Lecture 10. Analysis of Association -- Or and RR

Research Methodology Workshop – Hanoi 7-12/12/2010

Professor Tuan V. Nguyen Garvan Institute of Medical Research

University of New South Wales Sydney – Australia

Analysis of Association: Odds Ratio and Relative Risk


Contents

•  Types of study design

•  Risk, odds ratio, and relative risk

•  Estimates of OR, RR

•  Effects of information framing

•  Interpretation of RR or RR


Mortality in the Titanic incident

Class Dead Survived Total

I 123 200 (62%) 323

II 158 119 (43%) 277

III 528 181 (26%) 709

Total 809 500 (38%) 1309 http://lib.stat.cmu.edu/S/Harrell/data/descriptions/titanic3info.txt

Is there an association between passenger class and and death?


Zoledronate and fracture

Randomized controlled clinical trial

Placebo n = 1062, Zoledronate n = 1065

Length of follow-up: 3 years Lyles KW, et al. Zoledronic acid and clinical fractures and mortality after hip fracture. N Engl J Med 2007;357. DOI: 10.1056/NEJMoa074941


Smoking and lung cancer

Sir Richard Doll (1912 – 2005)

http://en.wikipedia.org/wiki/Richard_Doll

Lung Cancer

Controls

Smokers 647 622

Non-smokers 2 27

R Doll and B Hill. BMJ 1950; ii:739-748

Is there an association between smoking and lung cancer?


Study design

PAST PRESENT FUTURE

Cohort study, RCT

(longitudinal, prospective)

Case-control study

Cross-sectional study


Distinction of study designs: prospective / longitudinal study

N subjects

Risk presence

Risk absence

Event: a

Event: c

No event: b

No event: d

Event No event

Risk presence a b

Risk absence c d

Follow-up


Distinction of study designs: case-control study

Event

No event

Risk presence: a

Risk presence: c

Risk absence: b

Risk absence: d

Event No event

Risk presence a b

Risk absence c d


Distinction of study designs: cross-sectional study

Event

No event

Risk presence: a

Risk presence: c

Risk absence: b

Risk absence: d

Event No event

Risk presence a b

Risk absence c d


Risk

The disease risk is defined as the probability that an individual who is disease-free at time T will develop a disease over a period of T + k.

In 2000 (T) there are 100 people who were 90 years old with no hip fracture. Two years later (k = 3), 5 people sustained a hip fracture.

The risk of hip fracture (over 3 years) is threfore: 3%.


Measures of effect size

•  Given two proportions p1 and p2, there are several measures of effect size:

•  Absolute difference

D = p1 – p2

•  Relative risk

RR = p1 / p2

•  Odds ratio

OR = [p1(1 - p2)] / [p2(1 - p1)]

•  Number needed to treat (NNT):

NNT = 1 / D


Appropriateness of effect size

Prospective study

Cross-sectional study

Case-control study

Relative risk

Odds ratio

NNT

D

Odds ratio

D

Odds ratio


Relationship between RR and OR

Odds ratio is an estimate of relative risk


Relative risk

•  Risk of developing disease Treatment: p1 = a / N1

Placebo: p2 = b / N2

•  Relative risk RR = p1 / p2

•  Implications:

RR = 1, there is no effect

RR < 1, the treatment is beneficial.

RR > 1, the treatment is harmful.

Treatment Control

Disease a b

No disease c d

Sample size N1 N2


95% confidence interval for RR

Treatment Control

Disease a b

No disease c d

Sample size N1 N2

Zoledronate

Placebo

Fracture 92 139

No fracture 973 923

Sample size 1065 1062

= 0.514 to 0.847


•  Odds of developing disease over no disease

Risk presence: O1 = a / b

Risk absence: O0 = c / d

•  Odds ratio OR = O1 / O0

•  Implications: OR = 1, there is no association OR < 1, the risk factor is associated with reduced disease risk RR > 1, the risk factor is associated with increased disease risk

Disease No disease

Risk presence a b

Risk absence c d

Sample size N1 N2

Odds ratio


Disease No disease

Risk presence

a b

Risk absence

c d

Lung K Control

Smoking 647 622

No smoking 2 27

= 3.32 to 59.03

95% Confidence interval for OR


Zoledronate and fracture: RR vs OR

Zoledronate

Placebo

Fracture 92 139

No fracture 973 923

Sample size 1065 1062

Not much difference!


