RR vs OR Bandit Thinkhamrop, PhD (Statistics) Department of Biostatistics and Demography Faculty of Public Health Khon Kaen University
Absolute vs Relative effect Risk of event among group A = 4% vs B = 2% Which one is correct? A is 2% points greater than B (A มากกว่า B อยู่ 2%) A is one time greater than B (A มากกว่า B หนึ่งเท่า) A is two times greater than B (A มากกว่า B สองเท่า) A is two times as much as B (A เป็นสองเท่าของ B) Ans: 1, 2, 4 are correct
Relative risk (RR) RR = P1/P2 RR = Risk of event in group A RR = a/(a+b) Risk of event in group B Disease Normal Total Exposed a b a+b Non-exposed c d c+d a+c b+d a+b+c+d c/(c+d)
Odds ratio (OR) OR = [P1/(1-P1)] / [P2/(1-P2)] OR = Odds of Exposed group having event OR = [a/(a+b)/(1-(a/(a+b)))] = a/b = ad Odds of Non-exposed group having event Disease Normal Total Exposed a b a+b Non-exposed c d c+d a+c b+d a+b+c+d [c/(c+d)/(1-(c/(c+d)))] c/d bc
OR approximate RR if event is rare (Rule of thumb: P < 0.1 or 10%) RR = P1/P2 RR = Risk of event in group A RR = [a/(a+b)] / [c/(c+d)] Risk of event in group B Disease Normal Total Exposed a b a+b Non-exposed c d c+d a+c b+d a+b+c+d a d = b c rare -> (a+b) b ; (c+d) d
Interpretation of relative risk (RR) RR = 1 means there is no difference in risk between the two groups. RR < 1 means the event is less likely to occur in the experimental group than in the control group. RR > 1 means the event is more likely to occur in the experimental group than in the control group.
Forest plot for RR or OR 0.25 0.33 0.50 1 2 3 4 Minimum meaningful level Low BMI of mother (3.20; 2.50 to 4.50) Received ANC (1.60; 1.02 to 2.18) Protective effect Risk effect 0.25 0.33 0.50 1 2 3 4
Risk vs Protective effect for RR Risk of event among group A = 4% vs B = 2% Then, RR (A/B)= 2; RR (B/A) = 0.5 or taking reciprocal 1/2 = 0.5 vs 1/0.5 = 2 Which one is correct? A is 2 times risk as much as B A is 100% more likely to develop the event than B B is 0.5 times risk as much as B B is 50% less likely to develop the event than A Ans: All are correct, but 3 could mislead
Comparing between Risk and Odds Risk Odds 0.05 or 5% 0.053 0.1 or 10% 0.11 0.2 or 20% 0.25 0.3 or 30% 0.43 0.4 or 40% 0.67 0.5 or 50% 1 0.6 or 60% 1.5 0.7 or 70% 2.3 0.8 or 80% 4 0.9 or 90% 9 0.95 or 95% 19
Risk vs Protective effect for OR Rare event Probability of event among group A = 4% vs B = 2% Then, odds of finding group A having event = 0.04/0.96 = 0.04 vs B = 0.02/0.98 = 0.02 OR (A/B)= 2; OR (B/A) = 0.5 or taking reciprocal 1/2 = 0.5 vs 1/0.5 = 2 Which one is correct? A is 2 times risk as much as B Odds of finding group A having the event is 2 times that of the corresponding odds of group B Odds of group A having the event is 100% more than … B Odds of group B having the event is 50% less than … A Ans: All are correct; Note that RR = 2
Risk vs Protective effect for OR Common event Probability of event among group A = 80% vs B = 40% Then, odds of finding group A having event = 0.8/0.2 = 4 vs B = 0.4/0.6 = 0.67 OR (A/B)= 6; OR (B/A) = 0.17 or taking reciprocal 1/6 = 0.17 vs 1/0.17 = 6 Which one is correct? A is 6 times risk as much as B Odds of finding group A having the event is 6 times that of the corresponding odds of group B Odds of group A having the event is 600% more than … B Odds of group B having the event is 83% less than … A Ans: 2, 3, and 4 are correct ; Note that RR = 2
Comparing between Risk ratio and Odds ratio Pm = Risk of dead in male; Pf = Risk of dead in female; Pm Pf RR OR 0.5 0.25 2 3 0.75 0.25 3 9 0.80 0.20 4 16 0.90 0.10 9 81
RR very much depends of baseline risk but the OR does not A: Risk of dead = 1% vs Risk of survival = 99% A: Odds of dead = 0.01 vs Odds of survival = 99 B: Risk of dead = 2% vs Risk of survival = 98% B: Odds of dead = 0.02 vs Odds of survival = 49 B-A: Absolute increase = 1% vs decrease 1% B-A: Absolute increase = 0.01 vs decrease 50 (B-A)/B: Relative increase = 100% vs decrease 10.1% (B-A/B: Relative increase = 100% vs decrease 50.5% B/A: Risk ratio of dead = 2 vs Risk ratio of survival = 0.99 B/A: Odds ratio of dead = 2 vs Odds ratio of survival = 0.49 Reciprocal of RR = 0.5 vs Reciprocal of RR = 1.01 Reciprocal of OR = 0.5 vs Reciprocal of OR = 2.04
RR vs OR by Incidence of the outcome
When can odds ratios mislead When can odds ratios mislead? Huw Talfryn Oakley Davies, Iain Kinloch Crombie, Manouche Tavakoli BMJ VOLUME 316 28 MARCH 1998 page 989 The difference between the odds ratio and the relative risk depends on the risks (or odds) in both groups. Odds ratios may be nonintuitive in interpretation, but in almost all realistic cases interpreting them as though they were relative risks is unlikely to change any qualitative assessment of the study findings. The odds ratio will always overstate the case when interpreted as a relative risk, and the degree of overstatement will increase as both the initial risk increases and the size of any treatment effect increases. However, there is no point at which the degree of over statement is likely to lead to qualitatively different judgments about the study. Substantial discrepancies between the odds ratio and the relative risk are seen only when the effect sizes are large and the initial risk is high. Whether a large increase or a large decrease in risk is indicated, our judgments are likely to be the same—they are important effects.
Zhang & Yu methods
Zhang & Yu methods Several authors argued the methods: Over simplifications and error in some situation Invalid when presentation of interaction effect [Louise-Anne McNutt, Jean-Paul Hafner, Xiaonan Xue. JAMA. 1999;282(6):529] Invalid in high incidence [Louise-Anne McNutt, Chuntao Wu, Xiaonan Xue, and Jean Paul Hafner. AJE 157, No.10, P.940-943 ] Solution -> Adjusted RR using log-binomial regression, or Poisson regression with robust variance
Remarks RR has a more natural interpretation but cannot be calculated from a cross-sectional and case-control study For any research, there are two ways to calculate RR The OR treats both side of event symmetrically and suitable for any study designs Interpretation OR requires cautions, in particular, a study involving common event