Continuous sequential boundaries for vaccine safety surveillance

Various recently developed sequential methods have been used to detect signals for post-marketing surveillance in drug and vaccine safety. Among these, the maximized sequential probability ratio test (MaxSPRT) has been used to detect elevated risks of adverse events following vaccination using large healthcare databases. However, a limitation of MaxSPRT is that it only provides a time-invariant flat boundary. In this study, we propose the use of time-varying boundaries for controlling how type I error is distributed throughout the surveillance period. This is especially useful in two scenarios: (i) when we desire generally larger sample sizes before a signal is generated, for example, when early adopters are not representative of the larger population; and (ii) when it is desired for a signal to be generated as early as possible, for example, when the adverse event is considered rare but serious. We consider four specific time-varying boundaries (which we call critical value functions), and we study their statistical power and average time to signal detection. The methodology we present here can be viewed as a generalization or flexible extension of MaxSPRT.