Early stopping to accept H(o) based on conditional power: approximations and comparisons

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.