The best replacement for incidence rate is prevalence rate.

The best alternatives to incidence rate are rated as following:
★★★★★  prevalence rate
★★★★  cumulative incidence
★★★★  incidence proportion
★★★  prevalence
★★★  attack rate
★★★  incidence
★★  mortality rate
★  incidence density
★  relative risk
  event rate
  cumulative incidence rate
  prevalence proportion
  response rate

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incidence rate
prevalence rate
cumulative incidence