基于精确度考虑的二分类数据样本量估计

目的:对传统的二分类数据样本量估计方法进行调整,以达到同时兼顾假设检验效能和精确度的要求。方法:采用"两步法"将效应估计的显著性和精确度结合起来估计样本含量。在传统方法计算所得样本量的基础上,逐步增加样本量,并同时计算可信区间宽度低于期望宽度的概率,当此概率超过预先设定的水平时即可停止,即直到可信区间宽度达到要求的宽度为止。结果:增大后的样本量可以较好的兼顾显著性和精确度的要求。结论:为达到一定的精确度要求,对传统样本含量估计过程进行调整是必要的。     

阳性药对照临床试验有效性的可信区间评价方法

目的　介绍阳性药对照临床试验中3种有效性评价的可信区间方法,并将其与传统的假设检验方法进行比较。方法与结果　用假设检验和可信区间方法分别对3个阳性药对照试验进行了计算与分析在3种情况下均显示了可信区间方法的适用性。结论　在阳性药对照临床试验中,传统假设检验方法具有明显的局限性,建议结合可信区间方法使用。     

百分率可信区间的精确计算

目的:用EXCEL精确计算百分率的可信区间。方法:利用EXCEL单变量求解计算技术,直接精确计算百分率的可信区间。结果:用单变量求解技术计算的百分率可信区间,可任意定义可信区间的计算范围,比查表法精确、灵活和简便。结论:在EX-CEL中可计算任意范围的百分率可信区间,结果精确而简便。     

均匀分布资料总体中位数可信区间估计Bootstrap法样本含量的设置

探讨了Bootstrap样本含量n*对Bootstrap法总体中位数可信区间估计效果的影响。首先模拟从均匀分布总体中随机抽样;然后用Bootstrap法进行总体中位数可信区间估计,重复1000次,得到1000个可信区间,统计1000个可信区间包含总体中位数的正确率。结果表明,Bootstrap样本含量n*对总体中位数可信区间估计的正确率影响很大,Bootstrap样本含量n*越小,正确率越高;Bootstrap样本含量n*越大,正确率越低;Bootstrap样本含量n*不能任意设置,当Bootstrap样本含量n*=n-3时,效果最好。     

圆形分布角均数可信区间的计算

目的:计算圆形分布角均数的可信区间。方法:利用EXCEL函数功能计算圆形分布角均数的可信区间。结果:当样本量足够大时,角均数可信区间的计算精度较高。结论:不需要查表,利用EXCEL精确计算角均数的可信区间,应用于方向性资料的正常值计算和可信限的估计。     

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。     

精度法估计OR或RR研究中的样本含量

提出了在确定可信区间概率时选择较高精度估计病例对照研究中 OR和队列研究中 RR所需样本含量的公式。由公式计算的样本含量能使研究者了解由样本所获得的点估计值接近总体真实值的程度 ,从而能较为准确地判断研究结果的实际意义。     

logistic回归系数可信区间估计及假设检验的三种方法比较

目的:比较logistic回归分析中估计回归系数可信区间及假设检验的三种方法。方法:从理论上介绍Wald、Bootstrap和轮廓似然三种方法,比较其应用前提。应用Monte-Carol模拟方法,分别产生自变量为二分类变量和连续型变量的二分类logistic分析数据,比较三种方法的准确性和稳定性。结果:无论自变量为连续型或二分类变量,Bootstrap法和轮廓似然法的检验效能均高于Wald法,该差异在小样本情形下更为明显。但Bootstrap方法的稳定性较差,对I类错误的控制也欠佳。结论:轮廓似然方法最为稳健,能严格控制I类错误率,且检验效能优于Wald方法,值得推荐。     

圆形分布函数曲线下面积的计算

目的:计算圆形分布函数曲线下的面积,用于角度资料正常值范围的估计和角均数的可信限计算。方法:利用EX-CEL工程函数和辛普森积分计算技术,计算Vonmises函数曲线下的面积,精确计算圆形分布函数曲线下的面积。结果:用辛普森积分精确计算圆形分布函数曲线下的面积,比查表法精确和方便。结论:精确计算圆形分布函数曲线下的面积,用于角度资料正常值范围的估计和角均数的可信限计算,扩展了圆形分布的应用范围。     

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。     

A Review of: “Interpreting and Reporting Clinical Trials: A Guide to the CONSORT Statement and the Principles of Randomised Controlled Trials,by A. Keech,V. Gebski,and R. Pike (eds.)”

Traditionally, Phase II trials have been conducted as single-arm trials to compare the response probabilities between an experimental therapy and a historical control. Historical control data, however, often have a small sample size, are collected from a different patient population, or use a different response assessment method, so that a direct comparison between a historical control and an experimental therapy may be severely biased. Randomized Phase II trials entering patients prospectively to both experimental and control arms have been proposed to avoid any bias in such cases. The small sample sizes for typical Phase II clinical trials imply that the use of exact statistical methods for their design and analysis is appropriate. In this article, we propose two-stage randomized Phase II trials based on Fisher’s exact test, which does not require specification of the response probability of the control arm for testing. Through numerical studies, we observe that the proposed method controls the type I error accurately and maintains a high power. If we specify the response probabilities of the two arms under the alternative hypothesis, we can identify good randomized Phase II trial designs by adopting the Simon’s minimax and optimal design concepts that were developed for single-arm Phase II trials.     

