Sample Size Re-estimation Designs In Confirmatory Clinical Trials—Current State,Statistical Considerations,and Practical Guidance

A sample size re-estimation (SSR) design is a flexible, adaptive design with the primary purpose of allowing sample size of a study to be reassessed in the mid-course of the study to ensure adequate power. In real world drug product, biologic, and device development, there may be large uncertainty in key factors that drive the sample size estimation for a confirmatory clinical trial. For example, early phase studies may have encouraging results but could be of shorter duration, or use a different endpoint than what is required for confirmatory phase clinical trials. The negative impact of high uncertainty at design stage for a confirmatory trial can be mitigated by an SSR design. Recent surveys have reported an encouraging upward trend in the use of SSR designs in clinical trials since the release of the draft guidance for adaptive design clinical trials for drugs and biologics by the U.S. Food and Drug Administration in 2010 (U.S. Food and Drug Administration (FDA) (February, 2010), Draft Guidance for Industry: Adaptive Design Clinical Trials for Drugs and Biologics). To support broad understanding and acceptance of SSR designs in confirmatory settings, especially unblinded SSR designs, we summarize statistical methods pertaining to SSR designs, including recent development in this field, and discuss design alternatives among blinded SSR, unblinded SSR, and conventional group sequential designs. To support appropriate implementation of SSR designs, we make recommendations on operational logistics for trial conduct based on accumulated experience in recent years, and provide points to consider for final data analysis and reporting for studies where the sample size has been increased following either a blinded or an unblinded SSR algorithm.     

Sample sizes for comparative inhaled corticosteroid trials with emphasis on showing therapeutic equivalence

In the near future it is to be expected that many new inhaled corticosteroids or formulations of these drugs will be compared with older ones, to discover whether they are therapeutically equivalent or not. The statistical evaluation of these trials differs from the classic methods. When two averages are similar or differ only slightly, power is very low. The regulatory bodies demand a power of at least 80%. This problem was initially solved by using the so-called power approach. Researchers included enough volunteers to enable them to detect a predefined difference, considered to be without any clinical significance, with a power of 80%. This approach, however, has been shown to be incorrect and has been replaced by the two one-sided tests procedure, where a new sample size equation is derived. Important elements of this new equation are the coefficient of variation of the parameter measured, the difference between the averages of the two groups and the equivalence limit (the difference between the means still tolerable). This equation was used in the present study to estimate the number of volunteers needed in a parallel inhaled corticosteroids equivalence trial. The end points chosen were the changes in FEV₁ and PC₂₀ due to the corticosteroid effect. Calculations were performed by extracting data from published placebo-controlled trials, and defining a range of equivalence limits and differences between the group averages. It was shown that a huge number of volunteers (500–1000) will be needed, as a result of the small corticosteroid effect and the high variance. In the case of inhaled corticosteroids, the equivalence limit is not known and needs defining to avoid discussions on the outcome. Due to the high number of patients who need to be included, the trial will most probably be multicentre and take place in several countries. Such a trial will suffer from several sources of bias. For instance, the definition of asthma can differ from country to country and from researcher to researcher, resulting in non-comparable groups of patients. The many sources of bias will make the outcome difficult to interpret. Therefore alternative methods to establish therapeutic equivalence are proposed and discussed.     

Adaptive strategies in designing the simultaneous global drug development program

Many methods have been proposed to account for the potential impact of ethnic/regional factors when extrapolating results from multiregional clinical trials (MRCTs) to targeted ethnic (TE) patients, i.e., “bridging.” Most of them either focused on TE patients in the MRCT (i.e., internal bridging) or a separate local clinical trial (LCT) (i.e., external bridging). Huang et al. (2012) integrated both bridging concepts in their method for the Simultaneous Global Drug Development Program (SGDDP) which designs both the MRCT and the LCT prospectively and combines patients in both trials by ethnic origin, i.e., TE vs. non-TE (NTE). The weighted Z test was used to combine information from TE and NTE patients to test with statistical rigor whether a new treatment is effective in the TE population. Practically, the MRCT is often completed before the LCT. Thus to increase the power for the SGDDP and/or obtain more informative data in TE patients, we may use the final results from the MRCT to re-evaluate initial assumptions (e.g., effect sizes, variances, weight), and modify the LCT accordingly. We discuss various adaptive strategies for the LCT such as sample size reassessment, population enrichment, endpoint change, and dose adjustment. As an example, we extend a popular adaptive design method to re-estimate the sample size for the LCT, and illustrate it for a normally distributed endpoint.     

