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.     

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.     

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.     

多组间协变量均衡性评价方法的研究

目的构建用于评价三分组资料组间协变量均衡性的指标(简称FQ统计量);比较假设检验法、标准化差异法和FQ统计量这三种方法检验三分组资料组间协变量均衡性的能力。方法利用合并方差构建FQ统计量;采用有序多分类和无序多分类logistic回归计算各组研究个体的倾向性评分值;采用Monte Carlo模拟比较上述三种方法检验三分组资料组间协变量均衡性的能力。结果假设检验法检验三组间协变量均衡性的能力受样本量大小的影响,而标准化差异法和FQ统计量则不受样本量大小的影响。标准化差异法和FQ统计量检验三组间协变量均衡性的能力均高于假设检验法,且两者保持高度一致。当协变量的FQ统计量小于0.2时,认为协变量在三组间的分布达到均衡。结论标准化差异法与FQ统计量是有效的协变量均衡性检验方法,而FQ统计量的计算步骤较标准化差异法简便,因此更具有应用的优势。     

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。     

定量数据考虑基线与否的几种方差分析模型的模拟比较

目的比较几种考虑基线与否的方差分析模型的统计性能。方法应用Monte Carlo技术,在基线均衡和不均衡情况下,比较以下方差分析模型:以基线为协变量的变化量协方差分析(ANCOVA)、变化率协方差分析(PCS-ANCOVA)和对数变化率协方差分析(logPCS-ANCOVA);不考虑基线的变化量方差分析(ANOVA)、变化率方差分析(PCS-ANOVA)和对数变化率方差分析(logPCS-ANOVA)。以I类错误与检验效能评价各种方法的统计性能。结果在基线均衡的情况下,PCS-ANCOVA和ANOVA均可很好地控制I类错误,且检验效能都较高;在基线不均衡的条件下,若基线对因变量无影响,ANCOVA与ANOVA均可以较好地控制I类错误,此时ANOVA的检验效能高于ANCOVA;若基线对因变量有影响时,只有ANCOVA可以很好地控制I类错误,且检验效能较高,其他方法效果不佳。结论考虑到实际应用中绝大部分情况是基线对因变量有影响,即相关,建议优先采用以基线为协变量的协方差分析或变化量的协方差分析,无论基线是否均衡。用变化率做方差分析或协方差分析,有可能冒着比值的分布不满足参数方法条件的风险,应用时应慎重。     

样本量估计及其在nQuery和SAS软件上的实现——均数比较(九)

正1. 3多样本的均数比较1. 3. 1差异性检验1. 3. 1. 4协方差分析(ANCOVA)方法:Keppel(1991)~[1]给出的协方差分析样本量估计方法是建立在自由度为G-1,N-G-c,非中心参数为■的非中心F分布上。其检验效能的计算公式为:■式中,N代表总样本量,G代表组数,c代表协变量个数,ρ~2代表多变量决定系数(coefficient of multiple determination),反映协变量与结局变量间的关联强度,可     

方差不齐时两组及以上均数比较时不同分析方法的稳健性和把握度比较

目的本文着重比较秩和检验、调整自由度的t'检验、混合效应模型(mixed model)以及方差加权最小二乘法(VWLS)等方法在方差不齐时,用于两组/多组独立样本均数比较时的稳健性和把握度。方法本文通过模拟分析方法,分别设计总体均数相等或不等时,在不同标准差和样本量的条件下,用几种统计方法比较2组及3组样本均数的Ⅰ类错误和Power度。结果 (1)证实样本量相等时,t检验对于方差不齐的2组样本均数比较具有稳健性,但是样本量相等方差不齐的3组独立样本均数比较时,方差分析方法却不具有稳健性。(2)不论是2组还是3组样本均数比较,秩和检验在特定条件下对于方差不齐具有稳健性。(3)两组方差不齐样本均数比较时,t'检验和mixed model因为Ⅰ类错误更稳健,比VWLS方法更稳定,且这三种方法的Power值相互比较接近。(4)三组方差不齐样本均数比较,mixed model方法在样本量较少时比VWLS方法Ⅰ类错误更稳健,但是随着样本量增加,这一优势消失,而VWLS的Power值明显高于mixed model统计方法。结论 2组方差不齐样本均数比较时,可以使用t'检验、mixed model及VWLS等方法,其中首选更为稳健的t'检验、mixed model,3组方差不齐样本均数比较时可以使用mixed model及VWLS等方法,当样本量较小时首选mixed model方法,样本量增大时,以VWLS方法更优。     

