Transcript RR_VS_OR

RR vs OR
Bandit Thinkhamrop, PhD (Statistics)
Department of Biostatistics and Demography
Faculty of Public Health
Khon Kaen University
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Absolute vs Relative effect
Risk of event among group A = 4% vs B = 2%
Which one is correct?
1.
2.
3.
4.
A is 2% points greater than B (A มากกว่า B อยู่ 2%)
A is one time greater than B (A มากกว่า B หนึง่ เท่า)
A is two times greater than B (A มากกว่า B สองเท่า)
A is two times as much as B (A เป็ นสองเท่าของ B)
Ans: 1, 2, 4 are correct
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Relative risk (RR)
• RR = P1/P2
• RR = Risk of event in group A
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
Total
• RR = a/(a+b)
c/(c+d)
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Odds ratio (OR)
• OR = [P1/(1-P1)] / [P2/(1-P2)]
• OR = Odds of Exposed group having event
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
Total
• OR = [a/(a+b)/(1-(a/(a+b)))] = a/b = ad
[c/(c+d)/(1-(c/(c+d)))] c/d bc
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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
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
Total
• RR = [a/(a+b)] / [c/(c+d)]
rare -> (a+b)  b ; (c+d)  d
ad
= bc
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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 OR
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
0
0.25
Risk effect

0.33
0.50
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2
3
4
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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?
1.
2.
3.
4.
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
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Comparing between Risk and Odds
•
•
•
•
•
•
•
•
•
•
•
Risk
0.05 or 5%
0.1 or 10%
0.2 or 20%
0.3 or 30%
0.4 or 40%
0.5 or 50%
0.6 or 60%
0.7 or 70%
0.8 or 80%
0.9 or 90%
0.95 or 95%
Odds
0.053
0.11
0.25
0.43
0.67
1
1.5
2.3
4
9
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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?
1. A is 2 times risk as much as B
2. Odds of finding group A having the event is 2 times that
of the corresponding odds of group B
3. Odds of group A having the event is 100% more than … B
4. Odds of group B having the event is 50% less than … A
Ans: All are correct; Note that RR = 2
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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?
1. A is 6 times risk as much as B
2. Odds of finding group A having the event is 6 times that
of the corresponding odds of group B
3. Odds of group A having the event is 600% more than … B
4. Odds of group B having the event is 83% less than … A
Ans: 2, 3, and 4 are correct ; Note that RR = 2
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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
0.75
0.80
0.90
0.25
0.25
0.20
0.10
2
3
4
9
3
9
16
81
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RR very much depends of baseline risk
but the OR does not
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
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
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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 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.
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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 casecontrol 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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