I don't know...If every 3rd time I was alerted it was some relatively serious issue, vs how often there is a serious issue when just doing rounds that you stumble upon, I'd think that would be a pretty good alert rate compared to the norm. But then again, I'm not in healthcare.
Essentially, it depends on workplace integration, i.e. how much effort it takes to discover the alert trigger. From personal experience, I'd say the upper limit of inconvenience is 'click the alert' on mobile, and 'move mouse on alert label to see tooltip' on desktop. Anything more will be quickly discarded, especially if it involves a popup or opens a new window.