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AME循证杂谈021|两样本率比较的样本量计算——基于PASS软件实现

Published at: 2015年第1卷第S1期

周支瑞
关键词:

循证杂谈今天继续探讨临床研究样本量计算,第二弹,如题!

 

前文介绍了两样本均数比较的样本量计算,本文将以案例的形式介绍下两样本率比较的样本量计算。两样本均数比较及率的比较的情况在临床研究样本量计算中比较常见,所以笔者安排优先介绍。

【案例1】一个新的抗肿瘤药物A与安慰剂对照进行II期临床试验。已知安慰剂组的应答率为20%。如果新药A能够把应答率提高20%,则认为该药临床有效。按照1:1平行设计,取alpha=0.05,power=90%,双侧检验,每组需要多少样本?总计需要多少样本?

第一步,如图依次点击:

图1 依次选择Proportions----Two Independent Proportions----Test For Two Proportions [Proportions]

 

第二步,如图填入参数:

图2 设置参数

 

参数的具体含义及解释如下:

N1表示待计算的试验组样本量,此处为选择项;power=90%表示把握度为0.9,alpha=0.05表示检验水准为0.05;Use R,R=1.0的含义是,试验组与对照组按照1:1分组;已知安慰剂组的应答率为P2=20%。新药A(试验组)能够把应答率提高到P1=40%。

样本量计算结果及报道如下:

Two Independent Proportions (Null Case) Power Analysis

Numeric Results of Tests Based on the Difference: P1 - P2

H0: P1-P2=0. H1: P1-P2=D1<>0. Test Statistic: Z test with pooled variance

References

Chow, S.C.; Shao, J.; Wang, H. 2003. Sample Size Calculations in Clinical Research. Marcel Dekker. New York. D'Agostino, R.B., Chase, W., Belanger, A. 1988.'The Appropriateness of Some Common Procedures for Testing the Equality of Two Independent Binomial Populations', The American Statistician, August 1988, Volume 42 Number 3, pages 198-202.

Fleiss, J. L., Levin, B., Paik, M.C. 2003. Statistical Methods for Rates and Proportions. Third Edition. John Wiley & Sons. New York.

Lachin, John M. 2000. Biostatistical Methods. John Wiley & Sons. New York. Machin, D., Campbell, M., Fayers, P., and Pinol, A. 1997. Sample Size Tables for Clinical Studies, 2nd Edition. Blackwell Science. Malden, Mass.

Report Definitions

'Power' is the probability of rejecting a false null hypothesis. It should be close to one.

 

'N1 and N2' are the sizes of the samples drawn from the corresponding populations.

 

'P1' is the proportion for group one under H1. This is the treatment or experimental group.

 

'P2' is the proportion for group two. This is the standard, reference, or control group

 

'Target Alpha' is the probability of rejecting a true null hypothesis that was desired.

 

'Actual Alpha' is the value of alpha that is actually achieved.

 

'Beta' is the probability of accepting a false null hypothesis.

 

Summary Statements

 

Group sample sizes of 109 in group one and 109 in group two achieve 90% power to detect a difference between the group proportions of 0.2000. The proportion in group one (the treatment group) is assumed to be 0.2000 under the null hypothesis and 0.4000 under the alternative hypothesis. The proportion in group two (the control group) is 0.2000. The test statistic used is the two-sided Z test with pooled variance. The significance level of the test was targeted at 0.0500. The significance level actually achieved by this design is NA.

 

本例中共计需要218例标本,试验组对照组各需要109例标本。

 

【案例2】一个新的抗肿瘤药物A与标准药物B对照进行III期临床试验。已知药物B的应答率为30%。根据临床应用的实际情况,设置非劣效性的限值为10%。根据预实验,估计新药A应答率为25%。按照1:1平行非劣效性设计,alpha=0.05,power=90%,双侧检验,每组需要多少样本?总计需要多少样本?

