Estimate RR from OR under different scenarios,
estimation of confidence interval can be repeated using the same scenario

Scenario 1: Event rate (P) in the non-exposed group is known.[1]
Odds Ratio (OR) Event rate in control group (%)
Relative Risk (RR)
Risk Difference (RD)
Number Needed to Treat/Harm (NNT/NNH)

Formula: $$RR=\frac{OR}{(1-P_{control})+(P_{control}*OR)} $$ $$RD=(RR-1)*P_{control}$$

Scenario 2: Event rate (P) in the non-exposed group is unknown, but P > 10%[2]
Odds Ratio (OR)
Relative Risk (RR)

Formula: $$RR\approx\sqrt{OR} $$

Scenario 3: Event rate (P) in the non-exposed group is unknown, but P < 10%[2]
Relative Risk (RR) is approximately equal to OR

Formula: $$RR\approx{OR} $$

Referemce:

[1] Zhang J, Yu KF. What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes. JAMA. 1998 Nov 18;280(19):1690-1. PMID 9832001
[2] VanderWeele TJ. On a Square-Root Transformation of the Odds Ratio for a Common Outcome. Epidemiology. 2017;28(6):e58-e60. doi:10.1097/EDE.0000000000000733