In this paper the design of an event-based proportional-integral (PI) control scheme for stable first-order processes is considered. A novel triggering mechanism which decides the transmission instants based on an estimate of the PI control signal is proposed. This mechanism addresses some side-effects that have been discovered in previous event-triggered PI proposals, which trigger on the process output. In the proposed scheme, the classic PI controller is further replaced with PIDPLUS, a promising version of PI controller for networked control systems. Although PIDPLUS has been introduced to deal with packet losses and time delays, and, to the best of our knowledge, a stability analysis of the closed-loop system where such a controller is used has never been performed, here the performance of such a controller in an event-based fashion are analyzed, and a stability analysis is further provided. The proposed event-based scheme ensures set-point tracking and disturbance rejection as in classic time-periodic implementations of PI controller, while greatly reducing the number of sensor transmissions. The theoretical results are validated by simulations, where the benefits in using PIDPLUS in combination with the proposed PI event-based triggering rule are shown.