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。     

多样本变异系数比较的似然比检验

目的 通过求非中心t分布未知参数最大似然估计,由此提出一种比较多个样本变异系数差异的似然比检验(LRT)方法,并与现有的D'AD检验在第Ⅰ类错误率与检验效能两方面进行模拟比较.方法 由于样本变异系数的似然函数跟非中心t分布有关,本文首先提出一种求非中心t分布未知参数最大似然估计的算法,然后由此构造出比较多个样本变异系数的似然比检验统计量,并求出其Bartlett校正系数,对似然比检验统计量进行Bartlett校正,以便该方法也能用于小样本的情形.计算机模拟时从正态分布总体中抽样,模拟LRT的第Ⅰ类错误率与检验效能,并与D'AD检验做比较.将LRT方法编写成R语言程序,输出校正后的统计量值和相应P值,以方便实际应用.结果 校正的LRT方法能更好地控制第Ⅰ类错误率,并且其检验效能比D'AD检验更稳健.在小样本且样本量不均衡的情形下,其检验效能比D'AD方法高.结论 校正的LRT方法适用范围更广,检验效能高,可为检验多样本变异系数间差异提供更加有效的方法.     

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。     

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.     

Cochran-Armitage趋势检验不同赋值的模拟研究

目的比较Cochran-Armitage趋势检验中三种赋值方法的统计性能,以期为应用趋势检验提供指引。方法应用Monte Carlo模拟方法,以各等级的样本量和阳性率为参数,通过SAS9.2软件编程,比较趋势检验中等距、均秩和MERT三种赋值方法在不同参数组合下的Ⅰ类错误率和检验效能。结果Ⅰ类错误率以等距赋值最低,均秩赋值次之,MERT法最高。三种赋值方法的检验效能非常接近。当有一个等级的阳性率较小时(pi=0.05),三种赋值方法的检验效能普遍偏低。结论综合模拟结果和应用的便利性,有序分类数据的Cochran-Armitage趋势检验采用等距赋值更值得提倡。     

自适应设计中盲态和揭盲状态样本量调整的模拟比较

目的 通过对盲态和揭盲状态下内部预试验(IPS)样本量调整的模拟比较,确定自适应设计中相对合理的样本量调整方法.方法 利用蒙特-卡罗(Monte Carlo)模拟不断改变IPS的样本量,在盲态和揭盲状态下分别比较I型错误和检验效能.结果 两种状态下Ⅰ型错误和检验效能没有本质区别.结论 盲态样本量调整更可取.     

meta分析预测法在二分类终点临床试验中的应用

目的 探讨meta分析预测(meta analytic predictive, MAP)法在二分类终点临床试验中借用历史对照组数据的信息。方法 通过模拟试验评价历史试验数据的异质性及先验数据冲突对于研究的Ⅰ类错误及检验效能的影响，并对Secukinumab治疗强直性脊柱炎的实际案例进行分析。结果 当先验数据冲突不存在时，MAP方法能较好地控制Ⅰ类错误并提高检验效能。随着历史试验间异质性增加，Ⅰ类错误会略有膨胀而检验效能略有降低。当先验数据冲突时，会造成Ⅰ类错误膨胀，若历史试验利于试验组优于对照组的结论时检验效能会增加，反之检验效能会降低。Secukinumab治疗强直性脊柱炎的案例显示，MAP方法能够在新试验对照组样本量较少的情况下，借用历史试验信息，可以识别出试验药与对照药的差异。结论 本文对临床试验中信息借用的MAP方法提供了方法学和案例研究支持，评估了先验数据冲突及异质性对信息借用的影响，具有较强的实用价值。     

