非平衡设计对检验效能的影响

目的探究在完全随机设计的单因素方差分析中非平衡设计与检验效能大小的关系。方法通过SAS程序分别估计出两类检验资料在给定参数下所需的样本总量,然后利用蒙特卡洛模拟固定样本总量时改变样本比得到的检验效能变化,以及样本总量不固定,改变各样本量时检验效能的变化。并且推断出在达到多大的样本比时检验效能低于预警值0.8。结果在三组样本的单因素方差分析中,不固定样本总量时检验效能随样本总量增加或减少呈单调递增或递减。固定样本总量时检验效能与样本间的比例并不是呈简单的单调关系,而是受各样本均值与总均值之差平方和的影响。结论三组样本的单因素方差分析中固定总样本量时,检验效能随样本间比值的变化呈不规则变化。在给定理论检验效能值的情况下能得出一个样本比临界值,在大于该值时检验效能值会低于0.8。     

三种不同方法估算等效性检验的样本量与检验效能

关于等效性检验的样本量与检验效能估计,SAS中提供了一种方法的估算程序,即Phillips法,但是只是针对于单样本、两样本与配对设计而言。然而,在以等效性检验为目的的临床试验中,双处理、两阶段交叉设计应用最为广泛,并在1992年被美国FDA定义为用于等效性评价的标准方法〔1,2〕。这种设计能提供药物间的差(或比)的最优无偏估计;节约样本,兼有既平行、又配对两种设计的优点。本研究将Phillips方法进一步推广到2×2交叉设计并与其他估算等效性检验样本量与检验效能的两种方法作了比较,以期为研究者提供参考。方法简介1.一般方法通常情况下,…     

生存分析log-rank检验样本含量估计影响因素

目的探讨生存分析log-rank检验样本含量估计的影响因素。方法应用PASS软件中的Lachin-Foulkes方法模块,设置不同的参数计算实例的样本含量来研究log-rank检验样本含量估计的影响因素。结果检验水准(包括单、双侧检验)、预期的检验效能、风险比、试验组和对照组例数是否均衡、随访的时间、删失率等因素都会影响log-rank检验样本含量估计。结论生存分析log-rank检验样本含量估计受诸多因素影响,设计阶段样本含量估算应考虑这些影响因素。     

两组独立样本资料t检验中检验效能的探讨及SAS的实现

目的 探讨两组独立样本资料t检验中,检验效能的意义及SAS程序的实现.方法 用SAS 9.1对两组独立样本资料t检验的实例进行检验效能的分析.结果 当P>0.05时,可能是因为检验效能低下而造成的假阴性结果.结论 进行两组独立样本资料t检验时,若P>0.05时应进行检验效能的分析,以明确是由于样本含量不足导致检验效能过...     

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。     

小样本内部预试验自适应设计中Ⅰ型错误和检验效能的控制及模拟

目的 通过盲态下内部预试验IPS( internal pilot study)样本量调整的模拟分析,探索小样本下有效控制Ⅰ型错误、保证检验效能的合理统计方法.方法 利用蒙特-卡罗( Monte Carlo)模拟不断改变两总体间的均值差,固定方差,在盲态下采用随机化检验进行统计分析,计算Ⅰ型错误和检验效能随均值差的变化情况.结果 盲态下Ⅰ型错误未超过检验水准,检验效能略有降低.结论 盲态小样本下调整样本量时,采用随机化检验可有效控制Ⅰ型错误.     

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.     

样本含量估计中的检验效能及其应用

样本含量估计中的检验效能及其应用哈尔滨医科大学李洪源，李玉春在医学研究中，对两样本率或平均数进行对比研究时，需要估计所需的样本含量。估计样本含量的前提之一是研究者要根据所研究课题的特点对第一类错误概率（ａ）和第二类错误的概率（β）做出预先的设定。实际...     

样本率多重比较方法的模拟研究

目的 采用Monte Carlo方法模拟研究样本率多重比较方法特性.方法 用SAS9.13软件编程,模拟估算不同参数条件下各种样本率多重比较方法的总Ⅰ型错误率、检验效能和判对率.结果 不同方法各具特色,能较好控制总Ⅰ型错误率且检验效能较高的方法有Ryan、Perm、Boot和Hommel、Hoch、StepS、StepB方法.结论 如需严格控制总Ⅰ型错误率在α水准内,Hommel、Hoch、StepS、StepB效能较高;如允许总Ⅰ型错误率略溢出(1.15α以内),Ryan、Perm和Boot法效能较高.     

