安慰剂和阳性药对照的三臂非劣效临床试验的样本含量估计和统计推断

目的 介绍一种基于非劣效界值为标准对照药效应一部分的三臂非劣效临床试验的样本含量估计和统计检验的方法.方法 在介绍Pigeot法的基础上,实例探讨了如何计算样本含量及确定非劣效界值,并用模拟的方法比较了Pigeot法与传统检验方法的检验效能.结果 相同样本含量时Pigeot法的检验效能更高.结论 Pigeot法充分利用了所有样本量的信息,提高了检验效率,降低了临床试验的成本.     

对基于均差作推断的成组设计非劣效性试验功效分析及样本量估计公式正确性的探讨

样本量的估计是在试验设计阶段要考虑的一个重要问题.以对两正态总体均数差值作统计推断的成组设计非劣效性试验样本量估计为例,目前国内外已有一些教材、专著或论文介绍了一些公式[1-11],但这些公式不尽相同,而且绝大多数公式都是直接给出或引用的,没有给出详细、具体的理论推导过程,因此,读者并不清楚哪些公式正确,哪些公式不正确,难免会给实际工作者带来一些困惑.本文将根据对均差作统计推断的成组设计一元定量资料的非劣效性检验原理及检验功效的定义,从非劣效性检验的拒绝域或两均数差值的置信区间出发,对相应的检验功效分析及样本量估计公式进行理论推导,并采用Monte Carlo模拟方法对推导出来的公式进行正确性验证.     

率的非劣效试验中样本含量的估计——SAS和PASS实现

目的 提供二分类定性资料平行设计非劣效临床试验样本含量最常用的计算公式及其 SAS和PASS过程,并为相关参数的设置提供参考。方法 基于二项分布的正态近似理论推导样本含量的估计公式,通过SAS程序和PASS过程探讨各重要参数（样本率、非劣效界值）变化时样本含量及检验效能的变化情况。结果 对率的非劣效试验样本含量的计算,公式、SAS程序和PASS过程能得到一致结果;当检验水准和对照组样本率确定时,试验组样本率越大、检验效能越小、界值越大,所需样本含量越小。结论 利用本文提供的公式、SAS程序和PASS过程,可以帮助研究者系统快速得到二分类资料2组平行非劣效设计时的样本含量。试验组样本率、检验效能和非劣效界值是非劣效临床试验估计样本含量必须认真考虑的参数。     

模拟验证等效性检验中β的单、双侧取值

目的 研究临床试验中等效性检验的样本量的计算问题.方法 在概括总结影响等效性检验的样本量与检验效能的几个主要因素（α、β、θ、△、σ）的基础上,重点介绍了等效性检验中α与β的确定与含义,并指出了文献中所存在的分歧;然后利用计算机抽样模拟的方法,依据不同设计类型、不同参数取值下计算的样本量,模拟估算所对应的检验效能.结果 模拟验证了β应该取单侧还是双侧并给出了较为合理的解释.结论 在等效性检验的样本量估算中,当θ为0时,β取双侧;当θ不等于0时,β取单侧.     

PASS软件实现临床试验中非劣效、等效和优效性检验的样本量估算

用PASS 11软件对非劣效、等效和优效性设计的临床试验进行样本量估算,并与SAS软件运行结果进行比较,探讨PASS 11软件在临床科研中计算样本量的实用性和准确性,为科研工作者在临床试验设计阶段进行科学的样本量估算提供帮助。     

一种临床试验中的适应性样本量调整方法

目的介绍一种临床试验中的适应性样本量调整方法,并探讨样本量调整后统计分析方法的第Ⅰ类错误率及检验效能。方法通过montecarlo模拟的方法研究n1大小对最终样本量Nf的影响,并估计最终方差偏移大小;同时模拟研究样本量调整后统计分析方法的第Ⅰ类错误率及检验效能大小。结果(1)模拟结果显示运用该样本量调整方法所得到的最终样本量Nf非常接近其真实值N0,尤其在π=0.4时进行样本量调整。(2)同时模拟结果显示所介绍的样本量调整后的校正t检验方法不仅能有效控制第Ⅰ类错误率α并且能充分满足试验检验效能(1-β)。结论该样本量调整方法研究结果是在一般两样本单侧t检验条件下得到也可应用于优效或非劣效设计的临床试验中。     

