An empirical Bayes approach to evaluation of results for a specific region in multiregional clinical trials

To accelerate the drug development process and shorten approval time, the design of multiregional clinical trials (MRCTs) incorporates subjects from many countries/regions around the world under the same protocol. After showing the overall efficacy of a drug in all global regions, one can also simultaneously evaluate the possibility of applying the overall trial results to all regions and subsequently support drug registration in each of them. In this paper, we focus on a specific region and establish a statistical criterion to assess the consistency between the specific region and overall results in an MRCT. More specifically, we treat each region in an MRCT as an independent clinical trial, and each perhaps has different treatment effect. We then construct the empirical prior information for the treatment effect for the specific region on the basis of all of the observed data from other regions. We will conclude similarity between the specific region and all regions if the posterior probability of deriving a positive treatment effect in the specific region is large, say 80%. Numerical examples illustrate applications of the proposed approach in different scenarios. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Regional efficacy evaluation in multi-regional clinical trials using a discounting factor weighted Z test

Multi-regional clinical trial (MRCT) is an efficient design to accelerate drug approval globally. Once the global efficacy of test drug is demonstrated, each local regulatory agency is required to prove effectiveness of test drug in their own population. Meanwhile, the ICH E5/E17 guideline recommends using data from other regions to help evaluate regional drug efficacy. However, one of the most challenges is how to manage to bridge data among multiple regions in an MRCT since various intrinsic and extrinsic factors exist among the participating regions. Furthermore, it is critical for a local agency to determine the proportion of information borrowing from other regions given the ethnic differences between target region and non-target regions. To address these issues, we propose a discounting factor weighted Z statistic to adaptively borrow information from non-target regions. In this weighted Z statistic, the weight is derived from a discounting factor in which the discounting factor denotes the proportion of information borrowing from non-target regions. We consider three ways to construct discounting factors based on the degree of congruency between target and non-target regions either using control group data, or treatment group data, or all data. We use the calibrated power prior to construct discounting factor based on scaled Kolmogorov–Smirnov statistic. Comprehensive simulation studies show that our method has desirable operating characteristics. Two examples are used to illustrate the applications of our proposed approach.     

Establishing consistency across all regions in a multi-regional clinical trial

In recent years, global collaboration has become a conventional strategy for new drug development. To accelerate the development process and shorten approval time, the design of multi-regional clinical trials (MRCTs) incorporates subjects from many countries/regions around the world under the same protocol. After showing the overall efficacy of a drug in a global trial, one can also simultaneously evaluate the possibility of applying the overall trial results to all regions and subsequently support drug registration in each region. However, most of the recent approaches developed for the design and evaluation of MRCTs focus on establishing criteria to examine whether the overall results from the MRCT can be applied to a specific region. In this paper, we use the consistency criterion of Method 1 from the Japanese Ministry of Health, Labour and Welfare (MHLW) guidance to assess whether the overall results from the MRCT can be applied to all regions. Sample size determination for the MRCT is also provided to take all the consistency criteria from each individual region into account. Numerical examples are given to illustrate applications of the proposed approach.     

Bayes and empirical Bayes shrinkage estimation of regression coefficients

For a moderate or large number of regression coefficients, shrinkage estimates towards an overall mean are obtained by Bayes and empirical Bayes methods. For a special case, the Bayes and empirical Bayes shrinking weights are shown to be asymptotically equivalent as the amount of shrinkage goes to zero. Based on comparisons between Bayes and empirical Bayes solutions, a modification of the empirical Bayes shrinking weights designed to guard against unreasonable overshrinking is suggested. A numerical example is given.     

Empirical bayes shrinkage estimation of reliability in the exponential distribution

In this paper we propose two empirical Bayes shrinkage estimators for the reliability of the exponential distribution and study their properties. Under the uniform prior distribution and the inverted gamma prior distribution these estimators are developed and compared with a preliminary test estimator and with a shrinkage testimator in terms of mean squared error. The proposed empirical Bayes shrinkage estimator under the inverted gamma prior distribution is shown to be preferable to the preliminary test estimator and the shrinkage testimator when the prior value of mean life is clsoe to the true mean life.     

An application of a minimax Bayes rule and shrinkage estimators to the portofolio selection problem under the Bayesian approach

This paper shows that a minimax Bayes rule and shrinkage estimators can be effectively applied to portfolio selection under the Bayesian approach. Specifically, it is shown that the portfolio selection problem can result in a statistical decision problem in some situations. Following that, we present a method for solving a problem involved in portfolio selection under the Bayesian approach.     