随机模拟法验证非劣效临床试验样本量计算公式

目的探讨并验证非劣效临床试验样本量计算方法。方法通过理论公式的推导，得到非劣效临床试验样本量计算公式，并用随机模拟的方法，使用该公式计算出的样本量估计实际的检验效能，以验证公式的正确性。结果由概率论严格推导得到样本量计算公式，并通过SAS随机模拟宏程序验证了公式的正确性，即模拟出的检验效能与最初带入公式计算时设定的预期的检验效能一致。结论样本量计算与临床试验设计有机结合的方法，解决了现行临床试验样本量计算方法与研究设计脱节的问题。     

Modified exact sample size for a binomial proportion with special emphasis on diagnostic test parameter estimation

The design of epidemiologic studies for the validation of diagnostic tests necessitates accurate sample size calculations to allow for the estimation of diagnostic sensitivity and specificity within a specified level of precision and with the desired level of confidence. Confidence intervals based on the normal approximation to the binomial do not achieve the specified coverage when the proportion is close to 1. A sample size algorithm based on the exact mid-P method of confidence interval estimation was developed to address the limitations of normal approximation methods. This algorithm resulted in sample sizes that achieved the appropriate confidence interval width even in situations when normal approximation methods performed poorly.     

单组目标值试验样本量计算方法的比较研究

目的探讨设计以率作为终点评价指标的单组目标值试验时,不同样本量计算方法间的区别。方法通过样本量计算原理与计算结果的比较,分析不同样本量计算方法间的差异,进一步通过MonteCarlo随机模拟方法,探讨使用不同方法所得样本量估计实际的检验把握度,验证所得结果的正确性。结果当预计事件发生率P和目标值P。相差10％时,近似正态法和一般精确概率法所得样本量和把握度较相近,但是当P接近1．0时（P〉0．85）,精确概率法所得样本量略低于近似正态法,且把握度明显低于近似正态法。小概率事件的精确概率法所需样本量始终低于近似正态法和一般精确概率法。随机模拟显示,在相同的参数设置下,近似正态法给出的样本量能够提供足够的研究把握度,而小概率事件的精确概率法所得样本量能提供的把握度过低。结论如果要检验某医疗器械的使用成功率是否不低于某个临床认可的标准,按照近似正态法计算的样本量,更能提供足够的检验把握度,尤其对于小规模的临床试验。     

How conservative is Fisher's exact test? A quantitative evaluation of the two‐sample comparative binomial trial

The debate as to which statistical methodology is most appropriate for the analysis of the two-sample comparative binomial trial has persisted for decades. Practitioners who favor the conditional methods of Fisher, Fisher's exact test (FET), claim that only experimental outcomes containing the same amount of information should be considered when performing analyses. Hence, the total number of successes should be fixed at its observed level in hypothetical repetitions of the experiment. Using conditional methods in clinical settings can pose interpretation difficulties, since results are derived using conditional sample spaces rather than the set of all possible outcomes. Perhaps more importantly from a clinical trial design perspective, this test can be too conservative, resulting in greater resource requirements and more subjects exposed to an experimental treatment. The actual significance level attained by FET (the size of the test) has not been reported in the statistical literature. Berger (J. R. Statist. Soc. D (The Statistician) 2001; 50:79-85) proposed assessing the conservativeness of conditional methods using p-value confidence intervals. In this paper we develop a numerical algorithm that calculates the size of FET for sample sizes, n, up to 125 per group at the two-sided significance level, alpha = 0.05. Additionally, this numerical method is used to define new significance levels alpha(*) = alpha+epsilon, where epsilon is a small positive number, for each n, such that the size of the test is as close as possible to the pre-specified alpha (0.05 for the current work) without exceeding it. Lastly, a sample size and power calculation example are presented, which demonstrates the statistical advantages of implementing the adjustment to FET (using alpha(*) instead of alpha) in the two-sample comparative binomial trial.     

Exact test size and power of a Gaussian error linear model for an internal pilot study.

Wittes and Brittain recommended using an 'internal pilot study' to adjust sample size. The approach involves five steps in testing a general linear hypothesis for a general linear univariate model, with Gaussian errors. First, specify the design, hypothesis, desired test size, power, a smallest 'clinically meaningful' effect, and a speculated error variance. Second, conduct a power analysis to choose provisionally a planned sample size. Third, collect a specified proportion of the planned sample as the internal pilot sample, and estimate the variance (but do not test the hypothesis). Fourth, update the power analysis with the variance estimate to adjust the total sample size. Fifth, finish the study and test the hypothesis with all data. We describe methods for computing exact test size and power under this scenario. Our analytic results agree with simulations of Wittes and Brittain. Furthermore, our exact results apply to any general linear univariate model with fixed predictors, which is much more general than the two-sample t-test considered by Wittes and Brittain. In addition, our results allow for examination of the impact on test size of internal pilot studies for more complicated designs in the framework of the general linear model. We examine the impact of (i) small samples, (ii) allowing the planned sample size to decrease, (iii) the choice of internal pilot sample size, and (iv) the maximum allowable size of the second sample. All affect test size, power and expected total sample size. We present a number of examples including one that uses an internal pilot study in a three-group analysis of variance.     