率指标非劣效性界值设定范围的探讨

目的 探讨非劣效试验研究中率指标非劣效性界值的设定问题.方法 从一个实例入手,通过理论推导与软件模拟相结合,分析不同样本量及样本率条件下非劣效性界值的变化.结果 非劣效性界值△主要由两部分组成:△(～)△E+△0,即非劣效性界值的最低要求限△0和期望检验的最大率差△E.当样本量相同时,样本率越接近0.5,则△值越大.当样本率相同时,随着样本量的增大,△值逐渐减小.结论 非劣效性试验中率指标非劣效性界值的设定应同时考虑最低要求限△0和期望检验的最大率差△E,这将为实际工作提供指导和参考.     

抽样调查法和单组目标值法对诊断试验样本量计算差异的分析

探讨设计以验证灵敏度和特异度为目的 的诊断试验时,不同样本量计算方法间的区别.通过直观的样本量公式与计算结果比较,分析不同样本量计算方法间的差异,进一步通过Monte Carlo随机模拟方法,验证所得结果的正确性.抽样调查法计算所需的样本量明显低于单组目标值法,随机模拟显示,在相同的参数设置下,单组目标值法给出的样本量能够提供更高的研究把握度.两种样本量设计方法的适用条件不同,存在本质区别,研究者必须根据研究目的 设置相应参数,如果在以检验某种诊断方法的诊断能力是否不低于某个临床认可的标准时,按照单组目标值法设计的样本量,才能提供足够的检验把握度,证明新诊断方法的有效性.     

三臂非劣效性设计生存时间数据的半参数统计推断方法

目的 推荐并改进一种用于新药临床试验中生存分析三臂非劣效性设计的半参数统计推断方法.方法 采用Cox比例风险模型建立用于生存时间数据的三臂非劣效检验方法,通过模拟试验验证该方法的有效性,并给出样本含量估计的R语言程序.结果 模拟试验结果证实,在样本删失风险率维持在一定水平时,三臂Cox模型能有效地控制Ⅰ类错误发生概率,并保证较高的检验效能,实际应用简单有效.结论 本文推荐的方法,可以有效地应用于三臂生存时间数据的非劣效性研究.     

含安慰剂组三臂临床试验基于bootstrap再抽样的非劣效评判

目的探讨含安慰剂组三臂临床试验基于bootstrap再抽样的非劣效评判的方法。方法用Monte Carlo模拟方法,产生服从正态分布、对数正态分布和Gamma分布的随机样本,进行Welch校正t检验法和bootstrap法的α-模拟和power模拟的验证和比较。结果当数据服从正态分布,在样本量较大时,Welch校正t检验法和bootstrap法均表现出较好的统计性能,但当数据呈偏态分布时,Welch校正t检验法的第一类错误率会偏离预先给定的α-水平,而bootstrap法在样本量较大时,第一类错误率基本保持在预先给定的水平。Welch校正t检验法和bootstrap法的power模拟结果基本相同。结论含安慰剂组的三臂临床试验在数据不服从正态分布时,bootstrap法可作为一种有效的非劣效评判方法。     

A U‐statistics based approach to sample size planning of two‐arm trials with discrete outcome criterion aiming to establish either superiority or noninferiority

In current practice, the most frequently applied approach to the handling of ties in the Mann–Whitney‐Wilcoxon (MWW) test is based on the conditional distribution of the sum of mid‐ranks, given the observed pattern of ties. Starting from this conditional version of the testing procedure, a sample size formula was derived and investigated by Zhao et al. (Stat Med 2008). In contrast, the approach we pursue here is a nonconditional one exploiting explicit representations for the variances of and the covariance between the two U‐statistics estimators involved in the Mann–Whitney form of the test statistic. The accuracy of both ways of approximating the sample sizes required for attaining a prespecified level of power in the MWW test for superiority with arbitrarily tied data is comparatively evaluated by means of simulation. The key qualitative conclusions to be drawn from these numerical comparisons are as follows:

• With the sample sizes calculated by means of the respective formula, both versions of the test maintain the level and the prespecified power with about the same degree of accuracy.
• Despite the equivalence in terms of accuracy, the sample size estimates obtained by means of the new formula are in many cases markedly lower than that calculated for the conditional test.