A sufficient condition for the MSE dominance of the positive-part shrinkage estimator when each individual regression coefficient is estimated in a misspecified linear regression model

In this paper, assuming that there exist omitted explanatory variables in the specified model, we derive the exact formula for the mean squared error (MSE) of a general family of shrinkage estimators for each individual regression coefficient. It is shown analytically that when our concern is to estimate each individual regression coefficient, the positive-part shrinkage estimators have smaller MSE than the original shrinkage estimators under some conditions even when the relevant regressors are omitted. Also, by numerical evaluations, we showed the effects of our theorem for several specific cases. It is shown that the positive-part shrinkage estimators have smaller MSE than the original shrinkage estimators for wide region of parameter space even when there exist omitted variables in the specified model.     

Strong consistency of non parametric kernel regression estimator for strong mixing samples

For α-mixing samples, we study Priestley–Chao kernel estimator for non parametric regression model. By using the moment inequality and the exponential inequality, the strong consistency and the uniformly strong consistency of the estimator are obtained for some weak conditions.     

Nonparametric empirical Bayes method for comparison of treatment effects with application to stress urinary incontinence data

Hierarchical models are widely used in medical research to structure complicated models and produce statistical inferences. In a hierarchical model, observations are sampled conditional on some parameters and these parameters are sampled from a common prior distribution. Bayes and empirical Bayes (EB) methods have been effectively applied in analyzing these models. Despite many successes, parametric Bayes and EB methods may be sensitive to misspecification of prior distributions. In this paper, without specific restriction on the form of the prior distribution, we propose a nonparametric EB method to estimate the treatment effect of each group and develop a testing procedure to compare between-group differences. Simulation studies demonstrate that the proposed EB method was more efficient than some standard procedures. An illustrative example is provided with data from a clinical trial evaluating a new treatment for patients with stress urinary incontinence.     

An efficient sequential design of clinical trials

We propose an efficient group sequential monitoring rule for clinical trials. At each interim analysis both efficacy and futility are evaluated through a specified loss structure together with the predicted power. The proposed design is robust to a wide range of priors, and achieves the specified power with a saving of sample size compared to existing adaptive designs. A method is also proposed to obtain a reduced-bias estimator of treatment difference for the proposed design. The new approaches hold great potential for efficiently selecting a more effective treatment in comparative trials. Operating characteristics are evaluated and compared with other group sequential designs in empirical studies. An example is provided to illustrate the application of the method.     

Alone,together: On the benefits of Bayesian borrowing in a meta-analytic setting

It is common practice to use hierarchical Bayesian model for the informing of a pediatric randomized controlled trial (RCT) by adult data, using a prespecified borrowing fraction parameter (BFP). This implicitly assumes that the BFP is intuitive and corresponds to the degree of similarity between the populations. Generalizing this model to any $K\ge 1$ historical studies, naturally leads to empirical Bayes meta-analysis. In this paper we calculate the Bayesian BFPs and study the factors that drive them. We prove that simultaneous mean squared error reduction relative to an uninformed model is always achievable through application of this model. Power and sample size calculations for a future RCT, designed to be informed by multiple external RCTs, are also provided. Potential applications include inference on treatment efficacy from independent trials involving either heterogeneous patient populations or different therapies from a common class.     

The potential for bias in reporting of industry-sponsored clinical trials

Concerns about potentially misleading reporting of pharmaceutical industry research have surfaced many times. The potential for duality (and thereby conflict) of interest is only too clear when you consider the sums of money required for the discovery, development and commercialization of new medicines. As the ability of major, mid-size and small pharmaceutical companies to innovate has waned, as evidenced by the seemingly relentless decline in the numbers of new medicines approved by Food and Drug Administration and European Medicines Agency year-on-year, not only has the cost per new approved medicine risen: so too has the public and media concern about the extent to which the pharmaceutical industry is open and honest about the efficacy, safety and quality of the drugs we manufacture and sell. In 2005 an Editorial in Journal of the American Medical Association made clear that, so great was their concern about misleading reporting of industry-sponsored studies, henceforth no article would be published that was not also guaranteed by independent statistical analysis. We examine the precursors to this Editorial, as well as its immediate and lasting effects for statisticians, for the manner in which statistical analysis is carried out, and for the industry more generally.     

Asymptotic normality and mean consistency for the weighted estimator in nonparametric regression models

In this paper, we mainly study the asymptotic properties of weighted estimator for the nonparametric regression model based on linearly negative quadrant dependent (LNQD, for short) errors. We obtain the rate of uniformly asymptotic normality of the weighted estimator which is nearly $O\left(n^{?1∕4}\right)$ when the moment condition is appropriate. The results generalize the corresponding ones of Yang (2003) from NA samples to LNQD samples and improve or extend the corresponding one of Li et al. (2012) for LNQD samples. Moreover, we obtain some results on mean consistency, uniformly mean consistency, and the rate of mean consistency for the weighted estimator. Finally we carry out some simulations to verify the validity of our results.     

