Mixed Poisson models are often used for the design of clinical trials involving recurrent events since they provide measures of treatment effect based on rate and mean functions and accommodate between individual heterogeneity in event rates. Planning studies based on these models can be challenging when there is a little information available on the population event rates, or the extent of heterogeneity characterized by the variance of individual-specific random effects. We consider methods for adaptive two-stage clinical trial design, which enable investigators to revise sample size estimates using data collected during the first phase of the study. We describe blinded procedures in which the group membership and treatment received by each individual are not revealed at the interim analysis stage, and a 'partially blinded' procedure in which group membership is revealed but not the treatment received by the groups. An EM algorithm is proposed for the interim analyses in both cases, and the performance is investigated through simulation. The work is motivated by the design of a study involving patients with immune thrombocytopenic purpura where the aim is to reduce bleeding episodes and an illustrative application is given using data from a cardiovascular trial.