Perhaps, a still more important advantage of the nonconditional approach based on U ‐statistics is that it can be also adopted for noninferiority trials. Copyright © 2016 John Wiley & Sons, Ltd.     

A noniterative sample size procedure for tests based on t distributions

A noniterative sample size procedure is proposed for a general hypothesis test based on the t distribution by modifying and extending Guenther's 6 approach for the one sample and two sample t tests. The generalized procedure is employed to determine the sample size for treatment comparisons using the analysis of covariance (ANCOVA) and the mixed effects model for repeated measures in randomized clinical trials. The sample size is calculated by adding a few simple correction terms to the sample size from the normal approximation to account for the nonnormality of the t statistic and lower order variance terms, which are functions of the covariates in the model. But it does not require specifying the covariate distribution. The noniterative procedure is suitable for superiority tests, noninferiority tests, and a special case of the tests for equivalence or bioequivalence and generally yields the exact or nearly exact sample size estimate after rounding to an integer. The method for calculating the exact power of the two sample t test with unequal variance in superiority trials is extended to equivalence trials. We also derive accurate power formulae for ANCOVA and mixed effects model for repeated measures, and the formula for ANCOVA is exact for normally distributed covariates. Numerical examples demonstrate the accuracy of the proposed methods particularly in small samples.     

Sample size determination for assessing equivalence based on proportion ratio under a randomized trial with non-compliance and missing outcomes

When a generic drug is developed, it is important to assess the equivalence of therapeutic efficacy between the new and the standard drugs. Although the number of publications on testing equivalence and its relevant sample size determination is numerous, the discussion on sample size determination for a desired power of detecting equivalence under a randomized clinical trial (RCT) with non-compliance and missing outcomes is limited. In this paper, we derive under the compound exclusion restriction model the maximum likelihood estimator (MLE) for the ratio of probabilities of response among compliers between two treatments in a RCT with both non-compliance and missing outcomes. Using the MLE with the logarithmic transformation, we develop an asymptotic test procedure for assessing equivalence and find that this test procedure can perform well with respect to type I error based on Monte Carlo simulation. We further develop a sample size calculation formula for a desired power of detecting equivalence at a nominal alpha-level. To evaluate the accuracy of the sample size calculation formula, we apply Monte Carlo simulation again to calculate the simulated power of the proposed test procedure corresponding to the resulting sample size for a desired power of 80 per cent at 0.05 level in a variety of situations. We also include a discussion on determining the optimal ratio of sample size allocation subject to a desired power to minimize a linear cost function and provide a sensitivity analysis of the sample size formula developed here under an alterative model with missing at random.     

Sample size calculation for the Andersen-Gill model comparing rates of recurrent events

Recurrent events arise frequently in biomedical research, where the subject may experience the same type of events more than once. The Andersen-Gill (AG) model has become increasingly popular in the analysis of recurrent events particularly when the event rate is not constant over time. We propose a procedure for calculating the power and sample size for the robust Wald test from the AG model in superiority, noninferiority, and equivalence clinical trials. Its performance is demonstrated by numerical examples. Sample SAS code is provided in the Supplementary Material.     

Sample size determination in complex clinical trials comparing more than two groups for survival endpoints

This paper presents a sample size formula for testing the equality of k (⩾2) survival distributions using the Tarone–Ware class of test statistics in the presence of non-proportional hazards, time dependent losses, non-compliance and drop-in. This method extends the derivation by Lakatos of a sample size formula for comparing two survival distributions. A sample size formula is also presented for the stratified logrank test. We describe how one can utilize these generalized formulae in calculating sample sizes and assessing power in complex multi-arm clinical trials. © 1998 John Wiley & Sons, Ltd.     

