Evaluating treatment effects in group sequential multivariate longitudinal studies with covariate adjustment.

Jeffries et al. (2018) investigated testing for a treatment difference in the setting of a randomized clinical trial with a single outcome measured longitudinally over a series of common follow-up times while adjusting for covariates. That paper examined the null hypothesis of no difference at any follow-up time versus the alternative of a difference for at least one follow-up time. We extend those results here by considering multivariate outcome measurements, where each individual outcome is examined at common follow-up times. We consider the case where there is interest in first testing for a treatment difference in a global function of the outcomes (e.g., weighted average or sum) with subsequent interest in examining the individual outcomes, should the global function show a treatment difference. Testing is conducted for each follow-up time and may be performed in the setting of a group sequential trial. Testing procedures are developed to determine follow-up times for which a global treatment difference exists and which individual combinations of outcome and follow-up time show evidence of a difference while controlling for multiplicity in outcomes, follow-up, and interim analyses. These approaches are examined in a study evaluating the effects of tissue plasminogen activator on longitudinally obtained stroke severity measurements.