and existing methods in small‐size clinical trials. The proposed test can calculate the exact P value, and as a result of simulations, the empirical type 1 error rate for the proposed test did not exceed the significance level regardless of the setting, and the empirical power for the proposed test is not much different from the other methods based on large‐sample theory. Therefore, it is considered that the proposed exact test is useful when the type 1 error rate needs to be controlled strictly.     

Decision‐making in a phase II clinical trial: a new approach combining Bayesian and frequentist concepts

The aim of a phase II clinical trial is to decide whether or not to develop an experimental therapy further through phase III clinical evaluation. In this paper, we present a Bayesian approach to the phase II trial, although we assume that subsequent phase III clinical trials will have standard frequentist analyses. The decision whether to conduct the phase III trial is based on the posterior predictive probability of a significant result being obtained. This fusion of Bayesian and frequentist techniques accepts the current paradigm for expressing objective evidence of therapeutic value, while optimizing the form of the phase II investigation that leads to it. By using prior information, we can assess whether a phase II study is needed at all, and how much or what sort of evidence is required. The proposed approach is illustrated by the design of a phase II clinical trial of a multi‐drug resistance modulator used in combination with standard chemotherapy in the treatment of metastatic breast cancer. Copyright © 2005 John Wiley & Sons, Ltd     

A simulation study of methods for selecting subgroup‐specific doses in phase 1 trials

Patient heterogeneity may complicate dose‐finding in phase 1 clinical trials if the dose‐toxicity curves differ between subgroups. Conducting separate trials within subgroups may lead to infeasibly small sample sizes in subgroups having low prevalence. Alternatively,it is not obvious how to conduct a single trial while accounting for heterogeneity. To address this problem,we consider a generalization of the continual reassessment method on the basis of a hierarchical Bayesian dose‐toxicity model that borrows strength between subgroups under the assumption that the subgroups are exchangeable. We evaluate a design using this model that includes subgroup‐specific dose selection and safety rules. A simulation study is presented that includes comparison of this method to 3 alternative approaches,on the basis of nonhierarchical models,that make different types of assumptions about within‐subgroup dose‐toxicity curves. The simulations show that the hierarchical model‐based method is recommended in settings where the dose‐toxicity curves are exchangeable between subgroups. We present practical guidelines for application and provide computer programs for trial simulation and conduct.