Sample size calculation based on efficient unconditional tests for clinical trials with historical controls

In historical clinical trials, the sample size and the number of success in the control group are often considered as given. The traditional method for sample size calculation is based on an asymptotic approach developed by Makuch and Simon (1980). Exact unconditional approaches may be considered as alternative to control for the type I error rate where the asymptotic approach may fail to do so. We provide the sample size calculation using an efficient exact unconditional testing procedure based on estimation and maximization. The sample size using the exact unconditional approach based on estimation and maximization is generally smaller than those based on the other approaches.     

Single-Arm Phase II Survival Trial Design Under the Proportional Hazards Model

For designing single-arm phase II trials with time-to-event endpoints, a sample size formula is derived for the modified one-sample log-rank test under the proportional hazards model. The derived formula enables new methods for designing trials that allow a flexible choice of the underlying survival distribution. Simulation results showed that the proposed formula provides an accurate estimation of sample size. The sample size calculation has been implemented in an R function for the purpose of trial design. Supplementary materials for this article are available online.     

Sample Size and Power Analysis for Endometrial Safety Studies

ABSTRACT

Endometrial safety studies are required for the approval of progestin components. The Committee for Proprietary Medicinal Products requirement is the actual percentage below 2% and the upper limit of the one-sided exact 95% confidence interval not more than 2% above the point estimate. The more recent U.S. Food and Drug Administration requirement is the actual percentage ≤ 1% and the upper limit of the one-sided exact 95% confidence interval ≤4%. I studied the sample size and power needed to satisfy both requirements based on the exact confidence intervals for the binomial parameter and the Poisson parameter. I discovered that a larger sample size does not always lead to a higher power. I presented a best sample size that satisfies both requirements and recommended that the patient enrollment should be closely monitored during the study.     

Sample size and power analysis for endometrial safety studies

Endometrial safety studies are required for the approval of progestin components. The Committee for Proprietary Medicinal Products requirement is the actual percentage below 2% and the upper limit of the one-sided exact 95% confidence interval not more than 2% above the point estimate. The more recent U.S. Food and Drug Administration requirement is the actual percentage < or = 1% and the upper limit of the one-sided exact 95% confidence interval < or =4%. I studied the sample size and power needed to satisfy both requirements based on the exact confidence intervals for the binomial parameter and the Poisson parameter. I discovered that a larger sample size does not always lead to a higher power. I presented a best sample size that satisfies both requirements and recommended that the patient enrollment should be closely monitored during the study.     

A Free Gift: An Adaptive Strategy in a Single-Arm Trial Using an Exact Test Through the Binomial Distribution

For medical product development within the same generation, single-arm trial designs are commonly implemented to test the performance of the new product against an objective performance criterion. When the primary endpoint is binary and the sample size is moderate, an exact test through the binomial distribution is usually used. This article shows that it is a free gift to add an adaptive component to a fixed-sample-size design so that when the interim result is marginal, the adaptive feature can be activated without any penalty. A hypothetical example is used to illustrate the application of this method.     

临床随访研究中样本含量的估计

目的:介绍临床随访研究中生存分析资料的log-rank检验所需样本含量的估计法.方法:以离散性Markov链拟合生存过程,据此计算log-rank统计量的数学期望和方差,导出样本含量估计公式.结果:实例分析表明,该法能较好反映实际情况,应用灵活.结论:本法是一种有效、可行的样本含量估计法,值得推荐.     

漫谈区间估计的精度与置信度

在区间估计问题中,置信区间的精度与置信度是一对矛盾,置信区间的精度与置信度同时又与样本容量相关联。讨论对于给定的样本,当置信区间的置信度确定时,如何尽可能地提高置信区间的精度以及如何通过样本容量的调节,使置信区间的精度能达到预先的要求。     

Review and evaluation of methods for computing confidence intervals for the ratio of two proportions and considerations for non-inferiority clinical trials

This article reviews several methods for forming confidence intervals for a risk ratio of two independent binomial proportions (which are both less than 0.50) and evaluates their statistical performance. These methods include use of a Taylor Series expansion to estimate variance, solutions to a quadratic equation, and maximum likelihood methods. In addition, for improvement of the properties of the methods based on large sample approximations, situations where either binomial count was less than or equal to 3 were managed conservatively by having an exact confidence interval for the odds ratio become the confidence interval for its risk ratio counterpart. Methods were initially evaluated by computing confidence limits for certain cases. Second, simulations were used to identify the better methods for controlling the Type I error rate while maintaining power. Last, relationships between methods were evaluated by calculating the percent of disagreement in the decision made regarding non inferiority. Methods in the group using a Taylor Series expansion in variance estimation perform similarly to the Pearson method preferred in the literature. In addition, the group of methods using a Taylor Series expansion are most easily computed. Applications of these findings are discussed for ratios that arise in randomized clinical trials that are conducted to show noninferiority of a new medical product to a reference control. Consideration is given as well to sample size calculations for noninferiority clinical trials.     

Confidence interval of the difference between two proportions with overdispersion

In confidence interval estimation of the difference between two proportions with overdispersion due to positive correlations, the usual asymptotic normality-based method generally has lower coverage rates than desired, especially when sample size is moderate. Applying the concept of effective sample size to existing methods for independent data, we propose three new asymptotic normality-based methods. It is demonstrated through an extensive Monte Carlo study that the proposed methods generally perform better than the usual method. The proposed methods are illustrated in the application to a motivating data example.