Inference on treatment effects for targeted clinical trials under enrichment design

After completion of a human genome project, the disease targets at molecular level can be identified. As a result, treatment modality for molecular targets can be developed. In practice, targeted clinical trials are usually conducted for evaluation of the possibility and feasibility of the individualized treatment of patients. However, the accuracy of diagnostic devices for identification of such molecular targets is usually not perfect. Therefore, some of the patients enrolled in targeted clinical trials with a positive result by the diagnostic device might not have the specific molecular targets and hence the treatment effects of the targeted drugs estimated from targeted clinical trials could be biased for the patient population truly with the molecular targets. Under an enrichment design for targeted clinical trials, we propose to use the EM algorithm and bootstrap method for obtaining the inference of the treatment effects of the targeted drugs in the patient population truly with molecular targets. A simulation study was conducted to empirically investigate the bias and variability of the proposed estimator and the size and power of the proposed testing method. Simulation results demonstrate that the proposed estimator is unbiased with adequate precision and the confidence interval can provide satisfactory coverage probability. In addition, the proposed testing procedure can adequately control the size with sufficient power. A practical example illustrates the utility of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Proposed best practice for statisticians in the reporting and publication of pharmaceutical industry‐sponsored clinical trials

In this paper we set out what we consider to be a set of best practices for statisticians in the reporting of pharmaceutical industry‐sponsored clinical trials. We make eight recommendations covering: author responsibilities and recognition; publication timing; conflicts of interest; freedom to act; full author access to data; trial registration and independent review. These recommendations are made in the context of the prominent role played by statisticians in the design, conduct, analysis and reporting of pharmaceutical sponsored trials and the perception of the reporting of these trials in the wider community. Copyright © 2010 John Wiley & Sons, Ltd.     

Global benefit-risk assessment in designing clinical trials and some statistical considerations of the method

When characterizing a therapy, the efficacy and the safety are two major aspects under consideration. In prescribing a therapy to a patient, a clinician puts the two aspects together and makes a decision based on a consolidated thought process. The global benefit-risk (GBR) measures proposed by Chuang-Stein et al. (Stat. Med. 1991; 10:1349-1359) are useful in facilitating the thinking, and creating the framework for making statistical comparisons based on benefit-risk point of view. This article describes how a GBR linear score was defined and used as the primary outcome measure in a clinical trial design. The robustness of the definitions of 'benefit' and 'risk' are evaluated using different criteria. The sensitivity of the pre-specified weights is also analyzed using alternative weights; one of those was determined by the relative to an identified distribution integral transformation approach (Biometrics 1958; 14:18-38). Statistical considerations are illustrated using pooled data from clinical trials studying antidepressant. The pros and cons for using GBR assessments in the setting of clinical trials are discussed.     

Exploring changes in treatment effects across design stages in adaptive trials

The recently published Committee for Medicinal Products for Human Use reflection paper on flexible designs highlights a controversial issue regarding the interpretation of adaptive trials. The guideline suggests that a test for heterogeneity should be preplanned and if treatment effect estimates differ significantly between design stages then data collected before and after the interim analysis might not be combined in a formal analysis. In this paper we investigate error rates for such a procedure in the presence of calendar-time effects. Furthermore, we present an alternative testing strategy based on change point methods. In a simulation study we demonstrate that our procedure performs well in comparison to that suggested by the guideline.     

Methods for exploring treatment effect heterogeneity in subgroup analysis: an application to global clinical trials

Multi‐country randomised clinical trials (MRCTs) are common in the medical literature, and their interpretation has been the subject of extensive recent discussion. In many MRCTs, an evaluation of treatment effect homogeneity across countries or regions is conducted. Subgroup analysis principles require a significant test of interaction in order to claim heterogeneity of treatment effect across subgroups, such as countries in an MRCT. As clinical trials are typically underpowered for tests of interaction, overly optimistic expectations of treatment effect homogeneity can lead researchers, regulators and other stakeholders to over‐interpret apparent differences between subgroups even when heterogeneity tests are insignificant. In this paper, we consider some exploratory analysis tools to address this issue. We present three measures derived using the theory of order statistics, which can be used to understand the magnitude and the nature of the variation in treatment effects that can arise merely as an artefact of chance. These measures are not intended to replace a formal test of interaction but instead provide non‐inferential visual aids, which allow comparison of the observed and expected differences between regions or other subgroups and are a useful supplement to a formal test of interaction. We discuss how our methodology differs from recently published methods addressing the same issue. A case study of our approach is presented using data from the Study of Platelet Inhibition and Patient Outcomes (PLATO), which was a large cardiovascular MRCT that has been the subject of controversy in the literature. An R package is available that implements the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd.