新药临床非劣性及等效性试验中的例数估计和等效标准

根据新药临床研究的要求和特点，提出临床非劣性及等效性试验例数估计的简算法和查表法，并探讨确定等效标准(δ)的几种方法，可供例数估算时参考。     

新药生物统计的若干问题

根据新药临床研究指导原则，结合新药申报资料及审评体会，对新药研究的设计和统计中若干问题进行了论述。在临床前药理研究中讨论了动物剂量估算，剂量对应和复方研究问题。在临床研究中介绍了10年临床研究设计方式，讨论了等效性检验，非劣性检验，多中心资料，跨年度资料等问题，在统计分析方面列出了国内外新药研究常用的统计方法，讨论了计数资料和计量资料统计分析中应注意的问题。     

成组设计定性资料的三种特殊检验及其SAS实现

对于成组设计定性资料,人们常用成组设计定性资料(常称为四格表资料)的χ2检验或Fisher精确检验。事实上,这里提及的常用的假设检验都属于一般的差异性检验方法。然而,在新药或医疗器械临床试验研究中,还有3种特殊的差异性检验方法,即:优效性检验、非劣性检验和等效性检验。本文将介绍这3种特殊检验的概念、计算方法、应用实例,以及用SAS编程法实现其统计计算的方法。     

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。     

美国FDA更新抗生素开发指南

美国FDA公布了盼望已久的抗生素开发指南修订版，指南明确指出，非劣性研究设计不能推荐用于急性细菌性鼻窦炎（ABS）试验，建议ABS研究只采用优效性试验。FDA认为以往进行的ABS审查不能确定令人信服的治疗利益程度，而这正是非劣性试验的前提条件。     

生物等效性数据处理的有关问题及其计算机软件研制

笔者查阅有关生物利用度测定的大量文献,发现有关等效性评价存在采用的统计方法不统一的问题,有用配对t检验,有自身对照t检验,有正交试验的方差分析等等.事实上按照一般的科研原则,试验设计应包含数理统计和数据处理方法等内容,药物等效性的人体试验方法-自身双交叉设计,其统计方法相关内容黄圣凯等已有报道,但可能由于计算较繁琐等原因.未被广泛采用.为此,笔者特地编制一套生物等效性统计处理软件,为生物等效性数据统计提供合理、规范、方便的处理方法.1 计算原理     

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。     

等效性评价方法研究现状

目的：阐明生物等效性与临床等效性的研究现状及发展方向。方法：介绍新药等效性评价方法的原理，生物等效性分析方法的新进展包括总体或(和)个体生物等效性和多变量生物等效性检验的方法，以及临床等效性中等效界值、目标参数及有待解决的问题，并结合实例进行论述。结论：等效性评价的基本方法已得到推广使用，但在应用上还存在很大的可塑性，不利于新药审评标准的把握，应加强等效性评价方法的正确应用与发展。     

双单侧检验方法的功效计算问题

双单侧检验方法是药物生物等效性评价中的重要统计方法。本文应用贝叶斯统计理论,提出了一种计算其检验功效的新的简便方法。     

群体生物等效性和个体生物等效性检验的统计评价方法及其比较分析

目的:对群体生物等效性(PBE)和个体生物等效性(IBE)检验进行评价,并通过模拟分析和实例分析证明评价方法的可行性。方法:建立混合效应模型,采用小样本置信区间法、自助法和广义P-值法评价PBE和IBE检验,通过模拟分析考察了三种统计评价方法的检验功效以及Ⅰ型误差率,最后进行实例分析,用统计软件R编程实现。结果:三种统计评价方法是可行的,自助法和广义P-值法的检验功效优于小样本置信区间法,广义P-值法的Ⅰ型误差率较大,但可以通过增加样本量的方法来减小Ⅰ型误差率。结论:在样本量较大时,采用广义P-值法进行PBE和IBE检验的评价最为合适。     

配对二项数据等效性／非劣效性评价的样本含量估计和假设检验

新药及医疗器械临床试验中，有时会涉及到两比较组采用配对设计获得的二项反应数据（配对二项数据）的等效性／非劣效性问题。两独立组率之间等效性／非劣效试验的样本含量估计及假设检验方法已较为成熟，但对于配对二项数据两组率之间的等效性／非劣效性试验的样本含量估计及假设检验方法还应用不多。本文介绍了一种渐进的基于约束极大似然估计的方法用于配对二项数据两组率之间的等效性／非劣效性试验的样本含量估计和假设检验，借助一个超声诊断仪临床试验的例子阐明了本方法的应用，还就有关实际问题进行了讨论。     

