LAUSR

Xia and Hoover (2007) proposed a group sequential clinical trial design for the trial with Poisson outcome. Although it is a very practical clinical trial problem, the presentation of the article is still facing some technical challenges. First, there is still a debate on the sequential analyses to decide if it is a properly defined statistical problem. In the presentation of this manuscript. the sample space of the sequential analyses is not a fixed space, but a sequence of embeding spaces. The discussion of probability has to be associated with the mapping between these embeding spaces. Second, the trial design was built on an assumption that the repeated significance tests will inflate the inference error. In fact, the introduction of the group sequential design into the clinical trial does not only require the existence of the error inflation to be shown explicitly, but also need the error inflation to be intrinsic. Xia and Hoover (2007) did not show either of them, and it did not even list them as prerequisites. Armitage and colleagues (1969) showed that repeated significance tests at a fixed level on accumulating data increase the probability of obtaining a significant result under the null hypothesis. For example, with a significance level 0.05 in a two-sided fixed-sample test, the critical value is 1.96. If this value is used in a five-stage group sequential trial with early stopping to reject the null hypothesis, then the probability of rejecting the null hypothesis at or before the fifth stage is 0.14169, much larger than the nominal value 0.05. The above statements are true but also misleading. The nominal level of significance for a sample space does not mean the same for different sample spaces. If the statement is made for different sample space, 0.14169 and 0.05 is not comparable. On the other hand, the impact of the estimation methodology is significant for the error inflation. It can be shown that the error inflation caused by the repeated significance tests is not intrinsic, more efficient estimation algorithm may minimize the impact of the repeated significance tests and even eliminate the need for the error spending (Lan & DeMets, 1983).