Intermediate methods in observational epidemiology 2008

Intermediate methods in observational epidemiology

2008

Confounding - I

800 200 500 500

80 100 50 250

180 300Mortality

18% 30%

Deaths

Intervention No intervention

240 240

24% 24%

65 175 65 175


Experimental(n=2000)

1300 700

650 350 650 350

1300 700

Observational(n= 2000)

OBSERVATION VS. EXPERIMENT

Absent, mortality = 10%

Present, mortality = 50%

Confounding variable:

Confounding variable

Less common in the group that undergoes the intervention

Increased mortality (“outcome”)

(DUAL) ASSOCIATION OF CONFOUNDING VARIABLE WITH BOTH OUTCOME AND INDEPENDENT

VARIABLE

Mortality according to the intervention, stratified by the confounder


Intervention: N No. of deaths

Mortality

Present Yes 200 100 50.0%

No 500 250 50.0%

Absent Yes 800 80 10.0%

No 500 50 10.0%

800 200 500 500

80 100 50 250

180 300

18% 30%


No. Deaths:

Mortality:

Absent, mortality = 10%

Present, mortality = 50%


One of the solutions to eliminate confounding: stratify

Israeli Study, see Kahn & Sempos, pp. 105

MI Case Control

140 29 711 SBP (mmHg)

< 140 27 1244

OR= 1.88

• Is the association causal? •Is it due to a third (confounding) variable (e.g., age)?

BP MI?

Age

A variable is onlya confounder if dualassociation is present

Age Vs SBP 140 <140

60 124 79 Age

< 60 616 1192

OR= 3.0

Age Vs MI MI Controls

60 15 188 Age

< 60 41 1767

OR= 3.4

Does age meet the criteria to be a confounder? Yes

Age

Increased odds of systolic hypertension (“exposure”)

Increased odds of myocardial infarction (“outcome”)

(DUAL) ASSOCIATION OF AGE WITH BOTH SYSTOLIC HYPERTENSION AND MYOCARDIAL INFARCTION

Confounder

Exposure

Outcome

CONFOUNDING EFFECT

… and not in the causality pathway between exposure and outcome:

Confounder

Exposure

Outcome

Blood Pressure MI Risk

Age SBP MI CONT

60 140 9 115

<140 6 73 OR=

<60 140 20 596

<140 21 1171 OR=

0.9

1.9

• Is it appropriate to calculate an adjusted OR? NO

Odds Ratios not homogeneous

Assumption when doing adjustment: Homogeneity of odds ratios (no multiplicative interaction).

Ways to assess if confounding is present:

Strategy 1:Does the variable meet the criteria to be a confounder (relation with exposure and outcome)?

Strategy 2: If the effect of that variable (on exposure and outcome) is controlled for (e.g., by stratification or adjustment) does the association change?

Ways to control for confounding

• During the design phase of the study:– Randomized trial– Matching– Restriction

• During the analysis phase of the study:– Stratification– Adjustment

• Stratified methods – Direct method– Mantel-Haenszel adjustment of Odds Ratios

• Regression methods

Matching in Case-Control Studies

Matching in a Case-Control Study

• Objective: To achieve comparability between cases and controls with regard to confounding variables

• Technique: For each case, choose a control without the case disease, of the same or similar age, at same service, same sex, etc.

Example of Matched Case-Control Study

• Cases: aplastic anemia seen in Baltimore from 1978-80

• Controls: patients with non-hematologic/nonmalignant disorders, matched to cases on age (± 5 years), sex, ethnic background and hospital of admission

• Hypothesis: subclinical HBV is associated with Aplastic Anemia

Matched case-control study

• 42 yr old black woman• 40 yr old white male• 57 yr old white woman• 55 yr old white woman• 48 yr old black men

• 44 yr old AA woman- diab.• 37 yr old white male- MI• 60 yr old white woman- AP• 55 yr old white woman- lupus• 49 yr old AA men- meningioma

Cases of Aplastic Anemia Controls (Patients)*

(*Admitted to the same hospital as index case with other diseases)

