非劣效性/等效性试验中的统计学分析

随着医药事业的发展进步,许多疾病的治疗已有现成的有效药物,以阳性标准治疗而不是安慰剂作为对照的临床试验愈来愈多,导致了许多新药临床研究的目的发生转变,更多遇到的情形是要确认新药的临床疗效是否不差于或者相当于标准的有效药物,因而非劣交性／等效性试验在新药临床试验中占有较大的比例。为此,本文主要根据国际上实施非劣效性／等效性试验的原则和要求,对相应的一些统计学事项进行论述。结合有关的事例,作者较为系统地介绿了临床非劣效性／等效性界值的确定、统计学推断的假设检验和可信区间方法、样本含量及检验效能的计算等。就实际应用中的有关问题,作者还提出进一步的建议和讨论。相信这对于加强生物统计学在我国临床试验中的正确应用,推动我国临床试验与国际的接轨具有重要的现实意义。     

对临床试验统计学假设检验中非劣效、等效和优效性设计的认识

在对国内药物注册临床试验报告的审评中，常遇到以传统显著性检验代替非劣效、等效和优效性检验的错误，就它们的区别及适用范围，本文对判断界值的确定、样本含量、推断结论及审评中的主要关注点进行了阐释。     

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。     

率的等效性检验方法的比较

目的 :对 10种率的等效性检验方法的Ⅰ型误差和检验效能进行比较 ,并据此选择较好的方法估计样本含量 ,以便实际工作者应用。方法 :采用MonteCarlo模拟试验。结果 :10种方法中 ,以Dun nett Gent方法为最佳 ,并按该方法估计了样本含量。模拟试验表明 ,率的等效性检验所需要的样本含量非常大 ,当试验组和参考组各只有 10 0例时 ,任何等效性检验方法的检验效能均较低。结论 :按目前国家食品药品监督管理局规定的最低样本含量 10 0对 ,相应的检验效能很低 ,建议用统计学方法进行估计。     

单组临床试验目标值法的精确样本含量估计及统计推断

目的:针对结局为二分类变量以率作为终点评价指标的单组临床试验,探讨基于二项分布原理进行单组目标值法样本含量估计及统计推断的精确方法。方法:系统综合和全面论述了单组临床试验目标值法所涉及到的样本含量计算、可信区间估计和假设检验的精确方法。结果:按目标值起点为75%,间隔1%增加,给出预期事件发生率起点为76%,间隔1%增加,与目标值对应的精确样本含量结果,并列表给出β在0.20条件下,α分别取单侧和双侧0.05水平下的两套结果,可供直接查用。提供了可信区间估计及假设检验的精确计算公式。结论:为单组临床试验目标值法的样本含量计算、可信区间估计及假设检验提供了系统、实用的方法学支持。     

等效试验的基本概念及其在溶栓药物试验中的应用

近年来等效试验越来越普及，其目的是为了证实2种治疗效果相等。以溶栓药物的临床试验为例，说明在优效试验、等效试验及非劣效试验中疗效相等的基本概念。     

非劣性/等效性试验的样本含量估计及统计推断

就近年应用逐渐增多的非劣性/等效性试验中涉及的一些关键统计学问题进行详细介绍，其中包括设计过程中的非劣性/等效性界值的确定、样本含量的估计方法和统计推断过程中的检验假设建立、检验统计量计算以及可信区间计算方法。结合7个有针对性的应用实例有助于对相关事项的理解和在非劣性/等效性试验时进行参照。     

两均数比较的优效性临床试验样本量估计

如何正确估计两均数比较的优效性临床试验样本量是试验设计阶段的主要研究内容之一。在介绍优效性试验基本概念和样本量估计公式的基础上,通过实例介绍两均数比较的样本量估计,并采用PASS软件演示估计过程,为随机对照临床试验正确估计样本量提供参考。     

临床非劣效性/等效性评价的统计学方法

以安慰剂作为对照的随机双盲临床试验一直被视为药物开发中的金标准,它在确认新的试验药物的疗效优于安慰剂方面发挥着重要的作用。然而,如果有现成的疗效肯定的药物,仍用安慰剂对照做临床试验,会面临伦理上的困难。随着愈来愈多可供应用的有效药物的出现,疗效有突破的新药愈来愈少,因而药物临床研究的目的发生了转变。在阳性对照试验中,更多的情形是探求新药与标准的有效药物相比其疗效是否不差或疗效相等（严格地说,疗效相等应该是既不比标准药差,也不比标准药好）,而并不一定要知道新药是否优于标准药,由此而提出了非劣效性／等效性试验(…     

生物等效性研究现状概述

本文从试验设计、样本含量的估计、受试者的选择以及生物等效性评价方面综述了目前国内外生物等效性研究的现状,总结了生物等效性评价的各种统计分析方法,并提出了一些存在问题.     