Adaptive clinical endpoint bioequivalence studies with sample size re-estimation based on a nuisance parameter

ABSTRACT

A clinical endpoint bioequivalence (BE) study is often used to establish bioequivalence (BE) between a locally acting generic drug (T) and an innovator drug (R), which is a double-blind, randomized three-arm (T, R and placebo: P) parallel clinical trial. BE is established if two superiority tests (T vs. P, R vs. P) and one equivalence test (T vs. R) all pass. An accurate estimate of the nuisance parameter (e.g. variance) is vital in determining an accurate sample size to attain sufficient power. However, due to potential study design variations between NDA and Abbreviated NDA (ANDA) studies and high variability of clinical endpoints, variance may be over- or under-estimated, resulting in unnecessary extra costs or underpowered studies. Traditionally, clinical endpoint BE studies use a fixed study design. In this work, we propose four sample size re-estimation approaches based on a nuisance parameter and recommend one approach after comparing various operating characteristics by simulation.

The proposed adaptive design with sample size re-estimation provides a more accurate estimate of sample size without wasting resources or under-powering the study and controls the Type 1 error rate under a negligible level, both for the family-wise alpha and individual alpha for superiority and equivalence tests.     

Adaptive design clinical trials and trial logistics models in CNS drug development

In central nervous system therapeutic areas, there are general concerns with establishing efficacy thought to be sources of high attrition rate in drug development. For instance, efficacy endpoints are often subjective and highly variable. There is a lack of robust or operational biomarkers to substitute for soft endpoints. In addition, animal models are generally poor, unreliable or unpredictive. To increase the probability of success in central nervous system drug development program, adaptive design has been considered as an alternative designs that provides flexibility to the conventional fixed designs and has been viewed to have the potential to improve the efficiency in drug development processes. In addition, successful implementation of an adaptive design trial relies on establishment of a trustworthy logistics model that ensures integrity of the trial conduct.In accordance with the spirit of the U.S. Food and Drug Administration adaptive design draft guidance document recently released, this paper enlists the critical considerations from both methodological aspects and regulatory aspects in reviewing an adaptive design proposal and discusses two general types of adaptations, sample size planning and re-estimation, and two-stage adaptive design. Literature examples of adaptive designs in central nervous system are used to highlight the principles laid out in the U.S. FDA draft guidance. Four logistics models seen in regulatory adaptive design applications are introduced. In general, complex adaptive designs require simulation studies to access the design performance. For an adequate and well-controlled clinical trial, if a Learn-and-Confirm adaptive selection approach is considered, the study-wise type I error rate should be adhered to. However, it is controversial to use the simulated type I error rate to address a strong control of the study-wise type I error rate.     

临床试验中平行组设计二分类指标样本量的计算

临床试验中所需病例数应符合统计学要求,以确保对所提出的问题给予可靠的回答。样本的大小通常以试验的主要指标来确定,同时应考虑试验设计类型、比较类型等。针对优效/非劣效/等效性试验的目的及统计假设检验和方差,文中介绍了二分类指标平行组试验设计样本量的计算方法和通用公式,并结合临床试验的实际案例对样本量计算进行了应用分析。     

A new statistical procedure for testing equivalence in two-group comparative bioavailability trials

The clinical problem of testing for equivalence in comparative bioavailability trials is restated in terms of the proper statistical hypotheses. A simple t-test procedure for these hypotheses has been devloped that is more powerful than the methods based on usual (shortest) and symmetric confidence intervals. In this note, this new procedure is explained and an example is given, including the method for sample size determination.     

An evaluation of increasing sample size based on conditional power

We evaluate properties of sample size re-estimation (SSR) designs similar to the promising zone design considered by Mehta and Pocock (2011). We evaluate these designs under the assumption of a true effect size of 1.1 down to 0.4 of the protocol-specified effect size by six measures: 1. The probability of a sample size increase, 2. The mean proportional increase in sample size given an increase; 3 and 4. The mean true conditional power with and without a sample size increase; 5 and 6. The expected increase in sample size and power due to the SSR procedure. These measures show the probability of a sample size increase and the cost/benefit for given true effect sizes, particularly when the SSR may either be pursuing a small effect size of little clinical importance or be unnecessary when the true effect size is close to the protocol-specified effect size. The results show the clear superiority of conducting the SSR late in the study and the inefficiency of a mid-study SSR. The results indicate that waiting until late in the study for the SSR yields a smaller, better targeted set of studies with a greater increase in overall power than a mid-study SSR.     