PAIRS

Cases

smoker nonsmoker

Controls

smoker

nonsmoker

Pair No. Case Control

1 smoker nonsmoker

2 smoker nonsmoker

3 nonsmoker smoker

4 smoker nonsmoker

5 nonsmoker nonsmoker


7 nonsmoker smoker

8 smoker nonsmoker


10 smoker smoker

Pairs of Cases and Controls Individually Matched by Age and Sex

PAIRS

Cases

smoker nonsmoker

Controls

smoker

nonsmoker


1 smoker nonsmoker

2 smoker nonsmoker

3 nonsmoker smoker

4 smoker nonsmoker



7 nonsmoker smoker

8 smoker nonsmoker


10 smoker smoker


PAIRS

Cases

smoker nonsmoker

Controls

smoker

nonsmoker XXXX


1 smoker nonsmoker

2 smoker nonsmoker

3 nonsmoker smoker

4 smoker nonsmoker



7 nonsmoker smoker

8 smoker nonsmoker


10 smoker smoker


PAIRS

Cases

smoker nonsmoker

Controls

smoker X X

nonsmoker XXXX


1 smoker nonsmoker

2 smoker nonsmoker

3 nonsmoker smoker

4 smoker nonsmoker



7 nonsmoker smoker

8 smoker nonsmoker


10 smoker smoker


PAIRS

Cases

smoker nonsmoker

Controls

smoker X X

nonsmoker XXXX X X X


1 smoker nonsmoker

2 smoker nonsmoker

3 nonsmoker smoker

4 smoker nonsmoker



7 nonsmoker smoker

8 smoker nonsmoker


10 smoker smoker


PAIRS

Cases

smoker nonsmoker

Controls

smoker X X X

nonsmoker XXXX X X X


1 smoker nonsmoker

2 smoker nonsmoker

3 nonsmoker smoker

4 smoker nonsmoker



7 nonsmoker smoker

8 smoker nonsmoker


10 smoker smoker


= 4/2= 2.0

Odds Ratio for Matched Case-Control Studies

ORNo Pairs C a Co

No Pairs C a Co

. /

. /

Favors hypothesis

Against hypothesis

PAIRS

Cases

smoker nonsmoker

Controls

smoker 1 2

nonsmoker 4 3

Risk Factors for Brain Tumors in Subjects Aged <20 years: A Case-Control Study

(Gold et al, Am J Epidemiol 1979;109:309-19)

• Exploratory study of risk factors for brain tumors

• Subjects < 20 yrs old

• Cases: primary malignant brain tumors in Baltimore in 1965-75

• Normal controls: chosen from birth certificates on file, and matched on cases by sex, date of birth (±1 year) and race

• Interviews with parents of children

Risk Factors for Brain Tumors: Birthweight

3818<3629 g

783629+ gControls’ birthweight

<3629 g3629+ g

Cases’ birth weightExposed: 3629+ g

Unexposed: <3629 g

Odds Ratio= 18/7= 2.6

(Gold et al, Am J Epidemiol 1979;109:309-19)

A few notes on “Matching”• Most frequently used in case-control studies• Frequency vs. individual matching• Advantages:

– Intuitive, easy to explain– Guarantees certain degree of comparability in small studies– Efficient (if matching on a strong confounder)– Particularly useful when outpatients are studied, and sample size is

relatively small (e.g., <100 cases and <100 controls)• Example: Case-control study of risk factors for emphysema:

– For each newly diagnosed case of emphysema seen in an Outpatient Unit, select the next (control) patient without diabetes, with an age ± 2 years, of the same sex, and educational status

• Disadvantages:– Costly, usually logistically complicated– Inefficient if matching on a weak confounder– Questionable representativiness of control group (limits its use for other

case-control comparisons)– Cannot study the matching variable (and additive interaction)– Possibility of residual confounding

Further issues for discussion

• Types of confounding• Confounding is not an “all or none”

phenomenon• Residual confounding• Confounder might be a “constellation” of

variables or characteristics• Considering an intermediary variable as

a “confounder” for examining pathways• Statistical significance and confounding

Types of confounding

• Positive confoundingWhen the confounding effect results in an

overestimation of the effect (i.e., the crude estimate is further away from 1.0 than it would be if confounding were not present).

• Negative confoundingWhen the confounding effect results in an

underestimation of the effect (i.e., the crude estimate is closer to 1.0 than it would be if confounding were not present).

10.1 10

Relative risk

3.0

5.0

3.02.0

0.40.3

0.4

0.7

0.7

3.0

Type of confounding:Positive Negative

TRUE, UNCONFOUNDED

OBSERVED, CRUDEx

x

x

x

X ?