基于生存资料的Ⅱ/Ⅲ期无缝设计期中分析方法评价

目的基于生存指标的无缝设计,考查PFS在什么条件下可以用于Ⅱ/Ⅲ期无缝设计期中分析时的剂量组筛选。方法采用模拟试验的手段,分别研究基于生存资料下Fisher合并法和加权逆正态法在利用和不利用OS的信息两种组别筛选策略下的总Ⅰ类错误率和检验效能。结果加权逆正态合并法与Fisher合并法相比,两者在控制总Ⅰ类错误率方面无明显差异,随着PFS和OS相关性增强,加权逆正态合并法的检验效能要高于Fisher合并法,并且合并PFS和OS的信息将获得更高检验效能。结论当PFS和OS的相关性较大,且效应趋势一致时,建议采用加权逆正态合并法合并两者的信息进行Ⅱ/Ⅲ期无缝临床试验的统计分析。     

基于α调整的国际多中心临床试验目标区二分类终点有效性研究的桥接方法

目的探索采用合理的调整后检验水准α'作为国际多中心临床试验(MRCT)在目标区的决策依据的可行性,为MRCT在目标区通过审批提供参考。方法利用Monte Carlo模拟构建二分类资料、优效性设计、包含目标区的MRCT数据模型,比较不同规模的MRCT在检验水准α=0.05水平显示试验组优效的前提下,目标区采用调整后检验水准α'作为决策依据的条件Ⅰ型错误率(CFPR)、条件检验效能(CP)随目标区样本量占总样本量比例K的变化情况。结果在不同规模的MRCT中,目标区的CFPR和CP均随着检验水准α'、样本比例K的增加而增加;当α'=0.5时,CFPR和CFPR'基本可以被控制在50%和5%左右。当样本比例K固定时,目标区CP相对稳定,尤其当K≥30%时随着α'的增加目标区CP几乎不受MRCT总样本量N的影响,且当α'不低于0.3时基本可以确保足够的CP(≥80%)。当K≥30%且设置α'=0.5时,即使目标区试验药物疗效略低于MRCT的疗效即f≥0.8,也可以确保目标区足够的CP和CP'(≥80%)。结论建议MRCT在方案设计时,目标区的样本比例不应低于30%,试验数据在目标区的检验水平不能超过0.5。该标准适用于目标区试验药物疗效略低于MRCT的疗效即f≥0.8的情形,若估计目标区试验药物疗效与MRCT的疗效相当,检验水平可适当降低,但不建议低于0.3。     

交叉滞后路径模型建模策略的模拟研究

目的 通过模拟试验,研究在不同样本量、随访间隔,以及不同交叉滞后路径系数组合的情形下,交叉滞后路径模型的表现。通过实例分析,比较不同建模情形下的模型结果。方法 首先基于两断面交叉滞后路径模型生成模拟数据集,然后在总数据集中随机抽样进行模型估计。通过遍历不同样本量及自相关系数,比较模型估计的Ⅰ类错误、检验效能、偏倚、标准误和均方误差。基于美国全国女性健康研究,使用两种建模策略探究身体质量指数(BMI)与血压之间的时序关系。结果 当样本量达到500后,模型拟合趋于稳定。当纳入到模型中样本的随访间隔不一致时,模型的检验效能未受到明显影响,但模型估计的Ⅰ类错误率达到0.12～0.15,标准误和均方误差也有所增大。当随访间隔一致时,自相关系数的大小对模型估计的误差影响较小,而模型估计的偏倚在自相关系数偏大或偏小时均有增大趋势。当两变量的自相关系数不相等时,模型的估计基本不受影响。实例分析结果显示,当纳入的研究对象随访间隔不一致时,BMI与血压之间为双向时序关系;而当纳入随访间隔一致的研究对象时,BMI与血压之间表现出BMI→血压的单向时序关系。结论 在交叉滞后路径模型建模过程中,样本量以及随访断...     

