Betensky R A
Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts 02115, USA.
Biometrics. 1997 Sep;53(3):794-806.
It is intuitively appealing to clinicians to stop a trial early to accept the null hypothesis Ho if it appears that this will be the likely outcome at the planned end of the trial. We consider procedures that calculate at each time point the conditional probability of rejecting Ho at the end of the trial given the current data and some value of the parameter of interest. Lan, Simon, and Halperin (1982, Communications in Statistics C1, 207-219) calculate this probability under the design alternative, and Pepe and Anderson (1992, Applied Statistics 41, 181-190) use an alternative based solely on the current data. We investigate a modification to Pepe and Anderson's (1992) procedure that has a more satisfying interpretation. We define all of these procedures as formal sequential tests with lower stopping boundaries and study them in this context. This facilitates an improved understanding of the interplay of parameters by introducing visual displays, and it leads to an approximation for power by treating it as a boundary crossing probability. We use these tools to compare the performances of the different designs under a variety of parameter configurations.
对于临床医生来说，如果在试验计划结束时似乎零假设(H_0)很可能成立，那么提前终止试验以接受零假设(H_0)在直觉上很有吸引力。我们考虑这样的程序，即在每个时间点计算给定当前数据和感兴趣参数的某个值时在试验结束时拒绝(H_0)的条件概率。Lan、Simon和Halperin（1982年，《统计通信》C1，207 - 219）在设计备择假设下计算此概率，而Pepe和Anderson（1992年，《应用统计学》41，181 - 190）使用仅基于当前数据的一种方法。我们研究对Pepe和Anderson（1992年）程序的一种修改，这种修改具有更令人满意的解释。我们将所有这些程序定义为具有较低停止边界的形式化序贯检验，并在此背景下对它们进行研究。通过引入可视化展示，这有助于更好地理解参数之间的相互作用，并且通过将检验功效视为边界穿越概率，从而得到检验功效的近似值。我们使用这些工具在各种参数配置下比较不同设计的性能。
