Two-stage adaptive designs with correlated test statistics

When performing a trial using an adaptive sequential design, it is usually assumed that the data for each stage come from different units; for example, patients. However, sometimes it is not possible to satisfy this condition or to check whether it is satisfied. In these cases, the test statistics and p-values of each stage may be dependent. In this paper we investigate the type I error of two-stage adaptive designs when the test statistics from the stages are assumed to be bivariate normal. Analytical considerations are performed under the restriction that the conditional error function is constant in the continuation region. We show that the decisions can become conservative as well as anticonservative, depending on the design parameters and on the sign of the correlation coefficient. Further, we discuss properties and advantages of this design and compare it with the Bauer-Köhne method.