Increasing the sample size when the unblinded interim result is promising

Increasing the sample size based on unblinded interim result may inflate the type I error rate and appropriate statistical adjustments may be needed to control the type I error rate at the nominal level. We briefly review the existing approaches which allow early stopping due to futility, or change the test statistic by using different weights, or adjust the critical value for final test, or enforce rules for sample size recalculation. The implication of early stopping due to futility and a simple modification to the weighted Z-statistic approach are discussed. In this paper, we show that increasing the sample size when the unblinded interim result is promising will not inflate the type I error rate and therefore no statistical adjustment is necessary. The unblinded interim result is considered promising if the conditional power is greater than 50 per cent or equivalently, the sample size increment needed to achieve a desired power does not exceed an upper bound. The actual sample size increment may be determined by important factors such as budget, size of the eligible patient population and competition in the market. The 50 per cent-conditional-power approach is extended to a group sequential trial with one interim analysis where a decision may be made at the interim analysis to stop the trial early due to a convincing treatment benefit, or to increase the sample size if the interim result is not as good as expected. The type I error rate will not be inflated if the sample size may be increased only when the conditional power is greater than 50 per cent. If there are two or more interim analyses in a group sequential trial, our simulation study shows that the type I error rate is also well controlled.     

两阶段自适应样本量调整中合并P值法和传统t检验的模拟比较

目的 探讨Fisher合并P值法在两阶段自适应设计样本量调整中对I型错误和检验效能的影响.方法 利用蒙特-卡罗（Monte Carlo）法模拟不同样本量时的两阶段自适应设计过程,分别采用合并P值法和t检验分析最后数据并比较二者对I型错误、检验效能值的影响.结果 第一阶段样本量较小时,t检验能够保证检验效能,但是不能很好的抑制I型错误;合并P值法能较好的抑制I型错误,但检验效能降低较大.结论 根据第一阶段的方差和组间均值差调整样本量时,第一阶段样本量大于计划样本量的三分之一而小于计划样本量的一半时,应选择合并P值法;超过计划样本量的一半,则应采用t检验法.     

Simple procedures for blinded sample size adjustment that do not affect the type I error rate

For normally distributed data, determination of the appropriate sample size requires a knowledge of the variance. Because of the uncertainty in the planning phase, two-stage procedures are attractive where the variance is reestimated from a subsample and the sample size is adjusted if necessary. From a regulatory viewpoint, preserving blindness and maintaining the ability to calculate or control the type I error rate are essential. Recently, a number of proposals have been made for sample size adjustment procedures in the t-test situation. Unfortunately, none of these methods satisfy both these requirements. We show through analytical computations that the type I error rate of the t-test is not affected if simple blind variance estimators are used for sample size recalculation. Furthermore, the results for the expected power of the procedures demonstrate that the methods are effective in ensuring the desired power even under initial misspecification of the variance. A method is discussed that can be applied in a more general setting and that assumes analysis with a permutation test. This procedure maintains the significance level for any design situation and arbitrary blind sample size recalculation strategy.     

Re-calculating the sample size in internal pilot study designs with control of the type I error rate

When designing a clinical trial, there is usually some uncertainty about the variability of the primary outcome variable. This may lead to an unnecessarily high or inadequately low sample size. The internal pilot study approach uses data from patients recruited up to an interim stage to re-estimate the variance and to re-calculate the final sample size accordingly. Previously, simulation studies have shown that this methodology may highly improve the chance to obtain a well-powered trial. However, it also turned out that the type I error rate may be inflated by this procedure. We quantify the maximum excess of the type I error rate for normally distributed outcomes. If strict control of the alpha-level is considered to be an important issue, a method is proposed to achieve this when re-calculating the sample size in internal pilot studies. The characteristics of the power distributions are investigated for various sample size adaptation rules and implications are discussed.     

Internal pilot studies I: type I error rate of the naive t-test

When sample size is recalculated using unblinded interim data, use of the usual t-test at the end of a study may lead to an elevated type I error rate. This paper describes a numerical quadrature investigation to calculate the true probability of rejection as a function of the time of the recalculation, the magnitude of the detectable treatment effect, and the ratio of the guessed to the true variance. We consider both 'restricted' designs, those that require final sample size at least as large as the originally calculated size, and 'unrestricted' designs, those that permit smaller final sample sizes than originally calculated. Our results indicate that the bias in the type I error rate is often negligible, especially in restricted designs. Some sets of parameters, however, induce non-trivial bias in the unrestricted design.     