Recommendation for catheterization?

Figure 1. Patients as Portrayed by Actors in the Video Component of the Survey. Panel A shows a 55-year-old black woman, Panel B a 55-year-old black man, Panel C a 70-year-old black woman, Panel D a 70-yearold black man, Panel E a 55-year-old white woman, Panel F a 55-year-old white man, Panel G a 70-year-old white woman, and Panel H a 70-year-old white man.


Race, sex, and catheterization

Catheterization

No Catheterizatio

n

Total

White 652 68 720

Black 610 110 720 Schulman et al. New England Journal of Medicine (25/2/1999 )

Logistic regression analysis indicated that women (odds ratio, 0.60; 95 percent confidence interval, 0.4 to 0.9; P=0.02) and blacks (odds ratio, 0.60; 95 percent confidence interval, 0.4 to 0.9; P=0.02) were less likely to be referred for cardiac catheterization than men and whites, respectively. Analysis of race–sex interactions showed that black women were significantly less likely to be referred for catheterization than white men (odds ratio, 0.4; 95 percent confidence interval, 0.2 to 0.7; P=0.004).


Media reaction


Where is the truth?

Catheterization No catheterizatio

n

Black 610 110

White 652 68

Very much difference!


Odds ratio overestimates relative risk

Study Risk of disease Odds of disease Comparison between RR and

OR

Group 1 (p1)

Group 2 (p2)

Nhóm 1 (odd1)

Nhóm 2 (odd2)

RR OR

1 0.001 0.003 0.002 0.003 3 3.01

2 0.01 0.03 0.01 0.03 3 3.06

3 0.02 0.06 0.02 0.06 3 3.13

4 0.05 0.15 0.05 0.18 3 3.35

5 0.10 0.30 0.11 0.43 3 3.86

6 0.15 0.45 0.18 0.82 3 4.64

7 0.20 0.60 0.25 1.50 3 6.00

8 0.25 0.75 0.33 3.00 3 9.00

9 0.30 0.90 0.43 9.00 3 21.0

10 0.33 0.99 0.49 99.0 3 2101.0


For a constant RR, OR increases with background risk


The effect of risk framing (communication)

Which (hypothetical) study is more likely to be funded?

T Fahey , et al. Evidence based purchasing: understanding results of clinical trials and systematic reviews. BMJ 1995;311:1056-1059

Mammography Cardiac rehabilitatio

n

RR 0.66 0.80

Absolute risk reduction 0.06% 3%

Percent of event-free 99.82 vs 99.80% 84% vs 87%

Number needed to treat 1592 31


The effect of risk framing (communication)

Which (hypothetical) study is more likely to be funded?

T Fahey , et al. Evidence based purchasing: understanding results of clinical trials and systematic reviews. BMJ 1995;311:1056-1059


Prescription of drug

Questionnaire A on relative risk reduction

1.  A cholesterol lowering drug treatment reduces the relative risk of a fatal and non-fatal myocardial infarction by 34%. This result is significant.

2.  2. A cholesterol lowering drug treatment reduces the relative risk of a fatal myocardial infarction by 26%. This result is not significant.

3.  3. A cholesterol lowering drug treatment increases the total mortality by 5.7%. This result is not significant.

4.  4. During a cholesterol lowering drug treatment, 71 patients have to be treated for five years to prevent one fatal or non-fatal myocardial infarction. This result is significant.

Questionnaire B on absolute risk reduction

1.  A cholesterol lowering drug treatment reduces the incidence of fatal and non-fatal myocardial infarction by 14 per 1000 patients and five years of treatment. This result is significant.

2.  2. A cholesterol lowering drug treatment decreases the incidence of fatal myocardial infarction by one per 1000 patients and five years of treatment. This result is not significant.

3.  3. A cholesterol lowering drug treatment increases the total mortality by 1.2 deaths per 1000 patients and five years of treatment. This result is not significant.

4.  4. During a cholesterol lowering drug treatment 71 patients have to be treated for five years to prevent one fatal or non-fatal myocardial infarction. This result is significant.


