A nonparametric test for proving noninferiority in clinical trials with ordered categorical data

We consider the problem of proving noninferiority when the comparison is based on ordered categorical data. We apply a rank test based on the Wilcoxon–Mann–Whitney effect where the asymptotic variance is estimated consistently under the alternative and a small‐sample approximation is given. We give the associated 100(1?α)% confidence interval and propose a formula for sample size determination. Finally, we illustrate the procedure and possible choices of the noninferiority margin using data from a clinical trial. Copyright © 2003 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.     

Bayesian borrowing from historical control data in a vaccine efficacy trial

In the context of vaccine efficacy trial where the incidence rate is very low and a very large sample size is usually expected, incorporating historical data into a new trial is extremely attractive to reduce sample size and increase estimation precision. Nevertheless, for some infectious diseases, seasonal change in incidence rates poses a huge challenge in borrowing historical data and a critical question is how to properly take advantage of historical data borrowing with acceptable tolerance to between-trials heterogeneity commonly from seasonal disease transmission. In this article, we extend a probability-based power prior which determines the amount of information to be borrowed based on the agreement between the historical and current data, to make it applicable for either a single or multiple historical trials available, with constraint on the amount of historical information to be borrowed. Simulations are conducted to compare the performance of the proposed method with other methods including modified power prior (MPP), meta-analytic-predictive (MAP) prior and the commensurate prior methods. Furthermore, we illustrate the application of the proposed method for trial design in a practical setting.     

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.     

Use of a historical control group in a noninferiority trial assessing a new antibacterial treatment: A case study and discussion of practical implementation aspects

When recruitment into a clinical trial is limited due to rarity of the disease of interest, or when recruitment to the control arm is limited due to ethical reasons (eg, pediatric studies or important unmet medical need), exploiting historical controls to augment the prospectively collected database can be an attractive option. Statistical methods for combining historical data with randomized data, while accounting for the incompatibility between the two, have been recently proposed and remain an active field of research. The current literature is lacking a rigorous comparison between methods but also guidelines about their use in practice. In this paper, we compare the existing methods based on a confirmatory phase III study design exercise done for a new antibacterial therapy with a binary endpoint and a single historical dataset. A procedure to assess the relative performance of the different methods for borrowing information from historical control data is proposed, and practical questions related to the selection and implementation of methods are discussed. Based on our examination, we found that the methods have a comparable performance, but we recommend the robust mixture prior for its ease of implementation.     

Vaccine clinical trials with dynamic borrowing of historical controls: Two retrospective studies

Traditional vaccine efficacy trials usually use fixed designs with fairly large sample sizes. Recruiting a large number of subjects requires longer time and higher costs. Furthermore, vaccine developers are more than ever facing the need to accelerate vaccine development to fulfill the public's medical needs. A possible approach to accelerate development is to use the method of dynamic borrowing of historical controls in clinical trials. In this paper, we evaluate the feasibility and the performance of this approach in vaccine development by retrospectively analyzing two real vaccine studies: a relatively small immunological trial (typical early phase study) and a large vaccine efficacy trial (typical Phase 3 study) assessing prophylactic human papillomavirus vaccine. Results are promising, particularly for early development immunological studies, where the adaptive design is feasible, and control of type I error is less relevant.     

Adaptive power priors with empirical Bayes for clinical trials

Incorporating historical information into the design and analysis of a new clinical trial has been the subject of much discussion as a way to increase the feasibility of trials in situations where patients are difficult to recruit. The best method to include this data is not yet clear, especially in the case when few historical studies are available. This paper looks at the power prior technique afresh in a binomial setting and examines some previously unexamined properties, such as Box P values, bias, and coverage. Additionally, it proposes an empirical Bayes‐type approach to estimating the prior weight parameter by marginal likelihood. This estimate has advantages over previously criticised methods in that it varies commensurably with differences in the historical and current data and can choose weights near 1 when the data are similar enough. Fully Bayesian approaches are also considered. An analysis of the operating characteristics shows that the adaptive methods work well and that the various approaches have different strengths and weaknesses.     

Tests for noninferiority trials with binomial endpoints: A guide to modern and quasi‐exact methods for biomedical researchers

Applied statisticians and pharmaceutical researchers are frequently involved in the design and analysis of clinical trials where at least one of the outcomes is binary. Treatments are judged by the probability of a positive binary response. A typical example is the noninferiority trial, where it is tested whether a new experimental treatment is practically not inferior to an active comparator with a prespecified margin δ. Except for the special case of δ = 0, no exact conditional test is available although approximate conditional methods (also called second‐order methods) can be applied. However, in some situations, the approximation can be poor and the logical argument for approximate conditioning is not compelling. The alternative is to consider an unconditional approach. Standard methods like the pooled z‐test are already unconditional although approximate. In this article, we review and illustrate unconditional methods with a heavy emphasis on modern methods that can deliver exact, or near exact, results. For noninferiority trials based on either rate difference or rate ratio, our recommendation is to use the so‐called E‐procedure, based on either the score or likelihood ratio statistic. This test is effectively exact, computationally efficient, and respects monotonicity constraints in practice. We support our assertions with a numerical study, and we illustrate the concepts developed in theory with a clinical example in pulmonary oncology; R code to conduct all these analyses is available from the authors.     

