Transfusion medicine trials often involve repeated administration of blood products for therapeutic and prophylactic reasons. Patients with immune thrombocytopenia will require prophylactic platelet transfusion to mitigate the risk of bleeding, but the transfusion frequency may vary across individuals. We consider group sequential designs of transfusion trials when the goal is to assess the relative effectiveness of a new blood product on the response to transfusions. A multivariate probability mass function is used to model the intervention effect and dependence of the binary responses across serial transfusions from each individual. The sample size formula is derived to ensure power requirements are met when analyses are based on generalized estimating equations and robust variance estimation. Strategies for interim monitoring using error spending functions are developed based on a robust covariance matrix for estimates of treatment effect over successive analyses.