The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Sample Size Determination for Comparing Tail Probabilities

극소 비율의 비교에 대한 표본수 결정

  • Lee, Ji-An (Department of Biostatistics, The Catholic University of Korea) ;
  • Song, Hae-Hiang (Department of Biostatistics, The Catholic University of Korea)
  • 이지안 (가톨릭대학교 의학통계학과) ;
  • 송혜향 (가톨릭대학교 의학통계학과)
  • Published : 2007.03.31
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Abstract

The problem of calculating the sample sizes for comparing two independent binomial proportions is studied, when one of two probabilities or both are smaller than 0.05. The use of Whittemore(1981)'s corrected sample size formula for small response probability, which is derived based oB multiple logistic regression, demonstrates much larger sample sizes compared to those by the asymptotic normal method, which is derived for the comparison of response probabilities belonging to the normal range. Therefore, applied statisticians need to be careful in sample size determination with small response probability to ensure intended power during a planning stage of clinical trials. The results of this study describe that the use of the sample size formula in the textbooks might sometimes be risky.

이 논문에서는 두 독립인 이항 확률의 비교에서 이항 확률 중 하나 또는 모두가 0.05보다 작을 경우의 두 확률의 비교에 대한 표본수 계산의 문제를 다루었다. Whitte-more(1981)는 여러 공변량에 근거한 로지스틱 회귀를 이용하여 극소 확률의 경우에 대한 수정 표본수 공식을 제안하였다. 이를 독립된 비율의 비교에 적용하여 이로부터 계산한 표본수는 일반적으로 많이 사용하는 근사 정규 방법, 특히 극소 비율의 비교에 대한 방법이 아닌 근사 정규 방법의 표본수 보다도 훨씬 큰 표본수를 제시하고 있다. 그러므로, 응용분야의 통계인들은 극소 반응 확률에 근거한 임상 시험을 계획할 경우 계획의 단계에서 의도하는 검정력을 확보하기 위해 교과서에 제시된 표본수 공식이나 부표에 의존한다면 위험할 수 있음을 이 논문의 결과가 말해 주고 있다.

Keywords

References

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