 

第一步,如图依次点击:

图3 依次选择Proportions----Two Independent Proportions----Non-Inferiority Test For Two Proportions [proportions]

 

第二步,如图依次填入参数:

图4 设置参数

 

参数的具体含义及解释如下:

N1表示待计算的试验组样本量,此处为选择项;power=90%表示把握度为0.9,alpha=0.05表示检验水准为0.05;Use R,R=1.0的含义是,试验组与对照组按照1:1分组;P1.0 (Non-Inferiority Proportion)=0.2(对照药物应答率30%-非劣效限值10%);P1.1 (Actual Proportion)= 25%;P2 (Reference Group Proportion)=30%。

样本量计算结果及报道如下:

Power Analysis of Non-Inferiority Tests of Two Independent Proportions

Numeric Results for Non-Inferiority Tests Based on the Difference: P1 - P2

H0: P1-P2<=D0. H1: P1-P2=D1>D0. Test Statistic: Z test (unpooled)

Note: exact results based on the binomial were only calculated when both N1 and N2 were less than 100.

 

References

 

Chow, S.C.; Shao, J.; Wang, H. 2003. Sample Size Calculations in Clinical Research. Marcel Dekker. New York.Farrington, C. P. and Manning, G. 1990. 'Test Statistics and Sample Size Formulae for Comparative Binomial Trials with Null Hypothesis of Non-Zero Risk Difference or Non-Unity Relative Risk.' Statistics in Medicine, Vol. 9, pages 1447-1454.Fleiss, J. L., Levin, B., Paik, M.C. 2003. Statistical Methods for Rates and Proportions. Third Edition. John Wiley & Sons. New York. Gart, John J. and Nam, Jun-mo. 1988. 'Approximate Interval Estimation of the Ratio in Binomial Parameters: A Review and Corrections for Skewness.' Biometrics, Volume 44, Issue 2, 323-338.Gart, John J. and Nam, Jun-mo. 1990. 'Approximate Interval Estimation of the Difference in Binomial Parameters: Correction for Skewness and Extension to Multiple Tables.' Biometrics, Volume 46, Issue 3,637-643.

 

Lachin, John M. 2000. Biostatistical Methods. John Wiley & Sons. New York.

 

Machin, D., Campbell, M., Fayers, P., and Pinol, A. 1997. Sample Size Tables for Clinical Studies, 2nd Edition. Blackwell Science. Malden, Mass.

 

Miettinen, O.S. and Nurminen, M. 1985. 'Comparative analysis of two rates.' Statistics in Medicine 4: 213-226.

 

Report Definitions

 

'Power' is the probability of rejecting a false null hypothesis.

 

'N1 and N2' are the sizes of the samples drawn from the corresponding groups.

 

'P2' is the response rate for group two which is the standard, reference, baseline, or control group.

 

'P1.0' is the smallest treatment-group response rate that still yields a non-inferiority conclusion.

 

'P1.1' is the treatment-group response rate at which the power is calculated.

 

'D0' is the non-inferiority margin. It is the difference P1-P2 assuming H0.

 

'D1' is the actual difference, P1-P2, at which the power is calculated.

 

'Target Alpha' is the probability of rejecting a true null hypothesis that was desired.

 

'Actual Alpha' is the value of alpha that is actually achieved. Actual Alpha is only shown when Exact Calculations are used (see the Options tab).

 

'Beta' is the probability of accepting a false H0. Beta = 1 - Power.

 

'Grp 1' refers to Group 1 which is the treatment or experimental group.

 

'Grp 2' refers to Group 2 which is the reference, standard, or control group.

 

'Non-Inf.' refers to a small distance from the reference proportion that is still considered non-inferior.

 

'Actual' refers to the true value at which the power is computed.

 

Summary Statements

 

Sample sizes of 1362 in group one and 1362 in group two achieve 90% power to detect a non-inferiority margin difference between the group proportions of -0.1000. The reference group proportion is 0.3000. The treatment group proportion is assumed to be 0.2000 under the null hypothesis of inferiority. The power was computed for the case when the actual treatment group proportion is 0.2500. The test statistic used is the one-sided Z test (unpooled). The significance level of the test was targeted at 0.0500. The significance level actually achieved by this design is NA.

 

本例中共计需要2724例标本,试验组对照组各需要1362例标本。

至此,关于两样本率比较的样本量计算演示完毕。

 

笔者|周支瑞 ,复旦大学附属肿瘤医院放射治疗科在读博士

 

下期预告

样本量计算第三弹预告

诊断准确性研究的样本量计算----基于PASS软件实现

doi:10.3978/kysj.2014.1.1436

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