Tree-based scan statistics have been successfully used to study the safety of several vaccines without prespecifying health outcomes of concern. In this study, the binomial tree-based scan statistic was applied sequentially to detect adverse events in Days 1-28 compared with Days 29-56 after recombinant herpes zoster (RZV) vaccination, with 5 looks at the data and formal adjustment for the repeated analyses over time. IBM Marketscan data on commercially insured persons 50+ years of age receiving RZV during January 1, 2018-May 5, 2020 were used. With 999,876 doses of RZV included, statistically significant signals were detected only for unspecified adverse effects/complications following immunization, with attributable risks as low as 2 excess cases per 100,000 vaccinations. Ninety percent of cases in the signals occurred in the week after vaccination and, based on previous studies, likely represent non-serious events like fever, fatigue, and headache. Strengths of our study include its untargeted nature, self-controlled design, and formal adjustment for repeated testing. Although the method requires prespecification of the risk window of interest and may miss some true signals detectable using the tree-temporal variant of the method, it allows for early detection of potential safety problems through early initiation of ongoing monitoring.