Group-Sequential Designs in Clinical Trials

Methods

Group-sequential methods are clinical trial stopping rules that consist of series of interim analyses conducted at each visit so that any significant difference among treatment groups can be detected before the trial ends. Initially, before the trial begins, the number of visits and the sample size required at each interim visit are determined. Then, at each interim visit, a significance test is conducted. Once there is evidence for significant difference between the treatment groups at any interim visit, an early termination of the clinical trial is possible and there is no need to recruit any more subjects. For the significance testing, there are several available methods, among which Pocock's, O'Brien and Fleming's, and Wang and Tsiatis's tests are widely used in clinical trials.

Test Procedures

In this section, three tests are described for comparing two treatment groups based on a normal response with known variance. Significance tests for the other types of response variables (e.g., binomial or exponential) are not explained here, but are also available. In addition, if the main interest is to compare more than two treatment groups, it is possible to modify the tests using an F ratio test for one-way analysis of variance. All three tests are similar in the sense that they adjust critical values for multiple comparisons in order to prevent the increasing probability of Type I errors (rejection of a true null hypothesis).

For all tests, let K be the fixed number of visits, which is predetermined before the trial begins. Let xij be the jth subject from the ith treatment group, where i = 1, 2 and j = 1, …, n. Assume that each xij is independently drawn from a normal distribution with a mean of μi and a variance of ρ2i. Finally, nk is the number of accumulated subjects [Page 554]at the kth visit, and it is assumed that n1 and n2 are even.

...