协变量的不均衡对协方差分析的影响

目的探讨协变量的不均衡对协方差分析的影响。方法通过MonteCarlo模拟并结合临床试验实例对作协方差分析时引入不均衡的协变量来校正的前后变化作比较。结果协变量的不均衡对协方差分析的检验效能是存在一定影响的,无论协变量不均衡程度有多大,在作协方差分析时引入不均衡的协变量来校正总是有一定代价的。结论新药临床试验中常常存在病人的基线特征在处理组间不均衡从而影响对试验结果的正确评价。可以在作协方差分析时引入该不均衡的协变量去处理,但要根据协变量的不均衡程度及试验目的等实际情况加以权衡。     

两个非正态样本同分布检验的非参数法选择

目的 对检验两个非正态样本是否同分布的常用非参数方法进行评价,为合理选择检验方法提供参考依据.方法 采用Matlab7.5软件编程,模拟数据在不同的分布类型、样本量相等或不等、方差齐或不齐、方差与样本量顺向或反向、均数相等或不等等条件下,分别采用Wilcoxon检验、Wald-Wolfowitz游程检验(WWR)、Kolmogorov-Smirnov检验(K-S)和Hollander极端反应检验(Hollander)进行检验.结果 给出4种检验法的Ⅰ型和Ⅱ型误差估计值.结论 当两个总体均数相等时,建议选用Hollander检验;当两个总体方差相等时,建议选用Wilcoxon检验或K-S检验;而在两个总体方差、均数都不相等但差异不大时,则可选用Wilcoxon检验、K-S检验或Hollander检验中的任意一种.     

ANCOVA versus change from baseline: more power in randomized studies, more bias in nonrandomized studies [corrected

BACKGROUND AND OBJECTIVE: For inferring a treatment effect from the difference between a treated and untreated group on a quantitative outcome measured before and after treatment, current methods are analysis of covariance (ANCOVA) of the outcome with the baseline as covariate, and analysis of variance (ANOVA) of change from baseline. This article compares both methods on power and bias, for randomized and nonrandomized studies. METHODS: The methods are compared by writing both as a regression model and as a repeated measures model, and are applied to a nonrandomized study of preventing depression. RESULTS: In randomized studies both methods are unbiased, but ANCOVA has more power. If treatment assignment is based on the baseline, only ANCOVA is unbiased. In nonrandomized studies with preexisting groups differing at baseline, the two methods cannot both be unbiased, and may contradict each other. In the study of depression, ANCOVA suggests absence, but ANOVA of change suggests presence, of a treatment effect. The methods differ because ANCOVA assumes absence of a baseline difference. CONCLUSION: In randomized studies and studies with treatment assignment depending on the baseline, ANCOVA must be used. In nonrandomized studies of preexisting groups, ANOVA of change seems less biased than ANCOVA, but two control groups and two baseline measurements are recommended.     

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.     

