Detecting treatment differences in group sequential longitudinal studies with covariate adjustment

In longitudinal studies comparing two treatments over a series of common follow-up measurements, there may be interest in determining if there is a treatment difference at any follow-up period when there may be a non-monotone treatment effect over time. To evaluate this question, Jeffries and Geller (2015) examined a number of clinical trial designs that allowed adaptive choice of the follow-up time exhibiting the greatest evidence of treatment difference in a group sequential testing setting with Gaussian data. The methods are applicable when a few measurements were taken at prespecified follow-up periods. Here, we test the intersection null hypothesis of no difference at any follow-up time versus the alternative that there is a difference for at least one follow-up time. Results of Jeffries and Geller (2015) are extended by considering a broader range of modeled data and the inclusion of covariates using generalized estimating equations. Testing procedures are developed to determine a set of follow-up times that exhibit a treatment difference that accounts for multiplicity in follow-up times and interim analyses.