RR RR vsvs OR ORBandit Thinkhamrop, PhD (Statistics)

Department of Biostatistics and DemographyFaculty of Public HealthKhon Kaen University

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Absolute vs Relative effectAbsolute vs Relative effectRisk of event among group A = 4% vs B = 2%Which one is correct?

1. A is 2% points greater than B (A มากกว่�า B อยู่�� 2%)

2. A is one time greater than B (A มากกว่�า B หนึ่� งเท่�า)

3. A is two times greater than B (A มากกว่�า B สองเท่�า)

4. A is two times as much as B (A เป็�นึ่สองเท่�าของ B)Ans: 1, 2, 4 are correct

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Relative risk (RR)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

Total a+c b+d a+b+c+d

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c/(c+d)

Odds ratio (OR)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 eventDisease Normal Total

Exposed a b a+b

Non-exposed c d c+d

Total a+c b+d a+b+c+d

[c/(c+d)/(1-(c/(c+d)))] c/d bc4

OR approximate RR if event is rareOR 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

Total a+c b+d a+b+c+d

rare -> (a+b) b ; (c+d) da db c=

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Interpretation of relative risk (RR)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.

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Forest plot for RR or ORForest plot for RR or OR

0 1 2 3 40.500.330.25

Minimum meaningful level

Low BMI of mother (3.20; 2.50 to 4.50)

Protective effect Risk effect

Received ANC (1.60; 1.02 to 2.18)

Risk vs Protective effect for RRRisk 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 = 2Which one is correct?

1. A is 2 times risk as much as B2. A is 100% more likely to develop the event than B3. B is 0.5 times risk as much as B4. B is 50% less likely to develop the event than A

Ans: All are correct, but 3 could mislead 8

Comparing between Risk and OddsComparing 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

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Risk vs Protective effect for ORRisk vs Protective effect for ORRare eventRare 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 = 0.02OR (A/B)= 2; OR (B/A) = 0.5 or taking reciprocal 1/2 = 0.5 vs 1/0.5 = 2Which one is correct?

1. A is 2 times risk as much as B2. Odds of finding group A having the event is 2 times that

of the corresponding odds of group B3. Odds of group A having the event is 100% more than … B4. Odds of group B having the event is 50% less than … A

Ans: All are correct; Note that RR = 2 10

Risk vs Protective effect for ORRisk vs Protective effect for ORCommon eventCommon 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 = 0.67OR (A/B)= 6; OR (B/A) = 0.17 or taking reciprocal 1/6 = 0.17 vs 1/0.17 = 6Which one is correct?

1. A is 6 times risk as much as B2. Odds of finding group A having the event is 6 times that

of the corresponding odds of group B3. Odds of group A having the event is 600% more than … B4. Odds of group B having the event is 83% less than … A

Ans: 2, 3, and 4 are correct ; Note that RR = 211

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 0.252 3•0.75 0.253 9•0.80 0.204 16•0.90 0.109 81

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RR very much depends of baseline riskbut the OR does not

1. A: Risk of dead = 1% vs Risk of survival = 99%2. A: Odds of dead = 0.01 vs Odds of survival = 993. B: Risk of dead = 2% vs Risk of survival = 98%4. B: Odds of dead = 0.02 vs Odds of survival = 495. B-A: Absolute increase = 1% vs decrease 1%6. B-A: Absolute increase = 0.01 vs decrease 507. (B-A)/B: Relative increase = 100% vs decrease 10.1%8. (B-A/B: Relative increase = 100% vs decrease 50.5%9. B/A: Risk ratio of dead = 2 vs Risk ratio of survival = 0.99 10. B/A: Odds ratio of dead = 2 vs Odds ratio of survival = 0.4911. Reciprocal of RR = 0.5 vs Reciprocal of RR = 1.0112. Reciprocal of OR = 0.5 vs Reciprocal of OR = 2.04

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RR vs OR by Incidence of the outcome

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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 non intuitive 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.

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Zhang & Yu methods

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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

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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

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