8 Confounding, Adjusted Odds Ratios - KI

8 Confounding, Adjusted Odds Ratios

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Illustration from Lab 3, Exercise 3 (a) & (b)

We looked at the RR of breast cancer associated with high alcohol consumption, overall and in younger and older women:

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1

One possible explanation

We say age is a confounder (i.e. associated with exposure and outcome)

3

Marginal/Conditional Independence

Clinic 1

Treatment A B

Success 18 12

Failure 12 8

OR=1

2

A

B

2

8

OR=1

8

32

Total

A

B

20

20

20

40

OR=2

conditional independence: conditional on clinic, no association (OR=1) between

treatment and response. However, `marginally' (overall), OR=2

=> can be misleading to look only at marginal tables.

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2

Simpson's Paradox:

where the direction of association is reversed in the conditional and marginal tables

Example from Florida law review 43:1 - 34 (1991)

Victim's Race White

Black

Total

Defendant's Race White Black White Black White Black

Death Penalty % Yes

Y

N

53

414 11.3

11

37

22.9

0

16

0.0

4

139 2.8

53

430 11.0

15

176 7.9

Looking at defendant's race, we see more whites than blacks get death penalty. However, for each of Victim's Race = White and Victim's Race = Black, there are more blacks who get death penalty!

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Example: Lung Cancer and Drinking

Lung Cancer

Yes

No

Heavy 33 Drinker

Non

27

Drinker

60

1667 2273 3940

1700 2300 4000

OR=1.67

So it appears that heavy drinking may be associated with lung cancer The OR above is called the "crude odds ratio"

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3

Smoking is a potential confounder:

(Smoking is associated with lung cancer, and with drinking)

Stratified analysis: Smokers

Non-smokers

Lung Cancer

Lung Cancer

Heavy Drinkers

NonDrinkers

Yes

No

24

776

6

194

OR=1.0

Yes

No

9

891

21

2079

OR=1.0

Conclude: after controlling for confounding due to smoking, no association between lung cancer and drinking

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Example: OCP (Pill) user and MI in women

OCP Yes No

MI 29 205

No MI 135 1607

OR=1.7

However if we look at age categories:

25-29yr MI No 4 62 2 224

7.2

30-34yr MI No 9 33 12 390

8.9

35-39yr MI No 4 26 33 330

1.5

40-44yr MI No 6 9 65 362

3.7

45-49yr MI No 6 5 93 301

3.9

Note the OR is much higher than crude value (1.7) in all but one of the age strata

i.e. the association is "confounded" with age

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4

Control of Confounding

Detecting and removing spurious associations from related variables can be done at the design stage, and/or the analysis stage. Design stage:

? Randomisation ? Restriction ? Matching

Analysis stage:

? Stratification ? Standardisation ? Multivariable techniques

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Randomisation

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5

Restriction

Confounding cannot occur if the factor does not vary. For example if the study is limited to black women, then race and gender cannot be confounding variables.

Restriction also limits the interpretation of the study. Often partial restriction is used.

If restriction is carried to extremes the study may have a limited number of eligible participants!

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Matching

Matching is most common in case-control studies. Comparison group is chosen to be similar to the case group with respect

to one or more potential confounding variables. Matching may be done on an individual basis (pair-matching) or

on a group basis (frequency matching). If a pair-matched design is used, then matching must be taken

into account in the analysis (remember our paired data example in the Lab!).

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6

Mantel-Haenszel OR

If we assume there is a common OR in different strata, we can combine the tables to get a common ("adjusted", or "conditional") OR called the Mantel-Haenszel estimator as follows

Table k

Table 1

Table2

ak

bk

ck

dk

nk

a1 b1 c1 d1

n1

a2 b2

etc.

c2 d2

n2

^MH

ak dk

nk bkck

main diagonal terms off - diagonal terms

nk

1133

Example

To compute the Mantel-Haneszel OR for the lung cancer example

Smokers

Non-smokers

Lung Cancer

Lung Cancer

Yes

No

Yes

No

Heavy Drinkers

NonDrinkers

24

776

6

194

TOTAL=1000 OR=1.0

9

891

21

2079

TOTAL=3000 OR=1.0

( 24 )( 194 ) ( 9 )( 2079 )

OR MH

1000

3000

( 6 )( 776 ) ( 21 )( 891 )

1.0

1000

3000

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Calculating Adjusted Odds Ratios

If it is reasonable to assume a common (adjusted) OR then we can Calculate the M-H Odds Ratio by hand as shown, or by computer

(later in Lab) Or use "logistic regression" (Biostat II) When there is a large number of strata, logistic regression offers

the easiest/quickest method.

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What if the confounder is continuous?

We can also adjust for a linear term in age (or other confounding variable) in a logistic regression model: Example: two groups of 50 men asked whether they had seen a physician in the last 6 months (PHY=1 if yes, PHY=0 if no)

PHY=1

Group 1 30%

Group 2 80%

Age(mean)

40.2

Odds PHY=1

0.3

0.7

48.5

0.8 0.2

May reflect a component due to the fact that the groups are different ages.

OR=9.3

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