Choice of δ Noninferiority Margin and Dependency of the Noninferiority Trials∗

For a two-arm active control clinical trial designed to test for noninferiority of the test treatment to the active control standard treatment, data of historical studies were often used. For example, with a cross-trial comparison approach (also called synthetic approach or λ-margin approach), the trial is conducted to test the hypothesis that the mean difference or the ratio between the current test product and the active control is no larger than a certain portion of the mean difference or no smaller that a certain portion of the ratio of the active control and placebo obtained in the historical data when the positive response indicates treatment effective. For a generalized historical control approach (also known as confidence interval approach or δ -margin approach), the historical data is often used to determine a fixed value noninferiority margin δ for all trials involving the active control treatment. The regulatory agency usually requires that the clinical trials of two different test treatments need to be independent and in most regular cases, it also requires to have two independent positive trials of the same test treatment in order to provide confirmatory evidence of the efficacy of the test product. Because of the nature of information (historical data) shared in active-controlled trials, the independency assumption of the trials is not satisfied in general. The correlation between two noninferiority tests has been examined which showed that it is an increasing function of (1 ? λ ) when the response variable is normally distributed. In this article, we examine the relationship between the correlation of the two test statistics and the choice of the noninferiority margin, δ as well as the sample sizes and variances under the normality assumption. We showed that when δ is determined by the lower limit of the confidence interval of the adjusted effect size of the active control treatment (μ_C ? μ_P) using data from historical studies, dependency of the two noninferiority tests can be very high. In order to control the correlation under 15%, the overall sample size of the historical studies needs to be at least five times of the current active control trial.     

ON SAMPLE SIZE CALCULATION BASED ON ODDS RATIO IN CLINICAL TRIALS

Sample size calculation formulas for testing equality, noninferiority, superiority, and equivalence based on odds ratio were derived under both parallel and one-arm crossover designs. An example concerning the study of odds ratio between a test compound (treatment) and a standard therapy (control) for prevention of relapse in subjects with schizophrenia and schizoaffective disorder is presented to illustrate the derived formulas for sample size calculation for various hypotheses under both a parallel design and a crossover design. Simulations were performed to assess the adequacy of the sample size calculation formulas. Simulation results were given at the end of the paper.     

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.     

A NOTE ON SAMPLE SIZE CALCULATION FOR MEAN COMPARISONS BASED ON NONCENTRAL t-STATISTICS

One-sample and two-sample t-tests are commonly used in analyzing data from clinical trials in comparing mean responses from two drug products. During the planning stage of a clinical study, a crucial step is the sample size calculation, i.e., the determination of the number of subjects (patients) needed to achieve a desired power (e.g., 80%) for detecting a clinically meaningful difference in the mean drug responses. Based on noncentral t-distributions, we derive some sample size calculation formulas for testing equality, testing therapeutic noninferiority/superiority, and testing therapeutic equivalence, under the popular one-sample design, two-sample parallel design, and two-sample crossover design. Useful tables are constructed and some examples are given for illustration.     

Type I error probabilities based on design-stage strategies with applications to noninferiority trials

When testing the equality of means from two different populations, a t-test or large sample normal test tend to be performed. For these tests, when the sample size or design for the second sample is dependent on the results of the first sample, the type I error probability is altered for each specific possibility in the null hypothesis. We will examine the impact on the type I error probabilities for two confidence interval procedures and procedures using test statistics when the design for the second sample or experiment is dependent on the results from the first sample or experiment (or series of experiments). Ways for controlling a desired maximum type I error probability or a desired type I error rate will be discussed. Results are applied to the setting of noninferiority comparisons in active controlled trials where the use of a placebo is unethical.     

Sample size for comparing negative binomial rates in noninferiority and equivalence trials with unequal follow-up times

We derive the sample size formulae for comparing two negative binomial rates based on both the relative and absolute rate difference metrics in noninferiority and equivalence trials with unequal follow-up times, and establish an approximate relationship between the sample sizes required for the treatment comparison based on the two treatment effect metrics. The proposed method allows the dispersion parameter to vary by treatment groups. The accuracy of these methods is assessed by simulations. It is demonstrated that ignoring the between-subject variation in the follow-up time by setting the follow-up time for all individuals to be the mean follow-up time may greatly underestimate the required size, resulting in underpowered studies. Methods are provided for back-calculating the dispersion parameter based on the published summary results.     

Incorporating a companion test into the noninferiority design of medical device trials

Noninferiority trials are commonly utilized to evaluate the safety and effectiveness of medical devices. It could happen that the noninferiority hypothesis is rejected while the performance of the active control is clinically not satisfactory. This may pose a great challenge when making a regulatory decision. To avoid such a difficult situation, we propose to conduct a companion test to assess the performance of the active control when testing the main noninferiority hypothesis and to incorporate such a test into the study design. Under our proposal, the noninferiority of the investigational device to the active control can only be claimed when both hypotheses are rejected. The operating characteristics of the proposed study design based on these two tests can be fully evaluated at the design stage. This proposed approach is aimed to facilitate regulatory decision making in a more transparent manner.     

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.     

Multiple testing of noninferiority hypotheses in active controlled trials

For noninferiority testing with the maximum allowable noninferiority margin being prespecified, one can perform valid statistical testing at the same alpha level for multiple noninferiority hypotheses with margins being smaller than this maximum margin. This is easily comprehensible because only one confidence level is used to assess which margins within the interval bounded by the maximum margin can be ruled out. If different confidence intervals are used, e.g., the interval generated from the intent-to-treat population is used for testing superiority and the interval generated from the per-protocol population is used for testing noninferiority, the problem of multiplicity will surface and the adjustment of alpha for each testing may be needed. All these predicate on the condition that at least a certain element of the maximum allowable noninferiority margin, whether it is the entire margin or the fraction of the active control effect to be retained, must be fixed in advance. None of these elements can be allowed to be influenced directly or indirectly by any analysis of the noninferiority trial data. Otherwise, the noninferiority analysis may be invalid.