Group sequential designs for clinical trials with bivariate endpoints

Although all clinical trials are designed and monitored using more than one endpoint, methods are needed to assure that decision criteria are chosen to reflect the clinically relevant tradeoffs that assure the trial's scientific integrity. This article presents a framework for the design and monitoring clinical trials in a bivariate outcome space. The framework uses a rectangular hyperbola to define a bivariate null curve that divides outcome space into regions of benefit and lack of benefit. The curve is shown to be a flexible mapping of bivariate space that allows a continuous tradeoff between the two endpoints in a manner that captures many previous bivariate designs. The curve is extended to a distance function in bivariate space that allows different decisions in each of the four quadrants that comprise bivariate space. The distance function forms a statistic ( $$ ); the distribution of its estimate is derived and used as a basis for trial design and group sequential monitoring plans in bivariate space. A recursive form of the bivariate group sequential density is used to evaluate and control operating characteristics for the proposed design. The bivariate designs are shown to meet or exceed the usual standards for size and power. The proposed design is illustrated in the ongoing NHLBI-sponsored Kids-DOTT multinational randomized controlled trial comparing shortened versus conventional anticoagulation for the treatment of venous thromboembolism in patients less than 21 years of age. The proposed methods are broadly applicable to a wide range of clinical settings and trial designs.