Group sequential comparison of changes: ad-hoc versus more exact method

There are many clinical trials in which we are interested in comparing changes in responses between two treatment groups sequentially. Investigators might assume a simple linear model, take the average of the ordinary least square estimators of slope within each treatment group, and use the standardized difference between these two averages as the test statistic at each interim analysis. Ad-hoc construction of the boundary values for interim analysis might be based on group sequential methods which assume that the interim test statistics have independent increments even though it may not be true when a response variable is measured repeatedly over time for each subject. This ad-hoc method is very simple and appealing, and thus has been used in a clinical trial setting. Lee and DeMets (1991, Journal of the American Statistical Association 86, 757-762) have proposed a more exact group sequential method for comparing rates of change. Under the assumption that the response follows the linear mixed effects model, they have derived the asymptotic joint distribution of the sequentially computed statistics. Construction of group sequential boundaries is based on this distribution theory. By simulation studies, we first study the robustness of the more exact method to violations of the typical assumptions. In addition, we compare the ad-hoc method with the more exact method and examine how well these two methods work for various situations. The relationship between two different information times, Fisher information and a surrogate information, are also discussed from the simulation studies.