Tuesday, April 21, 2020

Odds Ratio Confidence Interval

Following formula is used to calculate the odds ratio (O.R.) and its confidence interval (C.I.). 

OR = a*d / b*c, where:

  • a is the number of times both A and B are present,
  • b is the number of times A is present, but B is absent,
  • c is the number of times A is absent, but B is present, and
  • d is the number of times both A and B are negative.

To calculate the confidence interval, we use the log odds ratio, log(OR) = log(a*d/b*c), and calculate its standard error:

se(log(OR)) = √1/a + 1/b + 1/c +1/d

The confidence interval, C.I., is calculated as:

CI = exp(log(OR) ± Zα/2­*√1/a + 1/b + 1/c + 1/d),

where Zα/2 is the critical value of the Normal distribution at α/2 (e.g. for a confidence level of 95%, α is 0.05 and the critical value is 1.96).

Note: The logarithms included in the formulae above are natural logarithms, i.e., log base e, sometimes denoted ln().


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