On adaptive error spending approach for group sequential trials with random information levels.

A group sequential analysis following the error spending approach of Lan and DeMets ( 1983 ) requires that the maximum information level be fixed in advance. In practice, however, the maximum information level is often random, making it impossible to determine the information fractions required by Lan and DeMets ( 1983 ) to calculate the sequential boundary. We propose an adaptive error spending approach that further expands practical applications to settings where the interim information levels can depend on blinded accumulating data. We use a simple weighting method to combine independent test statistics from different stages, which are then compared with adaptive boundary values for the group sequential test. We develop a measure-theoretic framework and show that the adaptive error spending approach controls the type 1 error rates. Methods for point estimates and confidence intervals are also proposed. We warn that an error spending approach can lead to serious inflation of the type 1 error rates when the number or timing of interim analyses is allowed to depend on unblinded accumulating data.