Efficient power computation for exact and mid-P tests for the common odds ratio in several 2 × 2 tables

When designing a study that may generate a set of sparse 2 × 2 tables, or when confronted with ‘negative’ results upon exact analysis of such tables, we need to compute the power of exact tests. In this paper we provide an efficient approach for computing exact unconditional power for four exact tests on the common odds ratio in a series of 2 × 2 tables. These tests are the traditional exact test; a test based on a probability ordering of the sample space; and two tests based on ordering the sample space according to distance from the mean, or median. For each test, we consider both a conservative version and a mid-P adjusted version. We explore three computational options for power determination: exact power computation, calculation of exact upper and lower bounds for power, and Monte Carlo confidence bounds for power. We present an interactive program implementing these options. For study design, the program may be run several times to arrive at a sample configuration with adequate power.     

Robustness of sample size re-estimation procedure in clinical trials (arbitrary populations)

In clinical trials, one of the main questions that is being asked is how many additional observations, if any, are needed beyond those originally planned. In a two-treatment double-blind clinical experiment, one is interested in testing the null hypothesis of equality of the means against one-sided alternative when the common variance sigma2 is unknown. We wish to determine the required total sample size when the error probabilities alpha and beta are specified at a predetermined alternative. Shih provided a two-stage procedure which is an extension of Stein's one-sample procedure, assuming normal response. He estimates sigma2 by the method of maximum likelihood via the EM algorithm and carries out a simulation study in order to evaluate the effective level of significance and the power. The author proposed a closed-form estimator for sigma2 and showed analytically that the difference between the effective and nominal levels of significance is negligible and that the power exceeds 1-beta when the initial sample size is large. Here we consider responses from arbitrary distributions in which the mean and the variance are not functionally related and show that when the initial sample size is large, the conclusions drawn previously by the author still hold. The effective coverage probability of a fixed-width interval is also evaluated. Proofs of certain assertions are deferred to the Appendix.     

完全随机设计两组t检验与秩和检验的功效比较

目的比较t检验与秩和检验检验完全随机设计两组资料的功效.方法用SAS软件编制电脑实验程序,模拟研究和比较不同总体条件下两组秩和检验与t检验的检验功效.结果若总体分布对称,小样本时t检验功效较高,大样本时两种方法功效相似;总体非对称分布时秩和检验的功效高于t检验.结论当样本量足够大时,可以用秩和检验代替t检验.     

Sample size determination for comparing several survival curves with unequal allocations

Ahnn and Anderson derived sample size formulae for unstratified and stratified designs assuming equal allocation of subjects to three or more treatment groups. We generalize the sample size formulae to allow for unequal allocation. In addition, we define the overall probability of death to be equal to one minus the censored proportion for the stratified design. This definition also leads to a slightly different definition of the non-centrality parameter than that of Ahnn and Anderson for the stratified case. Assuming proportional hazards, sample sizes are determined for a prespecified power, significance level, hazard ratios, allocation of subjects to several treatment groups, and known censored proportion. In the proportional hazards setting, three cases are considered: (1) exponential failures--exponential censoring, (2) exponential failures--uniform censoring, and (3) Weibull failures (assuming same shape parameter for all groups)--uniform censoring. In all three cases of the unstratified case, it is assumed that the censoring distribution is the same for all of the treatment groups. For the stratified log-rank test, it is assumed the same censoring distribution across the treatment groups and the strata. Further, formulae have been developed to provide approximate powers for the test, based upon the first two or first four-moments of the asymptotic distribution. We observe the following two major findings based on the simulations. First, the simulated power of the log-rank test does not depend on the censoring mechanism. Second, for a significance level of 0.05 and power of 0.80, the required sample size n is independent of the censoring pattern. Moreover, there is very close agreement between the exact (asymptotic) and simulated powers when a sequence of alternatives is close to the null hypothesis. Two-moment and four-moment power series approximations also yield powers in close agreement with the exact (asymptotic) power. With unequal allocations, our simulations show that the empirical powers are consistently above the target value of prespecified power of 0.80 when 50 per cent of the patients are allocated to the treatment group with the smallest hazard.