The best replacement for odds ratio is relative risk.

The best alternatives to odds ratio are rated as following:
★★★★★  relative risk
★★★★  risk ratio
★★★  hazard ratio
★★  likelihood ratio
★★  chi square
★  prevalence ratio
★  adjusted odds ratio
★  probability
★  absolute risk
★  rate ratio
★  marginal effects
  relative risk when to use
  log odds
  risk
  chi square test
  p value
  relative risk cohort study
  odds
  unadjusted odds ratio
  odds ratio
  hazards ratio

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Speaking about odds ratio, one probably shouldn't forget about 95 ci.

Other search terms related to odds ratio and their ratings are:
★★★★★ 95 ci
★ 95% ci
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odds ratio
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risk ratio