Confounding, Effect Modification, Confounding, Effect Modification, and Stratificationand Stratification

HRP 261 1/26/04HRP 261 1/26/04

Adding a Third Dimension to Adding a Third Dimension to the the RxCRxC picture picture

Exposure Disease?

Mediator

Confounder

Effect modifier

Some TermsSome Terms

1. What Agresti calls, “Marginally associated but conditionally independent”…epidemiologists call “confounding.”

2. What Agresti calls, “partial tables,”…epidemiologists call, “stratification.”

3. What epidemiologists call, “effect modification”…statisticians call, “interaction.”

1. Confounding1. Confounding

A confounding variable is associated with the exposure and it affects the outcome, but it is not an intermediate link in the chain of causation between exposure and outcome.

Examples of ConfoundingExamples of Confounding

Oral contraceptive use?

Cervical cancer

Infection with human papillomavirus (HPV)

Oral contraceptive use?

Breast cancer

Late age at first birth/ low parity

More ConfoundingMore Confounding

Poor nutrition?

Menstrual irregularity

Low weight

Menstrual irregularity?

Low bone strength

Late menarche

Confusion over Confusion over postmenopausal hormones: postmenopausal hormones:

Postmenopausal HRT Heart attacks (MI)?

High SES, high education, other confounders?

Mixture May Rival Estrogen in Preventing Heart Disease

August 15, 1996, Thursday    

“Widely prescribed hormone pills that combine estrogen and progestin appear to be just as effective as estrogen alone in preventing heart disease in women after menopause, a study has concluded.”

“Many women take hormones … to reduce the risk of heart disease and broken bones.”

“More than 30 studies have found that estrogen after menopause is good for the heart.”

Example: Nurse’s Health Study Example: Nurse’s Health Study

protective relative risks

Nurse’s Health StudyNurse’s Health Study

No apparent Confounding…No apparent Confounding…

e.g., the effect is the same among smokers and non-smokers, so the

association couldn’t be due to confounding by smokers (who may take less hormones and certainly get

more heart disease).

RCT: Women’s Health RCT: Women’s Health Initiative (2002)Initiative (2002)

On hormones

On placebo

Controlling for confounders in Controlling for confounders in medical studiesmedical studies

1. Confounders can be controlled for in the design phase of a study (randomization or restriction or matching).

2. Confounders can be controlled for in the analysis phase of a study (stratification or multivariate regression).

Analytical identification of Analytical identification of confounders through confounders through

stratification stratification

Mantel-Haenszel Procedure:Mantel-Haenszel Procedure:Non-regression technique used to Non-regression technique used to

identify confounders and to control identify confounders and to control for confounding in the for confounding in the statistical statistical

analysisanalysis phase rather than the phase rather than the designdesign phase of a study.phase of a study.

Stratification: “Series of 2x2 Stratification: “Series of 2x2 tables”tables”

Idea: Take a 2x2 table and break it into a series of smaller 2x2 tables (one table at each of J levels of the confounder yields J tables).

Example: in testing for an association between lung cancer and alcohol drinking (yes/no), separate smokers and non-smokers.

Stratification:“Series of 2xK Stratification:“Series of 2xK tables”tables”

Idea: Take a 2xK table and break it into a series of smaller 2xK tables (one table at each of J levels of the confounder yields J tables).

Example: In evaluating the association between lung cancer and being either a teetotaler, light drinker, moderate drinker, or heavy drinker (2x4 table), separate into smokers and non-smokers (two 2x4 tables).

Road MapRoad Map1. Test for Conditional Independence (Mantel-Haenszel, or “Cochran-Mantel-

Haenszel”, Test).Null hypothesis: when conditioned on the confounder, exposure and disease are

independent. Mathematically, (for dichotomous confounder): P(E&D/~C) = P(E/~C)*P(D/~C) and P(E&D/~C)=P(E/~C)*P(D/~C)Example: once you condition on smoking, alcohol and lung cancer are

independent; M-H test comes out NS.

2. Test for homogeneity. Breslow-Day.Null hypothesis: the relationship (or lack of relationship) between exposure and

disease is the same in each stratum (homogeneity). Example: B-D test would come out significant if alcohol aggravated the risk of

cigarettes on lung cancer but did not increase lung cancer risk in non-smokers. Homogeneity does NOT require independence!!

3. If homogenous, for series of 2x2 tables, you can take a weighted average of OR’s or RR’s (which should be similar in each stratum !) from the strata to get an overall OR or RR that has been controlled for confounding by C.

From Agresti…From Agresti…

“It is more informative to estimate the strength of association than simply to test a hypothesis about it.”

“When the association seems stable across partial tables, we can estimate an assumed common value of the k true odds ratios.”

Controlling for confounding by Controlling for confounding by stratificationstratification

Example: Gender Bias at Berkeley?(From: Sex Bias in Graduate Admissions: Data from Berkeley, Science 187: 398-403; 1975.)

