Odds Ratio and Relative Risk

 

OddsRatio = (ExpGroupPositive / (ExpGroupTotal - ExpGroupPositive)) / (ControlGroupPositive / (ControlGroupTotal - ControlGroupPositive))

RelativeRisk = (ExpGroupPositive / ExpGroupTotal) / (ControlGroupPositive / ControlGroupTotal)

 

Input:
 

Exp Group Positive		# index logit none number points score
Exp Group Total		# index logit none number points score
Control Group Positive		# index logit none number points score
Control Group Total		# index logit none number points score

 

Results:
 

Odds Ratio		% fraction rate ratio
Relative Risk		% fraction rate ratio
Decimal Precision   0 1 2 3

 

Notes

• Relative risk is approximated by the odds ratio when the outcome of a particular result is uncommon (15% or less).
• With a common result, the two numbers diverge.
• In logistic regression, the odds ratio equals the antilogarithm of a coefficient.

 

References

1. Katz MH. Multivariable analysis: a primer for readers of medical research. Ann Intern Med. 2003 Apr 15;138(8):644-50. PubMed ID: 12693887
2. Carney S, Doll H. Introduction to biostatistics: Part 2. Measures of association as used to address therapy, harm, and etiology questions. ACP J Club. 2005 Sep-Oct;143(2):A8. PubMed ID: 16134901
3. Page J, Attia J. Using Bayes' nomogram to help interpret odds ratios. ACP J Club. 2003 Sep-Oct;139(2):A11-2. PubMed ID: 12954046