The best replacement for mortality rate is morbidity rate.

The best alternatives to mortality rate are rated as following:
★★★★★  morbidity rate
★★★  life expectancy
★★  death rate
★★  case fatality rate
★★  mortality rate
★★  incidence rate
★  birth rate
★  survival rate
★  fatality rate
★  case fatality
  infant mortality rate
  mortality
  fertility rate

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mortality rate
morbidity rate
life expectancy