Slow slip events (SSEs) in subduction zones can trigger earthquake swarms, especially at shallow depth. The monitoring of seismicity rates has therefore the potential to help detect and characterize SSEs, and transient changes in coupling. However, the relationship between seismicity rate and slow slip rate during a SSE is unknown and made complicated by aftershock triggering within the swarm. Here we propose to complement geodetic methods with an objective measure of the seismicity rate that is directly associated with changes in slip rate. We show that this measure, applied to known occurrences of SSEs in the Boso area, Japan, yields an estimate, albeit indirect, of their seismic moment, hence their slip rate. We finally prove that the background rate in Boso has been accelerating since 1990; this explains previous observations of the shortening of the recurrence time between SSEs in Boso, that clearly predate the 2011 M(w)9.0 Tohoku-Oki earthquake.