Non-inferiority clinical trials: Practical issues and current regulatory perspective

Non-inferiority clinical trials are being performed with an increasing frequency now-a-days, because it helps in finding a new treatment that have approximately the same efficacy, but may offer other benefits such as better safety profile. Non-inferiority clinical trials aim to demonstrate that the test product is no worse than the comparator by more than a pre-specified small amount. There are several fundamental differences between non-inferiority and superiority trials. Some practical issues concerning the non-inferiority trials are assay sensitivity, choice of the non-inferiority margin, sample size estimation, choice of active-control, and analysis of non-inferiority clinical trials. For serious infections such as hospital-acquired bacterial pneumonia/ventilator-associated bacterial pneumonia, community-acquired bacterial pneumonia, and acute bacterial skin and skin structure infections, the United States Food and Drug Administration (US FDA) has recently recommended that it is possible to define a reliable and consistent estimate of the efficacy of active treatment relative to placebo from available data, which can serve as the basis for defining a new inferiority margin for an active-controlled, non-inferiority trial. But for some indications with a high rate of resolution without antibacterial drug therapy such as acute bacterial sinusitis (ABS), acute bacterial exacerbation of chronic bronchitis (ABECB), and acute bacterial otitis media (ABOM), the US FDA has recommended that the available data will not support the use of a non-inferiority design and other trial designs (i.e., superiority designs) should be used to provide the evidence of effectiveness in these three indications.     

Adaptive design clinical trials: Methodology, challenges and prospect

New drug development is a time-consuming and expensive process. Recently, there has been stagnation in the development of novel compounds. Moreover, the attrition rate in clinical research is also on the rise. Fearing more stagnation, the Food and Drug Administration released the critical path initiative in 2004 and critical path opportunity list in 2006 thus highlighting the need of advancing innovative trial designs. One of the innovations suggested was the adaptive designed clinical trials, a method promoting introduction of pre-specified modifications in the design or statistical procedures of an on-going trial depending on the data generated from the concerned trial thus making a trial more flexible. The adaptive design trials are proposed to boost clinical research by cutting on the cost and time factor. Although the concept of adaptive designed clinical trials is round-the-corner for the last 40 years, there is still lack of uniformity and understanding on this issue. This review highlights important adaptive designed methodologies besides covering the regulatory positions on this issue.     

Two-Stage Sample Size Reassessment Using Perturbed Unblinding

Sample size reassessment (SSR) is an increasingly popular strategy for designing and conducting clinical trials. In particular, SSR based on updating the variance estimate is a prudent practice accepted by the regulatory authorities to assure adequate power for a study. Since its development in the early 1990s, however, debate has continued over whether a treatment-blinded or unblinded approach should be used for SSR based on the variance estimate. A blind procedure is preferred from the regulatory standpoint, because it better preserves the study integrity; however, it does not provide the best-unbiased estimate of the variance. On the other hand, the usual unblinded analysis reveals the treatment effect, which leads to controversy regarding the interpretation of the targeted effect size as well as concerns of inflating the Type I error and possibly biasing the trial. In this article, we devise a novel solution to this problem, one that uses perturbed unblinding to estimate the variance but still keeps the treatment effect masked. We then give a bias-corrected final test, which preserves the Type I error rate. We also discuss several points of consideration, with a focus on the issues of SSR, that were raised at the recent workshop on adaptive designs held jointly by the U.S. Food and Drug Administration (FDA) and the Pharmaceutical Research and Manufacturers of America (PhRMA). In particular, we propose a switch of paradigm from SSR to a two-stage design for clinical trials to alleviate the concern of possible “change” of behavior due to “change” of sample size.     

Unified additional requirement in consideration of regional approval for multiregional clinical trials

To speed up the process of bringing a new drug to the market, more and more clinical trials are being conducted simultaneously in multiple regions. After demonstrating the overall drug’s efficacy across regions, the regulatory and drug sponsor may also want to assess the drug’s effect in specific region(s). Most of the recent approaches imposed a uniform criterion to assess the consistency of treatment effects between the interested region(s) and the entire study population regardless of the number of regions in multiregional clinical trials (MRCT). As a result, the needed sample size to achieve the desired probability of satisfying the regional requirement could be huge and implausible for the trial sponsors to implement.

In this paper, we propose a unified additional requirement for regional approval by differing the parameters in the additional requirement depending on the number of planned regions. In particular, the values of the parameters are determined by a reasonable sample size increase with the desired probability satisfying the additional requirement. Considering the practicality of the global trial or sample size increase, we recommend specific values of the parameters for a different number of planned regions. We also introduce the assurance probability curve to evaluate the performance of different regional requirements.     

