Alpha spending for historical versus surveillance Poisson data with CMaxSPRT.

Sequential analysis hypothesis testing is now an important tool for postmarket drug and vaccine safety surveillance. When the number of adverse events accruing in time is assumed to follow a Poisson distribution, and if the baseline Poisson rate is assessed only with uncertainty, the conditional maximized sequential probability ratio test, CMaxSPRT, is a formal solution. CMaxSPRT is based on comparing monitored data with historical matched data, and it was primarily developed under a flat signaling threshold. This paper demonstrates that CMaxSPRT can be performed under nonflat thresholds too. We pose the discussion in the light of the alpha spending approach. In addition, we offer a rule of thumb for establishing the best shape of the signaling threshold in the sense of minimizing expected time to signal and expected sample size. An example involving surveillance for adverse events after influenza vaccination is used to illustrate the method.