Sample Size Calculation for Comparing Two Poisson or Negative Binomial Rates in Noninferiority or Equivalence Trials

Poisson and negative binomial models are frequently used to analyze count data in clinical trials. While several sample size calculation methods have recently been developed for superiority tests for these two models, similar methods for noninferiority and equivalence tests are not available. When a noninferiority or equivalence trial is designed to compare Poisson or negative binomial rates, an appropriate method is needed to estimate the sample size to ensure the trial is properly powered. In this article, several sample size calculation methods for noninferiority and equivalence tests have been derived based on Poisson and negative binomial models. All of these methods accounted for potential over-dispersion that commonly exists in count data obtained from clinical trials. The precision of these methods was evaluated using simulations. Supplementary materials for this article are available online.     

Statistical Considerations for NonInferiority/Equivalence Trials in Vaccine Development

Noninferiority/equivalence designs are often used in vaccine clinical trials. The goal of these designs is to demonstrate that a new vaccine, or new formulation or regimen of an existing vaccine, is similar in terms of effectiveness to the existing vaccine, while offering such advantages as easier manufacturing, easier administration, lower cost, or improved safety profile. These noninferiority/equivalence designs are particularly useful in four common types of immunogenicity trials: vaccine bridging trials, combination vaccine trials, vaccine concomitant use trials, and vaccine consistency lot trials. In this paper, we give an overview of the key statistical issues and recent developments for noninferiority/equivalence vaccine trials. Specifically, we cover the following topics: (i) selection of study endpoints; (ii) formulation of the null and alternative hypotheses; (iii) determination of the noninferiority/equivalence margin; (iv) selection of efficient statistical methods for the statistical analysis of noninferiority/equivalence vaccine trials, with particular emphasis on adjustment for stratification factors and missing pre- or post-vaccination data; and (v) the calculation of sample size and power.     

On the use of the ratio or the odds ratio of cure rates in therapeutic equivalence clinical trials with binary endpoints

We discuss in this paper some issues related to the use of the ratio or the odds ratio of cure rates in therapeutic equivalence clinical trials with binary endpoints. Some two one-sided tests procedures are proposed and their fixed sample performances evaluated by Monte Carlo simulations. Sample size formulas are derived for most of these procedures. The con-sequences of applying acceptance limits proposed for pharmacokinetic responses in bioequivalence studies to clinical endpoints in therapeutic equivalence clinical trials are also described.     

Type I error and power in noninferiority/equivalence trials with correlated multiple endpoints: an example from vaccine development trials

Clinical trials necessary for the development of new treatment often require testing of multiple endpoints for equivalence or noninferiority relative to an existing effective standard therapy. An example is a vaccine study with multiple antibody measurements in sera of subjects receiving a combination vaccine such as a pneumococcal vaccine, which contains many different serotypes of the pneumococcal organism. This article describes testing methods for the demonstration of simultaneous marginal equivalence or noninferiority of two treatments on each component of the response vector that follows a multivariate normal distribution. Systematic simulation studies are conducted to evaluate the performance of the testing method and to examine under what conditions the power is substantially different if the multiple endpoints are assumed to be independent when they are actually strongly correlated. Data from an illustrative example are used to describe how the study power can be evaluated in the design of the trials.     

Analysis of time-to-event data with nonuniform patient entry and loss to follow-up under a two-stage seamless adaptive design with weibull distribution

In the pharmaceutical industry, a two-stage seamless adaptive design that combines two separate independent clinical trials into a single clinical study is commonly employed in clinical research and development. In practice, in the interest of shortening the development process, it is not uncommon to consider study endpoints with different treatment durations at different stages (Chow and Chang, 2006 ; Maca et al., 2006 ). In this study, our attention is placed on the case where the study endpoints of interest are time-to-event data where the durations at the two stages are different with nonuniform patient entry and losses to follow-up or dropouts. Test statistics for the final analysis based on the combined data are developed under various hypotheses for testing equality, superiority, noninferiority, and equivalence. In addition, formulas for sample size calculation and allocation between the two stages based on the proposed test statistic are derived.     

