The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Determination of Sample Sizes of Bivariate Efficacy and Safety Outcomes

이변량 효능과 안전성 이항변수의 표본수 결정방법

  • Lee, Hyun-Hak (Department of Biostatistics, Medical College, The Catholic University) ;
  • Song, Hae-Hiang (Department of Biostatistics, Medical College, The Catholic University)
  • 이현학 (가톨릭대학교 의학통계학과) ;
  • 송혜향 (가톨릭대학교 의학통계학과)
  • Published : 2009.04.30
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Abstract

We consider sample-size determination problem motivated by comparative clinical trials where patient outcomes are characterized by a bivariate outcome of efficacy and safety. Thall and Cheng (1999) presented a sample size methodology for the case of bivariate binary outcomes. We propose a bivariate Wilcoxon-Mann-Whitney(WMW) statistics for sample-size determination for binary outcomes, and this nonparametric method can be equally used to determine sample sizes of ordinal outcomes. The two methods of sample size determination rely on the same testing strategy for the target parameters but differs in the test statistics, an asymptotic bivariate normal statistic of the transformed proportions in Thall and Cheng (1999) and nonparametric bivariate WMW statistic in the other method. Sample sizes are calculated for the two experimental oncology trials, described in Thall and Cheng (1999), and for the first trial example the sample sizes of a bivariate WMW statistic are smaller than those of Thall and Cheng (1999), while for the second trial example the reverse is true.

두 군의 처리를 비교하는 임상시험에서 효능(efficacy)과 안전성(safety)이 동일하게 중요한 변수로 취급되는 경우에 이변량(bivariate) 반응변수로서 분석되고 연구계획의 단계에서도 이변량 표본수 결정방법이 사용되어야 한다. Thall과 Cheng (1999)은 효능과 안전성의 반응값이 이변량 이항(bivariate binary) 변수인 경우의 표본수 결정방법을 제시하였으며, 본 연구에서는 목표모수 설정과정은 기존의 연구와 같으나 월콕슨-만-휘트니(Wilcoxon-Mann-Whitney: WMW) 통계량에 근거한 검정법과 표본수 결정방법을 제시한다. Thall과 Cheng (1999)의 검정통계량은 변수 변환시킨 비율의 근사 정규성에 근거하는 반면에, WMW 통계량은 확률에 근거한 비모수적 방법으로 이변량 이항변수 뿐만 아니라 이변량 순위변수로 측정된 반응값에도 적용시킬 수 있다 Thall과 Cheng (1999)에 제시한 항암치료 임상연구의 두 예제에 위의 두 다른 방법으로 계산된 표본수를 비교한 결과, Thall과 Cheng (1999)의 첫째 예제에서는 이변량 WMW 방법에 의한 표본수가 더욱 작았으나 둘째 예제에서는 더욱 큰 것으로 나타났다.

Keywords

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