Cohen's kappa coefficient, which was introduced in 1960, serves as the most widely employed coefficient to assess inter-observer agreement for categorical outcomes. However, the original kappa can only be applied to cross-sectional binary measurements and, therefore, cannot be applied in the practical situation when the observers evaluate the same subjects at repeated time intervals. This study summarizes six methods of assessing agreement of repeated binary outcomes under different assumptions and discusses under which condition we should use the most appropriate method in practice. These approaches are illustrated using data from the CDC anthrax vaccine adsorbed (AVA) human clinical trial comparing the agreement for two solicited adverse events after AVA between the 1-3 day in-clinic medical record and the patient's diary on the same day. We hope this article can inspire researchers to choose the most appropriate method to assess agreement for their own study with longitudinal binary data.