Examining the effect of linkage disequilibrium between markers on the Type I error rate and power of nonparametric multipoint linkage analysis of two-generation and multigenerational pedigrees in the presence of missing genotype data

Because most multipoint linkage analysis programs currently assume linkage equilibrium between markers when inferring parental haplotypes, ignoring linkage disequilibrium (LD) may inflate the Type I error rate. We investigated the effect of LD on the Type I error rate and power of nonparametric multipoint linkage analysis of two-generation and multigenerational multiplex families. Using genome-wide single nucleotide polymorphism (SNP) data from the Collaborative Study of the Genetics of Alcoholism, we modified the original data set into 30 total data sets in order to consider six different patterns of missing data for five different levels of SNP density. To assess power, we designed simulated traits based on existing marker genotypes. For the Type I error rate, we simulated 1,000 qualitative traits from random distributions, unlinked to any of the marker data. Overall, the different levels of SNP density examined here had only small effects on power (except sibpair data). Missing data had a substantial effect on power, with more completely genotyped pedigrees yielding the highest power (except sibpair data). Most of the missing data patterns did not cause large increases in the Type I error rate if the SNP markers were more than 0.3 cM apart. However, in a dense 0.25-cM map, removing genotypes on founders and/or founders and parents in the middle generation caused substantial inflation of the Type I error rate, which corresponded to the increasing proportion of persons with missing data. Results also showed that long high-LD blocks have severe effects on Type I error rates.     

Effects of categorization method,regression type,and variable distribution on the inflation of Type‐I error rate when categorizing a confounding variable

The loss of signal associated with categorizing a continuous variable is well known, and previous studies have demonstrated that this can lead to an inflation of Type‐I error when the categorized variable is a confounder in a regression analysis estimating the effect of an exposure on an outcome. However, it is not known how the Type‐I error may vary under different circumstances, including logistic versus linear regression, different distributions of the confounder, and different categorization methods. Here, we analytically quantified the effect of categorization and then performed a series of 9600 Monte Carlo simulations to estimate the Type‐I error inflation associated with categorization of a confounder under different regression scenarios. We show that Type‐I error is unacceptably high (>10% in most scenarios and often 100%). The only exception was when the variable categorized was a continuous mixture proxy for a genuinely dichotomous latent variable, where both the continuous proxy and the categorized variable are error‐ridden proxies for the dichotomous latent variable. As expected, error inflation was also higher with larger sample size, fewer categories, and stronger associations between the confounder and the exposure or outcome. We provide online tools that can help researchers estimate the potential error inflation and understand how serious a problem this is. Copyright © 2014 John Wiley & Sons, Ltd.     

The performance of tests of publication bias and other sample size effects in systematic reviews of diagnostic test accuracy was assessed

BACKGROUND AND OBJECTIVE: Publication bias and other sample size effects are issues for meta-analyses of test accuracy, as for randomized trials. We investigate limitations of standard funnel plots and tests when applied to meta-analyses of test accuracy and look for improved methods. METHODS: Type I and type II error rates for existing and alternative tests of sample size effects were estimated and compared in simulated meta-analyses of test accuracy. RESULTS: Type I error rates for the Begg, Egger, and Macaskill tests are inflated for typical diagnostic odds ratios (DOR), when disease prevalence differs from 50% and when thresholds favor sensitivity over specificity or vice versa. Regression and correlation tests based on functions of effective sample size are valid, if occasionally conservative, tests for sample size effects. Empirical evidence suggests that they have adequate power to be useful tests. When DORs are heterogeneous, however, all tests of funnel plot asymmetry have low power. CONCLUSION: Existing tests that use standard errors of odds ratios are likely to be seriously misleading if applied to meta-analyses of test accuracy. The effective sample size funnel plot and associated regression test of asymmetry should be used to detect publication bias and other sample size related effects.     

Randomized controlled trials with time-to-event outcomes: how much does prespecified covariate adjustment increase power?