PLANNING AND REVISING THE SAMPLE SIZE FOR A TRIAL

The sample size for a trial depends on the type I and type II error rates and on the minimum relevant clinical difference, all of which are known, and on the anticipated, but unknown, value of a measure of variation for the key response. This measure is the overall response rate when the key response is binomially distributed, or the residual variance in each treatment group when the key response is continuous and normally distributed. Since the true value of the measure is unknown, it must be guessed or estimated from previous trials. We describe approaches to determining an appropriate value for it, both before the trial begins and after it has begun, for use in calculating the final sample size. These approaches differ from previously described ‘internal pilot’ methods in not requiring unblinding of the treatment assignments in the trial. They preserve the power and do not affect the type I error rate materially. The approaches can be applied to longitudinal studies where the rate of change over time is the response of interest, and to group sequential trials.     

Estimating the sample size for a t-test using an internal pilot.

If the sample size for a t-test is calculated on the basis of a prior estimate of the variance then the power of the test at the treatment difference of interest is not robust to misspecification of the variance. We propose a t-test for a two-treatment comparison based on Stein's two-stage test which involves the use of an internal pilot to estimate variance and thus the final sample size required. We evaluate our procedure's performance and show that it controls the type I and II error rates more closely than existing methods for the same problem. We also propose a rule for choosing the size of the internal pilot, and show that this is reasonable in terms of the efficiency of the procedure.     

Inflation of the type I error rate when a continuous confounding variable is categorized in logistic regression analyses

This paper demonstrates an inflation of the type I error rate that occurs when testing the statistical significance of a continuous risk factor after adjusting for a correlated continuous confounding variable that has been divided into a categorical variable. We used Monte Carlo simulation methods to assess the inflation of the type I error rate when testing the statistical significance of a risk factor after adjusting for a continuous confounding variable that has been divided into categories. We found that the inflation of the type I error rate increases with increasing sample size, as the correlation between the risk factor and the confounding variable increases, and with a decrease in the number of categories into which the confounder is divided. Even when the confounder is divided in a five-level categorical variable, the inflation of the type I error rate remained high when both the sample size and the correlation between the risk factor and the confounder were high.     

Operating characteristics of sample size re-estimation with futility stopping based on conditional power

Various methods have been described for re-estimating the final sample size in a clinical trial based on an interim assessment of the treatment effect. Many re-weight the observations after re-sizing so as to control the pursuant inflation in the type I error probability alpha. Lan and Trost (Estimation of parameters and sample size re-estimation. Proceedings of the American Statistical Association Biopharmaceutical Section 1997; 48-51) proposed a simple procedure based on conditional power calculated under the current trend in the data (CPT). The study is terminated for futility if CPT < or = CL, continued unchanged if CPT > or = CU, or re-sized by a factor m to yield CPT = CU if CL < CPT < CU, where CL and CU are pre-specified probability levels. The overall level alpha can be preserved since the reduction due to stopping for futility can balance the inflation due to sample size re-estimation, thus permitting any form of final analysis with no re-weighting. Herein the statistical properties of this approach are described including an evaluation of the probabilities of stopping for futility or re-sizing, the distribution of the re-sizing factor m, and the unconditional type I and II error probabilities alpha and beta. Since futility stopping does not allow a type I error but commits a type II error, then as the probability of stopping for futility increases, alpha decreases and beta increases. An iterative procedure is described for choice of the critical test value and the futility stopping boundary so as to ensure that specified alpha and beta are obtained. However, inflation in beta is controlled by reducing the probability of futility stopping, that in turn dramatically increases the possible re-sizing factor m. The procedure is also generalized to limit the maximum sample size inflation factor, such as at m max = 4. However, doing so then allows for a non-trivial fraction of studies to be re-sized at this level that still have low conditional power. These properties also apply to other methods for sample size re-estimation with a provision for stopping for futility. Sample size re-estimation procedures should be used with caution and the impact on the overall type II error probability should be assessed.