RR is for the higher probabilities and OR is for the smaller one to show an association between events
Also according to Cochrane´s Handbook, when dealing with very rare frequencies of events in at least one of the groups (n=0) it is recommended to calculate odds ratio with Peto method http://handbook.cochrane.org/chapter_9/9_4_4_2_peto_odds_ratio_method.htm
Chapter 5 in Joe Hilbe's book Logistic Regression Models provides one of the best explanations on this topic.
odd ratio (OR) which is a measure of the strength of the association between risk factor (e.g. smoking) and outcome (e.g cancer). Odds ratio is closely related to relative risk.
Risk Ratio is the same as Relative Risk
Risk - Risk is the probability that an event will happen latter
therefore Relative risk = no of events happened / Total no of risk
Another point to add to this is that relative risk has a tendency to underestimate in case of common outcomes.
Odds Ratio approximates Risk Ratio only if incidence is low in both the exposed and the unexposed group … If risk of incidence is high in either or both exposed and unexposed, then Risk Ratio and Odds Ratio differ.
What determines if incidence is high or low enough for RR or OR, is there a cut off point?
University of Nottingham
Palacký University of Olomouc
Hassan Ali Abdelwahid
Suez Canal University
Geoffrey Chima Nwakwuo
Indian Council of Medical Research
Indian Institute of Toxicology Research
Klinička bolnica "Sveti Duh"
University Health System