Blinded sample size re-estimation for recurrent event data with time trends

The use of an internal pilot study for blinded sample size re-estimation (BSSR) allows to reduce uncertainty on the appropriate sample size compared with conventional fixed sample size designs. Recently BSSR procedures for recurrent event data were proposed and investigated. These approaches assume treatment-specific constant event rates that might not always be appropriate as found in relapsing multiple sclerosis. On the basis of a proportional intensity frailty model, we propose methods for BSSR in situations where a time trend of the event rates is present. For the sample size planning and the final analysis standard negative binomial methods can be used, as long as the patient follow-up time is approximately equal in the treatment groups. To re-estimate the sample size at interim, however, a full likelihood analysis is necessary. Operating characteristics such as rejection probabilities and sample size distribution are evaluated in a simulation study motivated by a systematic review in relapsing multiple sclerosis. The key factors affecting the operating characteristics are the study duration and the length of the recruitment period. The proposed procedure for BSSR controls the type I error rate and maintains the desired power against misspecifications of the nuisance parameters.