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Table 2 RRs and ORs and corresponding CIs of associations between a rare event (incidence = 5%) and three independent variables, estimated by Log-binomial regression, ordinary logistic regression, Cox regression with robust variance and logistic regression with the proposed modification

From: A simple method for estimating relative risk using logistic regression

Independent
variable
Log-binomial
regression: RR
(CI)
Logistic
regression: OR
(CI)
Cox
regression -
robust: RR (CI)
Modified
Logistic
regression: RR (CI)
Predictor A     
   Unadjusted 6 (2.4 - 14.98) 6.41 (2.52 - 16.28) 6 (2.4 - 14.99) 6 (2.36 - 15.25)
   Adjusted * 4.96 (1.89 - 12.98) 5.26 (1.97 - 14.06) 4.97 (1.91 - 12.92) 4.99 (1.86 - 13.34)
Predictor B     
   Unadjusted 2.57 (1.4 - 4.71) 2.69 (1.43 - 5.06) 2.57 (1.4 - 4.71) 2.57 (1.37 - 4.83)
   Adjusted * 1.59 (0.85 - 2.97) 1.64 (0.85 - 3.18) 1.59 (0.84 - 3.01) 1.59 (0.82 - 3.09)
Predictor C     
   Unadjusted 1.28 (0.74 - 2.2) 1.29 (0.73 - 2.29) 1.28 (0.74 - 2.2) 1.28 (0.72 - 2.26)
   Adjusted * 0.98 (0.57 - 1.69) 0.97 (0.54 - 1.74) 0.97 (0.57 - 1.65) 0.96 (0.54 - 1.72)
  1. * Adjusted by the other independent variables.