随机自适应设计的统计模拟

自适应设计是允许在不破坏试验有效性与安全性的前提下,通过临床中期分析,来发现和更改试验设计之初不合理的假设,降低研发成本,缩短研究周期。本研究借助matlab软件及蒙特卡罗方法,模拟优效性试验中两个治疗组(试验组与控制组)主要终点治疗指标的变化,包括组间差异值,方差,分配比,变异系数及样本容量的取值变化,观察对检验功效的影响。并通过模拟确定临床Ⅱ期实验中所需的最低样本容量。     

Interval estimators of relative potency in toxicology and radiation countermeasure studies: comparing methods and experimental designs

The relative potency of one agent to another is commonly represented by the ratio of two quantal response parameters; for example, the LD₅₀ of animals receiving a treatment to the LD₅₀ of control animals, where LD₅₀ is the dose of toxin that is lethal to 50% of animals. Though others have considered interval estimators of LD₅₀, here, we extend Bayesian, bootstrap, likelihood ratio, Fieller’s and Wald’s methods to estimate intervals for relative potency in a parallel-line assay context. In addition to comparing their coverage probabilities, we also consider their power in two types of dose designs: one assigning treatment and control the same doses vs. one choosing doses for treatment and control to achieve same lethality targets. We explore these methods in realistic contexts of relative potency of radiation countermeasures. For larger experiments (e.g., ≥100 animals), the methods return similar results regardless of the interval estimation method or experiment design. For smaller experiments (e.g., < 60 animals), Wald’s method stands out among the others, producing intervals that hold closely to nominal levels and providing more power than the other methods in statistically efficient designs. Using this simple statistical method within a statistically efficient design, researchers can reduce animal numbers.     

Blinded sample size recalculation in clinical trials with binary composite endpoints

We consider clinical trials with a binary composite endpoint where the trial is successful when a significant result is achieved for the composite or one prespecified main component. Appropriate sample size planning is challenging in this situation, as in addition to the Type I error rate, power, and target difference the overall event rates and the correlation between the test statistics have to be defined. Reliable estimates of these quantities, however, are usually hard to obtain and therefore there is a high risk to not achieve the intended power in a fixed sample size design. In this article, we propose an internal pilot study design where the nuisance parameters are estimated in a blinded way at an interim stage and where the sample size is then revised accordingly. We investigate the characteristics of the proposed design with respect to the actual Type I error rate, power, and sample size. The application of this design is illustrated by a clinical trial example.     

Group-sequential three-arm noninferiority clinical trial designs

We discuss group-sequential three-arm noninferiority clinical trial designs that include active and placebo controls for evaluating both assay sensitivity and noninferiority. We extend two existing approaches, the fixed margin and fraction approaches, into a group-sequential setting with two decision-making frameworks. We investigate the operating characteristics including power, Type I error rate, maximum, and expected sample sizes, as design factors vary. In addition, we discuss sample size recalculation and its impact on the power and Type I error rate via a simulation study.     

临床试验Williams设计中样本含量的估算方法

在临床试验中,2组交叉设计应用已相当广泛,其样本含量估算方法也被研究者所熟悉。多组交叉试验由Williams首先提出,因此被称为Wil-liams设计。本文介绍基于Williams设计的样本含量估算方法,并提供示例分析,供研究者参考使用。     

Curricular considerations for pharmaceutical comparative effectiveness research

In the U.S. pharmacoepidemiology and related health professions can potentially flourish with the congressional appropriation of $1.1 billion of federal funding for comparative effectiveness research (CER). A direct result of this legislation will be the need for sufficient numbers of trained scientists and decision-makers to address the research and implementation associated with CER. An interdisciplinary expert panel comprised mostly of professionals with pharmaceutical interests was convened to examine the knowledge, skills, and abilities to be considered in the development of a CER curriculum for the health professions focusing predominantly on pharmaceuticals. A limitation of the panel's composition was that it did not represent the breadth of comparative effectiveness research, which additionally includes devices, services, diagnostics, behavioral treatments, and delivery system changes. This bias affects the generalizability of these findings. Notwithstanding, important components of the curriculum identified by the panel included study design considerations and understanding the strengths and limitations of data sources. Important skills and abilities included methods for adjustment of differences in comparator group characteristics to control confounding and bias, data management skills, and clinical skills and insights into the relevance of comparisons. Most of the knowledge, skills, and abilities identified by the panel were consistent with the training of pharmacoepidemiologists. While comparative effectiveness is broader than the pharmaceutical sciences, pharmacoepidemiologists have much to offer academic and professional CER training programs. As such, pharmacoepidemiologists should have a central role in curricular design and provision of the necessary training for needed comparative effectiveness researchers within the realm of pharmaceutical sciences.     

An Adaptive Approach to Designing Comparative Diagnostic Accuracy Studies

Comparative diagnostic studies usually involve comparison of the area under receiver operating characteristic curves when biomarkers are measured on a continuous or ordinal scales. In designing such studies, specification of a number of nuisance parameters is often required to compute sample sizes. When these parameters are incorrectly specified, statistical power to detect a meaningful difference in area can be substantially adversely affected. We propose an adaptive method to calculate the sample size and show these procedures to be effective in controlling error rates.