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.
Indian Council of Medical Research
University of Nottingham
University Health System
Klinička bolnica "Sveti Duh"
Geoffrey Chima Nwakwuo
University of Oviedo
Hassan Ali Abdelwahid
Suez Canal University
Palacký University of Olomouc
Indian Institute of Toxicology Research