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A plot of the population of Oldenburg at the end of each year against

the number of storks observed in that year, 1930-1936.

Ornitholigische Monatsberichte 1936;44(2)

Are people living in Costa Rica or Venezuela at lower risk of mortality than people in Canada or the US?

Yes

No

Mortality rate in six countries in the Americas, 1986

(assuming vital statistics are correct)

No

Mortality rate in six countries in the Americas, 1986

Next question:

Is the observed association causal in nature, i.e., is there something about living in Costa Rica or Venezuela that makes the population have lower risk of death than the population of Canada or the US?

N=14,054 middle age adults from 4 US communities

Comparing risk profile according to known CVD risk factors:

Low Risk individuals (n=623):

- Never smokers

- Total cholesterol <200 mg/dL

- HDL cholesterol >65mg/dL

- LDL cholesterol <100 mg/dL

- Triglycerides <170 mg/dL

- Glycemia <140 mg/dL

- BP<140/90 mm Hg, no Rx

- No Hx of CVD, htn, diabetes, high cholesterol

Rest (n=13,431): at least one of the above.

A variable can be a confounder if all the following conditions are met:

- It is associated with the exposure of interest (causally or not).
- It is causally related to the outcome.
- AND ... It is not part of the exposure outcomecausal pathway

Ways to assess if confounding is present:

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

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

Is male gender causally related to the risk of malaria?

Yes

No

Further study is needed

Strategy #1: Does the variable meet the criteria to be a confounder?Hypothetical case-control study of risk factors for malaria. 150 cases, 150 controls; gender distribution.

OR= [88 x 82] ÷ [68 x 62] = 1.71

First criterion: Is the putative confounder associated with exposure?

Male

gender

Outdoor

occupation

?

Malaria

Is outdoor occupation associated with male gender?

Yes

No

First criterion: Is the putative confounder associated with exposure?

.

OR=7.8

Second criterion: Is the putative confounder associated with the outcome (case-control status)?

Male

gender

Outdoor

occupation

?

Malaria

Is outdoor occupation (or something for which this variable is a marker of --e.g., exposure to mosquitoes) causally related to malaria?

Yes

No

Second criterion: Is the putative confounder associated with case-control status?

.

Malaria

OR=5.3

Yes, it could be

Outdoor

occupation

?

Probably not

Third criterion: Is the putative confounder in the causal pathway exposure outcome?.

Male

gender

Malaria

Note: Judgment and knowledge about the socio-cultural context are critical to answer this question

Question:

Provided that:

- Crude association between male gender and malaria: OR=1.71

and

- ... Outdoor occupation is more frequent among males, and
- ... Outdoor occupation is associated with greater risk of malaria …

What would be the expected magnitude of the association between male gender and malaria after controlling for occupation (i.e., assuming the same degree of outdoor occupation in males and females)?

The (adjusted) association estimate will be smaller than 1.71

The (adjusted) association estimate will =1.71

The (adjusted) association estimate will greater than 1.71

occupation

Outdoor

occupation

OR=1.00

OR=1.06

Strategy #2: Does controlling for the putative confounder change the magnitude of the exposure-outcome association?Malaria

OR=1.71

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

OR=1.71

LR

Rest

F

29.0

30.1

Indoor

occupation

Outdoor

occupation

M

16.8

19.1

OR=1.06

OR=1.00

Examples of stratificationNote that confounding is present when:

- RR/ORpooled different fromRR/ORstratified

and

- RR/OR1 = RR/OR2 = …= RR/ORz

*Adjusted by direct method using the 1960 population of Latin America as the standard population.

Examples of adjustmentMalaria

OR=1.71

Indoor

occupation

Outdoor

occupation

OR=1.00

OR=1.06

Adjusted OR*=1.01

*Using the Mantel-Haenszel method, to be discussed.

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
- Confounding: a type of bias?
- Statistical significance and confounding

Types of confounding

- Positive confounding

When 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 confounding

When 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).

0.4

0.4

3.0

1

0.1

10

Type of confounding:

PositiveNegative

3.0

UNCONFOUNDED

5.0

OBSERVED, CRUDE

2.0

0.3

0.7

?

0.7

“Qualitative

confounding”

Relative risk

Example of positive confounding

Malaria

OR=1.71

Indoor

occupation

Outdoor

occupation

OR=1.00

OR=1.06

Adjusted OR=1.01

Example of negative confounding

An occupational study in which workers exposed to a certain carcinogen are younger than those not exposed.