Conservative prior distributions for variance parameters in hierarchical models

Bayesian hierarchical models typically involve specifying prior distributions for one or more variance components. This is rather removed from the observed data, so specification based on expert knowledge can be difficult. While there are suggestions for “default” priors in the literature, often a conditionally conjugate inverse‐gamma specification is used, despite documented drawbacks of this choice. The authors suggest “conservative” prior distributions for variance components, which deliberately give more weight to smaller values. These are appropriate for investigators who are skeptical about the presence of variability in the second‐stage parameters (random effects) and want to particularly guard against inferring more structure than is really present. The suggested priors readily adapt to various hierarchical modelling settings, such as fitting smooth curves, modelling spatial variation and combining data from multiple sites.     

Marginalized transition random effect models for multivariate longitudinal binary data

Generalized linear models with random effects and/or serial dependence are commonly used to analyze longitudinal data. However, the computation and interpretation of marginal covariate effects can be difficult. This led Heagerty (1999, 2002) to propose models for longitudinal binary data in which a logistic regression is first used to explain the average marginal response. The model is then completed by introducing a conditional regression that allows for the longitudinal, within‐subject, dependence, either via random effects or regressing on previous responses. In this paper, the authors extend the work of Heagerty to handle multivariate longitudinal binary response data using a triple of regression models that directly model the marginal mean response while taking into account dependence across time and across responses. Markov Chain Monte Carlo methods are used for inference. Data from the Iowa Youth and Families Project are used to illustrate the methods.     

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.     

Bayesian design and analysis of composite endpoints in clinical trials with multiple dependent binary outcomes

The author considers studies with multiple dependent primary endpoints. Testing hypotheses with multiple primary endpoints may require unmanageably large populations. Composite endpoints consisting of several binary events may be used to reduce a trial to a manageable size. The primary difficulties with composite endpoints are that different endpoints may have different clinical importance and that higher‐frequency variables may overwhelm effects of smaller, but equally important, primary outcomes. To compensate for these inconsistencies, we weight each type of event, and the total number of weighted events is counted. To reflect the mutual dependency of primary endpoints and to make the weighting method effective in small clinical trials, we use the Bayesian approach. We assume a multinomial distribution of multiple endpoints with Dirichlet priors and apply the Bayesian test of noninferiority to the calculation of weighting parameters. We use composite endpoints to test hypotheses of superiority in single‐arm and two‐arm clinical trials. The composite endpoints have a beta distribution. We illustrate this technique with an example. The results provide a statistical procedure for creating composite endpoints. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.     

Design and analysis of a 3‐arm noninferiority trial with a prespecified margin for the hazard ratio

A 3‐arm trial design that includes an experimental treatment, an active reference treatment, and a placebo is useful for assessing the noninferiority of an experimental treatment. The inclusion of a placebo arm enables the assessment of assay sensitivity and internal validation, in addition to the testing of the noninferiority of the experimental treatment compared with the reference treatment. In 3‐arm noninferiority trials, various statistical test procedures have been considered to evaluate the following 3 hypotheses: (i) superiority of the experimental treatment over the placebo, (ii) superiority of the reference treatment over the placebo, and (iii) noninferiority of the experimental treatment compared with the reference treatment. However, hypothesis (ii) can be insufficient and may not accurately assess the assay sensitivity for the noninferiority of the experimental treatment compared with the reference treatment. Thus, demonstrating that the superiority of the reference treatment over the placebo is greater than the noninferiority margin (the nonsuperiority of the reference treatment compared with the placebo) can be necessary. Here, we propose log‐rank statistical procedures for evaluating data obtained from 3‐arm noninferiority trials to assess assay sensitivity with a prespecified margin Δ. In addition, we derive the approximate sample size and optimal allocation required to minimize the total sample size and that of the placebo treatment sample size, hierarchically.     

Bayesian predictive power: choice of prior and some recommendations for its use as probability of success in drug development

Bayesian predictive power, the expectation of the power function with respect to a prior distribution for the true underlying effect size, is routinely used in drug development to quantify the probability of success of a clinical trial. Choosing the prior is crucial for the properties and interpretability of Bayesian predictive power. We review recommendations on the choice of prior for Bayesian predictive power and explore its features as a function of the prior. The density of power values induced by a given prior is derived analytically and its shape characterized. We find that for a typical clinical trial scenario, this density has a u‐shape very similar, but not equal, to a β‐distribution. Alternative priors are discussed, and practical recommendations to assess the sensitivity of Bayesian predictive power to its input parameters are provided. Copyright © 2016 John Wiley & Sons, Ltd.     

