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. 2023 Jan 20;43(1):105-110.
doi: 10.12122/j.issn.1673-4254.2023.01.14.

[Comparison of 7 methods for sample size determination based on confidence interval estimation for a single proportion]

[Article in Chinese]
M Yu  1 , X Shi  1 , B Zou  1 , S An  1
Affiliations

[Comparison of 7 methods for sample size determination based on confidence interval estimation for a single proportion]

[Article in Chinese]
M Yu et al. Nan Fang Yi Ke Da Xue Xue Bao. .

Abstract
in English, Chinese

Objective: To compare different methods for calculating sample size based on confidence interval estimation for a single proportion with different event incidences and precisions.

Methods: We compared 7 methods, namely Wald, AgrestiCoull add z2, Agresti-Coull add 4, Wilson Score, Clopper-Pearson, Mid-p, and Jefferys, for confidence interval estimation for a single proportion. The sample size was calculated using the search method with different parameter settings (proportion of specified events and half width of the confidence interval [ω=0.05, 0.1]). With Monte Carlo simulation, the estimated sample size was used to simulate and compare the width of the confidence interval, the coverage of the confidence interval and the ratio of the noncoverage probability.

Results: For a high accuracy requirement (ω =0.05), the Mid-p method and Clopper Pearson method performed better when the incidence of events was low (P < 0.15). In other settings, the performance of the 7 methods did not differ significantly except for a poor symmetry of the Wald method. In the setting of ω=0.1 with a very low p (0.01-0.05), failure of iteration occurred with nearly all the methods except for the Clopper-Pearson method.

Conclusion: Different sample size determination methods based on confidence interval estimation should be selected for single proportions with different parameter settings.

目的: 在不同样本率和精度水平下，比较不同计算单组率的置信区间样本量估计方法。

方法: 基于Wald法、ADD4法、ADDZ2法、Wilson Score法、Clopper-Pearson法、Mid-p法和Jeffreys法这7种单组率置信区间的估计方法，在两种精度ω（0.05，0.1）、不同事件发生率p下，用“搜索法”计算出样本量，并通过Monte Carlo模拟，以估计出的样本量计算相应置信区间并比较其宽度、覆盖率和尾侧不覆盖率比值。

结果: 当精度要求较高时（ω=0.05），Mid-p法和Clopper-Pearson法在事件发生率较低（P < 0.15）时综合表现较优，其余情况，除Wald法对称性不好外，所有其他方法表现差异不大。在ω=0.1，且事件发生率极低p=（0.01-0.05）时，除Clopper-Pearson法外，其余方法都存在无法迭代的情况。

结论: 针对不同的预计发生率和精度要求，建议选择相对合适的样本量估计方法。

Keywords: binary data; interval width; sample size estimation; single proportion.

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Figures

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1
样本量随事件发生率p的变化情况 Influence of p on sample size estimation (ω=0.05, 0.1).
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区间覆盖率(CP)随事件发生率p的变化情况 Influence of event probability (p) on coverage probability (ω=0.05).
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尾侧不覆盖率比值(NCP)随事件发生率p的变化情况 Influence of p on noncoverage probability (ω =0.05; NCP= MNCP/(MNCP+DNCP)).
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置信区间宽度(CW)随事件发生率p的变化情况 Influence of p on confidence interval width (ω=0.05).
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