Need help determining proper method for analyzing Responses to Alerts

Hi, I've been struggling with some data provided to me by a coworker. Specifically, we have a sepsis alert that indicates that a patient meets the criteria for sepsis. The problem is that there are many false positive alerts. The problem is further enhanced by "inappropriate responses" to the alerts where the responder clicks "ignore" instead of acknowledging the alert. We created an intervention and I've been tracking to see if this intervention has decreased the incidence of "inappropriate responses" to the alert.

My colleague has decided to look at signal-to-noise ratios. Signal being "appropriate responses" and Noise being "inappropriate responses". For example, if there are 200 total alerts in a month and 50 are "ignored" then what we determined to be the signal-to-noise ratio is 150/50 = 3.

My questions are: 1) Is this the appropriate method for analyzing the responses to these alerts and 2) What other methods would you recommend. Thanks for your help. All responses are greatly appreciated.