 

 

Crude RR = (1276/1835)/(1486/2681) =1.25

(1.20 – 1.32)

Denied

Admitted

1835 2681

Female Male

1276 1486

559 1195

Program AProgram A

Stratum 1 = only those who applied to program A

 

 

Stratum-specific RR = .90 (.87-.94)

Denied

Admitted

108 825

Female Male

19 314

89 511

Program BProgram B

Stratum 2 = only those who applied to program B

 

 

Stratum-specific RR = .99 (.96-1.03)

Denied

Admitted

25 560

Female Male

8 208

17 352

Program CProgram C

Stratum 3 = only those who applied to program C

 

 

Stratum-specific RR = 1.08 (.91-1.30)

Denied

Admitted

593 325

Female Male

391 205

202 120

Program DProgram D

Stratum 4 = only those who applied to program D

 

 

Stratum-specific RR = 1.02 (.89-1.18)

Denied

Admitted

375 407

Female Male

248 265

127 142

Program EProgram E

Stratum 5 = only those who applied to program E

 

 

Stratum-specific RR = .88 (.67-1.17)

Denied

Admitted

393 191

Female Male

289 147

104 44

Program FProgram F

Stratum 6 = only those who applied to program F

 

 

Stratum-specific RR = 1.09 (.84-1.42)

Denied

Admitted

341 373

Female Male

321 347

20 26

SummarySummary

 

 

Crude RR = 1.25 (1.20 – 1.32)

Stratum specific RR’s:.90 (.87-.94)

.99 (.96-1.03)1.08 (.91-1.30) 1.02 (.89-1.18).88 (.67-1.17)

1.09 (.84-1.42)

Maentel-Haenszel Summary RR: .97

Cochran-Mantel-Haenszel Test is NS. Gender and denial of admissions are conditionally independent given program.The apparent association (RR=1.25) was due to confounding.

The Mantel-Haenszel The Mantel-Haenszel Summary Risk RatioSummary Risk Ratio

k

i i

iii

k

i i

iii

T

bacT

dca

1

1

)(

)(

Disease

Not Disease

Exposure Not Exposed

a c

b d

k strata

E.g., for Berkeley…E.g., for Berkeley…

97.

714)341(347

584)393(147

782)375(265

918)593(205

585)25(208

933)108(314

714)373(321

584)191(289

782)407(248

918)325(391

585)560(8

933)825(19

The Mantel-Haenszel The Mantel-Haenszel Summary Odds RatioSummary Odds Ratio

Exposed

Not Exposed

Case Control

a b

c d

k

i i

ii

k

i i

ii

T

cbT

da

1

1

 

 

Country

OR = 1.32 Spouse smokes

Spouse does not smoke

137 363

71 249US

Spouse smokes

Spouse does not smoke

19 38

5 16

Great

Britain

OR = 1.6

Spouse smokes

Spouse does not smoke

Lung Cancer Control

73 188

21 82Japan OR = 1.52

Source: Blot and Fraumeni, J. Nat. Cancer Inst., 77: 993-1000 (1986).

From Problem 3.9 in Agresti…

Summary ORSummary OR

38.1

820363*71

785*38

36421*188

820137*249

7816*19

36482*73

Not Surprising!

MH assumptionsMH assumptions

OR or RR doesn’t vary across strata. (Homogeneity!)

If exposure/disease association does vary for different subgroups, then the summary OR or RR is not appropriate…

advantages and limitationsadvantages and limitationsadvantages…• Mantel-Haenszel summary statistic is easy to interpret

and calculate• Gives you a hands-on feel for the datadisadvantages…• Requires categorical confounders or continuous

confounders that have been divided into intervals • Cumbersome if more than a single confounder

To control for 1 and/or continuous confounders, a multivariate technique (such as logistic regression) is preferable.

2. Effect Modification2. Effect Modification

Effect modification occurs when the effect of an exposure is different among different subgroups.

Years of Life Lost Due to Obesity Years of Life Lost Due to Obesity ((JAMA.JAMA. Jan 8 2003;289:187-193) Jan 8 2003;289:187-193)

Data from US Life Tables and the National Health and Nutrition Examination Surveys (I, II, III).

ConclusionConclusion

Race and gender modify the effect of obesity on years-of-life-lost.

Among white women, stage of breast cancer at detection is associated with education.

However, no clear pattern among black women.

Colon cancer and obesity in pre- Colon cancer and obesity in pre- and post-menopausal womenand post-menopausal women

Obesity appears to be a risk

factor in pre-menopausal

womenBut appears to be

protective or unrelated in post-menopausal

women

Hypothetical Example: Effect Hypothetical Example: Effect ModificationModification

  Feelings of Elation on 02/02

No change or depression

 

Watched the super-bowl

1250 2500

Did not watch the super-bowl

250 500

 

OR = 1.0

Conclusion: Watching the super-bowl doesn’t affect anyone’s mood?…

Football-team preference

 

OR = 1.5 Watched

Did not

450 300

375 375

Other/none

New England

Fans

 Watched

Did not

1240 10

125 125

OR = 124.0

PantherFans

Watched

Did not

Mood + Mood -

10 1240

125 125 OR = .008

Should have highly significant Breslow-Day statistic!