PURPOSE: We evaluated the effects of various strategies of covariate adjustment on type I error, power, and potential reduction in sample size in randomized controlled trials (RCTs) with time-to-event outcomes. METHODS: We used Cox models in simulated data sets with different treatment effects (hazard ratios [HRs] = 1, 1.4, and 1.7), covariate effects (HRs = 1, 2, and 5), covariate prevalences (10% and 50%), and censoring levels (no, low, and high). Treatment and a single covariate were dichotomous. We examined the sample size that gives the same power as an unadjusted analysis for three strategies: prespecified, significant predictive, and significant imbalance. RESULTS: Type I error generally was at the nominal level. The power to detect a true treatment effect was greater with adjusted than unadjusted analyses, especially with prespecified and significant-predictive strategies. Potential reductions in sample size with a covariate HR between 2 and 5 were between 15% and 44% (covariate prevalence 50%) and between 4% and 12% (covariate prevalence 10%). The significant-imbalance strategy yielded small reductions. The reduction was greater with stronger covariate effects, but was independent of treatment effect, sample size, and censoring level. CONCLUSIONS: Adjustment for one predictive baseline characteristic yields greater power to detect a true treatment effect than unadjusted analysis, without inflation of type I error and with potentially moderate reductions in sample size. Analysis of RCTs with time-to-event outcomes should adjust for predictive covariates.     

A simple sample size formula for analysis of covariance in randomized clinical trials

OBJECTIVE: Randomized clinical trials that compare two treatments on a continuous outcome can be analyzed using analysis of covariance (ANCOVA) or a t-test approach. We present a method for the sample size calculation when ANCOVA is used. STUDY DESIGN AND SETTING: We derived an approximate sample size formula. Simulations were used to verify the accuracy of the formula and to improve the approximation for small trials. The sample size calculations are illustrated in a clinical trial in rheumatoid arthritis. RESULTS: If the correlation between the outcome measured at baseline and at follow-up is rho, ANCOVA comparing groups of (1-rho(2))n subjects has the same power as t-test comparing groups of n subjects. When on the same data, ANCOVA is used instead of t-test, the precision of the treatment estimate is increased, and the length of the confidence interval is reduced by a factor 1-rho(2). CONCLUSION: ANCOVA may considerably reduce the number of patients required for a trial.     

Recommendations for choosing an analysis method that controls Type I error for unbalanced cluster sample designs with Gaussian outcomes

We used theoretical and simulation‐based approaches to study Type I error rates for one‐stage and two‐stage analytic methods for cluster‐randomized designs. The one‐stage approach uses the observed data as outcomes and accounts for within‐cluster correlation using a general linear mixed model. The two‐stage model uses the cluster specific means as the outcomes in a general linear univariate model. We demonstrate analytically that both one‐stage and two‐stage models achieve exact Type I error rates when cluster sizes are equal. With unbalanced data, an exact size α test does not exist, and Type I error inflation may occur. Via simulation, we compare the Type I error rates for four one‐stage and six two‐stage hypothesis testing approaches for unbalanced data. With unbalanced data, the two‐stage model, weighted by the inverse of the estimated theoretical variance of the cluster means, and with variance constrained to be positive, provided the best Type I error control for studies having at least six clusters per arm. The one‐stage model with Kenward–Roger degrees of freedom and unconstrained variance performed well for studies having at least 14 clusters per arm. The popular analytic method of using a one‐stage model with denominator degrees of freedom appropriate for balanced data performed poorly for small sample sizes and low intracluster correlation. Because small sample sizes and low intracluster correlation are common features of cluster‐randomized trials, the Kenward–Roger method is the preferred one‐stage approach. Copyright © 2015 John Wiley & Sons, Ltd.     

倾向指数匹配法与Logistic回归分析方法对比研究

[目的]比较倾向指数匹配法与Logistic回归分析方法的检验效能和I类错误。[方法]通过Monte Carlo模拟比较倾向指数匹配法和Logistic回归处理二分类资料的区别。[结果]倾向指数匹配法和Logistic回归的I类错误无差异,倾向指数全匹配法的检验效能略高。[结论]在观察性研究中,倾向指数匹配法具有很高的实用价值。