• Confounding is not an “all or none” phenomenonA confounding variable may explain the whole or just part of the observed

association between a given exposure and a given outcome.• Crude OR=3.0 … Adjusted OR=1.0• Crude OR=3.0 … Adjusted OR=2.0

• Residual confoundingControlling for one of several confounding variables does not guarantee that

confounding be completely removed. Residual confounding may be present when:

- the variable that is controlled for is an imperfect surrogate of the true confounder,

- other confounders are ignored,- the units of the variable used for adjustment/stratification are too broad- the confounding variable is misclassified

• The confounding variable may reflect a “constellation” of variables/characteristics– E.g., Occupation (SES, physical activity, exposure to environmental risk

factors)– Healthy life style (diet, physical activity)

Residual Confounding: Relationship Between Natural Menopause and Prevalent CHD (prevalent cases v. normal controls), ARIC

Study, Ages 45-64 Years, 1987-89

Model Odds Ratio (95% CI)

1 Crude 4.54 (2.67, 7.85)

2 Adjusted for age: 45-54 Vs. 55+ (Mantel-Haenszel)

3.35 (1.60, 6.01)

3 Adjusted for age:

45-49, 50-54, 55-59, 60-64 (Mantel-Haenszel)

3.04 (1.37, 6.11)

4 Adjusted for age: continuous (logistic regression)

2.47 (1.31, 4.63)

• Confounding is not an “all or none” phenomenonA confounding variable may explain the whole or just part of the observed

association between a given exposure and a given outcome.• Crude OR=3.0 … Adjusted OR=1.0• Crude OR=3.0 … Adjusted OR=2.0

• Residual confoundingControlling for one of several confounding variables does not guarantee that

confounding be completely removed. Residual confounding may be present when:

- the variable that is controlled for is an imperfect surrogate of the true confounder,

- other confounders are ignored,- the units of the variable used for adjustment/stratification are too broad- the confounding variable is misclassified

• The confounding variable may reflect a “constellation” of variables/characteristics– E.g., Occupation (SES, physical activity, exposure to environmental risk

factors)– Healthy life style (diet, physical activity)

• Treating an intermediary variable as a confounder (i.e., ignoring “the 3rd rule”)Under certain circumstances, it might be of interest to

treat an hypothesized intermediary variable acting as a mechanism for the [risk factor-outcome] association as if it were a confounder (for example, adjusting for it) in order to explore the possible existence of additional mechanisms/pathways.

Scenario 1: The relationship of obesity to mortality is confounded by hypertension, i.e., the relationship is

statistical but not causal

Confounding factor or part of the chain of causality?

Obesity

Mortality

Hypertension

confounder

exposure

outcome

Example: relationship of obesity to mortality

Scenario 2: The relationship of obesity to mortality is causal and mediated by hypertension

mediator

Obesity

Mortality

Hypertension

exposure

outcome



Scenario 3: In addition to being mediated by hypertension, the causal relationship of obesity to

mortality is direct

Obesity

Mortality

Hypertension

mediator

exposure

outcome



Scenario 4: In addition to being mediated by hypertension, the causal relationship of obesity to

mortality is mediated by other mechanisms

Hypertension

mediator

Obesity

MortalityMortality

exposure

outcome

Obesity

Other mechanisms, e.g., diabetes



The different scenarios are not mutually exclusive!

Hypertension

mediator

Obesity

MortalityMortality

exposure

outcome

Obesity

Other mechanisms, e.g., diabetes



Obesity and Mortality

Relative Risk

Unadjusted 2.5

Adjusted for age, gender and ethnic background 2.0

Adjusted for age, gender, ethnic background and systolic blood pressure (SBP)

1.3

Obesity and Mortality

Relative Risk

Unadjusted 2.5

Adjusted for age, gender and ethnic background 2.0

Adjusted for age, gender, ethnic background and systolic blood pressure (SBP)

1.3

For positive associations (exposures associated with a RR> 1.0):

%.

. .

. .Excess R isk E xp la ined

RR RR

RRUNAD J AD J

UNAD J

1 0

1 0 02 0 1 3

2 0 1 01 0 0 7 0 %

Statistical significance as criteria to assess the presence of confounding

E.g., a confounder might be ruled out in a case-control study solely because there is no statistically significant difference in the levels of the confounder comparing cases and controls.

Exposure

Case-cont

?Confounder

BAD IDEA!

If the confounder is strongly associated with the exposure, even a small difference between cases and controls (not statistically significant because of limited sample size) may still induce confounding… and vice versa

E.g., Study of menopause as predictor of myocardial infarction. Even a small difference in age between cases and controls (e.g., 1 year, NS) may result in confounding due to the strong association between age and “exposure” (menopause).

44

46

48

50

52

54

56

58

60

% p

os

t-m

en

op

au

sal

Age (years) 55 56

Odds Ratio= 60/40 ÷ 50/50 = 1.5

Example: Menopause as a risk factor

44

46

48

50

52

54

56

58

60

% p

os

t-m

en

op

au

sal

Age (years) 55 56

casescontrols

Odds Ratio= 60/40 ÷ 50/50 = 1.5

Intermediate methods in observational epidemiology 2008

Documents

casecontrol studiesmatching

casecontrol studyobjective

similar age

index case

case disease

diseasespairs of cases

association change

confounding variablestechnique