Sample size calculations for a split-cluster, beta-binomial design in the assessment of toxicity

Mouse embryo assays are recommended to test materials used for in vitro fertilization for toxicity. In such assays, a number of embryos is divided in a control group, which is exposed to a neutral medium, and a test group, which is exposed to a potentially toxic medium. Inferences on toxicity are based on observed differences in successful embryo development between the two groups. However, mouse embryo assays tend to lack power due to small group sizes. This paper focuses on the sample size calculations for one such assay, the Nijmegen mouse embryo assay (NMEA), in order to obtain an efficient and statistically validated design. The NMEA follows a stratified (mouse), randomized (embryo), balanced design (also known as a split-cluster design). We adopted a beta-binomial approach and obtained a closed sample size formula based on an estimator for the within-cluster variance. Our approach assumes that the average success rate of the mice and the variance thereof, which are breed characteristics that can be easily estimated from historical data, are known. To evaluate the performance of the sample size formula, a simulation study was undertaken which suggested that the predicted sample size was quite accurate. We confirmed that incorporating the a priori knowledge and exploiting the intra-cluster correlations enable a smaller sample size. Also, we explored some departures from the beta-binomial assumption. First, departures from the compound beta-binomial distribution to an arbitrary compound binomial distribution lead to the same formulas, as long as some general assumptions hold. Second, our sample size formula compares to the one derived from a linear mixed model for continuous outcomes in case the compound (beta-)binomial estimator is used for the within-cluster variance.     

Comparing sample size formulae for trials with unbalanced allocation using the logrank test.

This paper compares the sample size formulae given by Schoenfeld, Freedman, Hsieh and Shuster for unbalanced designs. Freedman's formula predicts the highest power for the logrank test when the sample size ratio of the two groups equals the reciprocal of the hazard ratio. The other three formulae predict highest powers when sample sizes in the two groups are equal. Results of Monte Carlo simulations performed for the power of the logrank test with various sample size ratios show that the power curve of the logrank test is almost flat between a sample size ratio of one and a sample size ratio close to the reciprocal of the hazard ratio. An equal sample-size allocation may not maximize the power of the logrank test. Monte Carlo simulations also show that, under an exponential model, when the sample size ratio is toward the reciprocal of the hazard ratio, Freedman's formula predicts more accurate powers. Schoenfeld's formula, however, seems best for predicting powers with equal sample size.     

Design of sequentially randomized trials for testing adaptive treatment strategies

An adaptive treatment strategy (ATS) is an outcome‐guided algorithm that allows personalized treatment of complex diseases based on patients' disease status and treatment history. Conditions such as AIDS, depression, and cancer usually require several stages of treatment because of the chronic, multifactorial nature of illness progression and management. Sequential multiple assignment randomized (SMAR) designs permit simultaneous inference about multiple ATSs, where patients are sequentially randomized to treatments at different stages depending upon response status. The purpose of the article is to develop a sample size formula to ensure adequate power for comparing two or more ATSs. Based on a Wald‐type statistic for comparing multiple ATSs with a continuous endpoint, we develop a sample size formula and test it through simulation studies. We show via simulation that the proposed sample size formula maintains the nominal power. The proposed sample size formula is not applicable to designs with time‐to‐event endpoints but the formula will be useful for practitioners while designing SMAR trials to compare adaptive treatment strategies. Copyright © 2015 John Wiley & Sons, Ltd.     

Incorporating pragmatic features into power analysis for cluster randomized trials with a count outcome

Cluster randomized designs are frequently employed in pragmatic clinical trials which test interventions in the full spectrum of everyday clinical settings in order to maximize applicability and generalizability. In this study, we propose to directly incorporate pragmatic features into power analysis for cluster randomized trials with count outcomes. The pragmatic features considered include arbitrary randomization ratio, overdispersion, random variability in cluster size, and unequal lengths of follow-up over which the count outcome is measured. The proposed method is developed based on generalized estimating equation (GEE) and it is advantageous in that the sample size formula retains a closed form, facilitating its implementation in pragmatic trials. We theoretically explore the impact of various pragmatic features on sample size requirements. An efficient Jackknife algorithm is presented to address the problem of underestimated variance by the GEE sandwich estimator when the number of clusters is small. We assess the performance of the proposed sample size method through extensive simulation and an application example to a real clinical trial is presented.