Logistic regression: relative risk

[Ganesalingam Narenthiran]

When I undertake Logistic Regression, I obtain the odds ratios for each variable relative to its reference variable. How can I get the relative risks through post estimation? Thank you

[Clyde Schechter]

Well, the first question is what is the study design? If you have a case-control study design, then the relative risk is inherently not estimable. If you have a cohort or cross-sectional design, then the relative risk at least exists. But it is not estimated in a logistic regression. If the outcome prevalence is low when the explanatory/predictor variable takes on its reference value, then to a reasonable approximation, the relative risk equals the odds ratio.

If the reference outcome prevalence is not low, then that approximation breaks down. In that case, you have to first get a good estimate of the reference outcome prevalence. Then you convert that to odds: reference odds = reference prevalence/(1-reference prevalence). Then you multiply that by the odds ratio to get the non-reference odds. Then you convert the non-reference odds back to a non-reference prevalence: non-reference prevalence = non-reference odds / (1+non-reference odds). Now you calculate the relative risk as non-reference prevalence/reference prevalence. (If your study design was prospective, then the outcome probabilities are incidence rates, not prevalence rates, but everything else works the same.)

[Rich Goldstein]

or, just estimate it directly using, e.g., -binreg- or, esp if that does not converge, -poisson- (be sure to use robust SE's); see the relevant help files

[Bruce Weaver]

https://stats.oarc.ucla.edu/stata/fa...ohort-studies/