A Bayesian adaptive design for biosimilar trials with time-to-event endpoint

A biosimilar drug is a biological product that is highly similar to and at the same time has no clinically meaningful difference from licensed product in terms of safety, purity, and potency. Biosimilar study design is essential to demonstrate the equivalence between biosimilar drug and reference product. However, existing designs and assessment methods are primarily based on binary and continuous endpoints. We propose a Bayesian adaptive design for biosimilarity trials with time-to-event endpoint. The features of the proposed design are twofold. First, we employ the calibrated power prior to precisely borrow relevant information from historical data for the reference drug. Second, we propose a two-stage procedure using the Bayesian biosimilarity index (BBI) to allow early stop and improve the efficiency. Extensive simulations are conducted to demonstrate the operating characteristics of the proposed method in contrast with some naive method. Sensitivity analysis and extension with respect to the assumptions are presented.     

Calibrating the prior distribution for a normal model with conjugate prior

For a normal model with a conjugate prior, we provide an in-depth examination of the effects of the hyperparameters on the long-run frequentist properties of posterior point and interval estimates. Under an assumed sampling model for the data-generating mechanism, we examine how hyperparameter values affect the mean-squared error (MSE) of posterior means and the true coverage of credible intervals. We develop two types of hyperparameter optimality. MSE optimal hyperparameters minimize the MSE of posterior point estimates. Credible interval optimal hyperparameters result in credible intervals that have a minimum length while still retaining nominal coverage. A poor choice of hyperparameters has a worse consequence on the credible interval coverage than on the MSE of posterior point estimates. We give an example to demonstrate how our results can be used to evaluate the potential consequences of hyperparameter choices.     

A novel equivalence probability weighted power prior for using historical control data in an adaptive clinical trial design: A comparison to standard methods

A standard two-arm randomised controlled trial usually compares an intervention to a control treatment with equal numbers of patients randomised to each treatment arm and only data from within the current trial are used to assess the treatment effect. Historical data are used when designing new trials and have recently been considered for use in the analysis when the required number of patients under a standard trial design cannot be achieved. Incorporating historical control data could lead to more efficient trials, reducing the number of controls required in the current study when the historical and current control data agree. However, when the data are inconsistent, there is potential for biased treatment effect estimates, inflated type I error and reduced power. We introduce two novel approaches for binary data which discount historical data based on the agreement with the current trial controls, an equivalence approach and an approach based on tail area probabilities. An adaptive design is used where the allocation ratio is adapted at the interim analysis, randomising fewer patients to control when there is agreement. The historical data are down-weighted in the analysis using the power prior approach with a fixed power. We compare operating characteristics of the proposed design to historical data methods in the literature: the modified power prior; commensurate prior; and robust mixture prior. The equivalence probability weight approach is intuitive and the operating characteristics can be calculated exactly. Furthermore, the equivalence bounds can be chosen to control the maximum possible inflation in type I error.     

Bayesian inference in two‐arm trials using relative belief ratios

Various methodologies proposed for some inference problems associated with two‐arm trails are known to suffer from difficulties, as documented in Senn (2001). We propose an alternative Bayesian approach to these problems that deals with these difficulties through providing an explicit measure of statistical evidence and the strength of this evidence. Bayesian methods are often criticized for their intrinsic subjectivity. We show how these concerns can be dealt with through assessing the bias induced by a prior model checking and checking for prior‐data conflict. Copyright © 2015 John Wiley & Sons, Ltd.     

Inference methods for saturated models in longitudinal clinical trials with incomplete binary data

In the longitudinal studies with binary response, it is often of interest to estimate the percentage of positive responses at each time point and the percentage of having at least one positive response by each time point. When missing data exist, the conventional method based on observed percentages could result in erroneous estimates. This study demonstrates two methods of using expectation-maximization (EM) and data augmentation (DA) algorithms in the estimation of the marginal and cumulative probabilities for incomplete longitudinal binary response data. Both methods provide unbiased estimates when the missingness mechanism is missing at random (MAR) assumption. Sensitivity analyses have been performed for cases when the MAR assumption is in question.     

A natural conjugate prior for the non-homogeneous poisson process with a power law intensity function

This paper develops a natural conjugate prior for the non-homogeneous Poisson process (NHPP) with a power law intensity function. This prior allows for dependence between the scale factor and the aging rate of the NHPP. The proposed prior has relatively simple closed-form expressions for its moments, facilitating the assessment of prior parameters. The use of this prior in Bayesian estimation is compared to other estimation approaches using Monte Carlo simulation. The results show that Bayesian estimation using the proposed prior generally performs at least as well as either maximum likelihood estimation or Bayesian estimation using independent prior