RR result and prescription of drug


Interpretation of RR: vitamin C and serious outcomes

NEJM April 27, 2006, 354: 1796-1806:

Authors’ conclusion: “Supplementation with vitamins C and E during pregnancy does not reduce the risk of preeclampsia in nulliparous women, the risk of intrauterine growth restriction, or the risk of death or other serious outcomes in their infants.”

FACTS:

•  Preeclampsia: RR 1.20 (0.82 – 1.75)

•  Growth restriction: RR 0.87 (0.66 – 1.16)

•  Serious outcomes: RR 0.79 (0.61 – 1.02)


Interpretation of RR: fat and breast cancer

Women’s Health Initiative study on fat consumption and breast cancer (JAMA): “Even diets with only 29% of calories coming from fat didn’t reduce the risk of disease.”

FACTS:

•  Invasive Breast Cancer: HR 0.91 (0.83-1.01), p=0.07

•  Breast Cancer Mortality: HR 0.77 (0.48-1.22)


What does 95% confidence interval mean?

Technical notes: logor = log(2.47) sd = log(5.2/1.17)/3.92 x = rannor(1000, logor, sd) or = exp(x) hist(or, breaks=20, xlim=c(0,10), ylim=c(0,250), xlab="Odds ratio")

95%CI

OR 2.47, 95%CI: 1.17, 5.20


Clinically harmful Clinically beneficial

0.7 1.3 1.0 2.0 3.0 4.0 0.5 0.3 0.2

Strong evidence against any substantial harm or benefit because we have strong evidence against any values outside the CI, both these cases argue strongly that any effect is clinically unimportant. Note that this is true even though one is statistically significant.

Relative risk


0.7 1.3 1.0 2.0 3.0 4.0 0.5 0.3 0.2

May be harmful. The estimate is in the harmful range, with the CI including some values that would be clinically important harm. Strong evidence against any substantial benefit The CI does not include any values that would be an important benefit.

Relative risk



0.7 1.3 1.0 2.0 3.0 4.0 0.5 0.3 0.2 Relative risk


0.7 1.3 1.0 2.0 3.0 4.0 0.5 0.3 0.2 Relative risk

Likely to be harmful. The estimate and most of the CI are in the substantial harm range, and the CI does not include no effect.

Results suggest substantial harm, but CI is too wide to permit a strong conclusion. Strong evidence against substantial benefit - the CI does not include any values that would be an important benefit



0.7 1.3 1.0 2.0 3.0 4.0 0.5 0.3 0.2 Relative risk

Suggestion of benefit - Estimate and most of CI are in the benefit range

Clinically meaningful benefit possible but not likely Some of the CI is in this range, but not the estimate

Strong evidence against substantial harm No values in the CI would constitute important harm

May be no effect (not statistically significant) The CI includes no effect



0.7 1.3 1.0 2.0 3.0 4.0 0.5 0.3 0.2 Relative risk

Suggestion of substantial benefit. The estimate would be an important benefit if true.

May be no effect (not statistically significant) The CI includes no effect Which of the two results would be more exciting? I think the lower one is, even though it has wider uncertainty, because the estimate is better.



0.7 1.3 1.0 2.0 3.0 4.0 0.5 0.3 0.2 Relative risk

Strong evidence of benefit (statistically significant)

Substantial benefit appears likely, but CI too wide to rule out clinically insignificant benefit The CI includes some benefits that would be too small to be clinically important. Studies almost never include this observation if they reach statistical significance.



0.7 1.3 1.0 2.0 3.0 4.0 0.5 0.3 0.2 Relative risk

Strong evidence of substantial clinical benefit This is the most satisfying type of result. Even the upper confidence bound is in the substantial benefit range.



0.7 1.3 1.0 2.0 3.0 4.0 0.5 0.3 0.2

No conclusions possible due to very wide CI This is the least satisfying type of result. There is very little information in the study data.

Relative risk


Summary

•  Relative risk is a common effect size measure

•  Odds ratio is an estimate of relative risk

–  In the absence of prospective study, case-control study can estimate RR by OR

•  For diseases with high risk, OR tends to overestimate effect size.

•  Confidence interval is more meaningful and more informative than p-value.

Documents

Lecture 10. Analysis of Association -- Or and RR