The recent development of closed-loop EEG phase-triggered transcranial magnetic stimulation (TMS) has advanced potential applications of adaptive neuromodulation based on the current brain state. Closed-loop TMS involves instantaneous acquisition of the EEG rhythm, timing prediction of the target phase, and triggering of TMS. However, the accuracy of EEG phase prediction algorithms is largely influenced by the system's transport delay, and their relationship is rarely considered in related work. This paper proposes a delay analysis that considers the delay of the closed-loop EEG phase-triggered TMS system as a primary factor in the validation of phase prediction algorithms. An in-silico validation using real EEG data was performed to compare the performance of commonly used algorithms. The experimental results indicate a significant influence of the total delay on the algorithm performance, and the performance ranking among algorithms varies at different levels of delay. We conclude that the delay analysis framework should be widely adopted in the design and validation of phase prediction algorithms for closed-loop EEG phase-triggered TMS systems.