A comparison of multiple imputation methods for incomplete longitudinal binary data

Longitudinal binary data are commonly encountered in clinical trials. Multiple imputation is an approach for getting a valid estimation of treatment effects under an assumption of missing at random mechanism. Although there are a variety of multiple imputation methods for the longitudinal binary data, a limited number of researches have reported on relative performances of the methods. Moreover, when focusing on the treatment effect throughout a period that has often been used in clinical evaluations of specific disease areas, no definite investigations comparing the methods have been available. We conducted an extensive simulation study to examine comparative performances of six multiple imputation methods available in the SAS MI procedure for longitudinal binary data, where two endpoints of responder rates at a specified time point and throughout a period were assessed. The simulation study suggested that results from naive approaches of a single imputation with non-responders and a complete case analysis could be very sensitive against missing data. The multiple imputation methods using a monotone method and a full conditional specification with a logistic regression imputation model were recommended for obtaining unbiased and robust estimations of the treatment effect. The methods were illustrated with data from a mental health research.     

Demonstrating Biosimilarity via Equivalence in Clinical Trials

The opportunities for biosimilar medicines have stimulated much legal and regulatory debates and actions around the world, most notably the passing of the Biologics Price Competition and Innovation Act in the United States in 2009. A key difference between the development of a biosimilar product versus a generic chemical entity is the requirement for well-controlled clinical studies to demonstrate similarity in efficacy and safety. The main objective of this article is to extend the clinical study design methods commonly used in noninferiority trials to equivalence trials within the context of biosimilar product development. We extend the synthesis method to the equivalence setting and provide sample size considerations. We show that while an equivalence trial in general requires a larger sample size than a noninferiority trial, the difference may not be substantial depending on the significance level required for the equivalence trial.     

Three-Arm Noninferiority Trials with a Prespecified Margin for Inference of the Difference in the Proportions of Binary Endpoints

The design of a three-arm trial including the experimental treatment, an active reference treatment, and a placebo is recommended as a useful approach to the assessment of noninferiority of the experimental treatment. The inclusion of the placebo arm enables the assessment of assay sensitivity and internal validation, in addition to testing the noninferiority of the experimental treatment to the reference. Generally, the acceptable noninferiority margin Δ has been defined as the maximum clinically irrelevant difference between treatments in many two-arm noninferiority trials. However, many articles have considered a design in which the noninferiority margin Δ is relatively defined as a prespecified fraction f of the unknown effect size of the reference treatment. Therefore, these methods cannot be applied to cases where the margin is defined as a prespecified difference between treatments. In this article, we propose score-based statistical procedures for a three-arm noninferiority trial with a prespecified margin Δ for inference of the difference in the proportions of binary endpoints. In addition, we derive the approximate sample size and optimal allocation to minimize the total sample size and that of the placebo arm. A randomized controlled trial on major depressive disorder based on the difference in the proportions of remission is used to demonstrate our proposed method.     

The Role of Multiple Imputation in Noninferiority Trials for Binary Outcomes

We consider the role of multiple imputation (MI) when analyzing noninferiority (NI) clinical trials with missing data. When the endpoint is measured longitudinally, direct-likelihood methods can be used. In this article, the focus is on the situation in which the endpoint is not measured longitudinally but other relevant data are measured at or after baseline prior to planned collection of the primary endpoint data. Simulation results are presented for various scenarios based on the missingness mechanism, the dropout rate, and the size of NI margin. When the endpoint is binary, the ratio of the amount of missing data to the noninferiority margin will affect the operating characteristics of any analysis strategy (whether imputation based or not), an issue that is unique to noninferiority trials. Biased estimates of treatment effect under missingness, not completely at random, may arise when using a misspecified imputation model lacking treatment effect, resulting in substantially inflated Type I error rates in noninferiority trials by making the two groups appear more similar, opposite the usual impact in superiority trials. As in superiority trials, MI will have most benefit when data are missing at random, and the important predictor variables are included in the imputation model.     

Design of Vaccine Equivalence/Non-Inferiority Trials with Correlated Multiple Binomial Endpoints

Immunogenicity trials that study the immune responses to vaccination are often used in the vaccine development process as alternatives to clinical efficacy trials. The comparisons of immune responses among various treatment groups are conducted in a non-inferiority or equivalence framework. When there exists a level of immune response that correlates with protection against disease, it is of interest to compare the proportion of responders as defined as response above a specific level or as a predefined increase in immune levels for post-vaccination levels above pre-vaccination levels. Since vaccines often contain several antigens, the correlations between the immune responses need to be taken into account in the analysis. In this paper, we describe appropriate testing methods for demonstrating the non-inferiority/equivalence of two treatments on each of the binomial endpoints. We conduct a comprehensive simulation study to shed light on how the Type I error and power are affected and to what extent when correlated multiple binomial endpoints are present in the vaccine trials. We also illustrate the computation of power for assessment of non-inferiority/equivalence in real studies.