If the risk of cancer increases with age, the crude association between exposure and cancer will underestimate the unconfounded (adjusted) association.

Age: negative confounder.

Rest

F

29.0

30.1

M

16.8

19.1

*Adjusted by direct method using the 1960 population of Latin America as the standard population.

Examples of qualitative confoundingRate ratioUS/Mex= 1.78 0.72

Confounding is not an “all or none” phenomenon

A 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 confounding

Controlling for one of several confounding variables does not guarantee that confounding is 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 may reflect a “constellation” of variables/characteristics
- E.g., Occupation (SES, physical activity, exposure to environmental risk factors)
- Healthy life style (diet, physical activity)

factors?

?

ERT

(adjusted)*

Low CHD

*Adjusted for family history, type of menopause, smoking, hypertension, diabetes, OC use, high cholesterol, age, obesity.

(Matthews KA et al. Prior to use of estrogen replacement therapy, are users healthier than nonusers? Am J Epidemiol 1996;143:971-978)

Placebo

Kaplan-Meier estimates of the cumulative incidence of primary coronary heart disease events.

JAMA 1998;280:605-13.

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. This is done by comparing the adjusted with the unadjusted values.

EXAMPLE:It has been argued that obesity is not a risk factor of mortality. The observed association between obesity and mortality in many studies might just be the product of the confounding effect of hypertension.

Obesity

?

Mortality

HOWEVER,Hypertension is probably not a real confounder but rather a mechanism whereby obesity causes hypertension.*

Obesity

Mortality

*Manson JE et al: JAMA 1987;257:353-8.

EVEN IF HYPERTENSION IS A MECHANISM LINKING OBESITY TO MORTALITY, it may be of interest to conduct analyses that control for hypertension, to assess whether alternative mechanisms may causally link obesity and mortality.

Obesity

Block by

adjustment

Hypertension

Mortality

EXAMPLE:Is maternal smoking a risk factor of perinatal death?Is the association confounded by low birth weight?

Maternal smoking

Low birth

weight

?

Perinatal mortality

OR RATHER:Is low birth weight the reason why maternal smoking is associated to higher risk of perinatal death?

Maternal smoking

Low birth

weight

Perinatal mortality

BUT THERE COULD BE AN ADDITIONAL QUESTION:Does maternal smoking cause perinatal death by mechanisms other than low birth weight?

Maternal smoking

Block by

adjustment

Direct toxic effect?

Low birth

weight

Perinatal mortality

Statistical significance should not be used to assess confounding effects

Odds Ratio [age 56/age 55] = 60/40 ÷ 50/50 = 1.5

Age (years)

55

56

Statistical significance should not be used to assess confounding effects

Odds Ratio [cases/controls] = 60/40 ÷ 50/50 = 1.5

% post-menopausal

Age (years)

55

56

Statistical significance should not be used to assess confounding effects

The main strategy must be to evaluate whether the difference in the confounder is large enough to explain the association.

Control of Confounding Variables

- Randomization
- Matching
- Adjustment
- Direct
- Indirect
- Mantel-Haenszel
- Multiple Regression
- Linear
- Logistic
- Poisson
- Cox

Stratified methods

Control of Confounding Variables

- Randomization
- Matching
- Adjustment
- Direct
- Indirect
- Mantel-Haenszel
- Multiple Regression
- Linear
- Logistic
- Poisson
- Cox

Stratified methods

Mantel-Haenszel Technique for Adjustment of the Odds Ratios and Rate Ratios

- Nathan Mantel and William Haenszel were two very productive statisticians:
- Test for homogeneity of stratified OR’s (see Schlesselman, pp. 193-6, or Kahn & Sempos, pp. 115-6): for the assessment of multiplicative interaction
- Mantel-Haenszel test for trend

a confounder if dual

association is present

?

MI

BP

Age

Mantel-Haenszel Technique for Adjustment of Odds Ratios-- Example (Israeli Study, see Kahn & Sempos, pp. 105)OR= 1.88

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

Increased odds of systolic hypertension (“exposure”)

Age

Increased odds of myocardial infarction (“outcome”)

Blood Pressure MI Risk

0.9

1.9

NO

- Is it appropriate to calculate an adjusted ORMH?

These findings fail to meet Mantel-Haenszel adjustment approach’s main assumption: that odds ratios are homogeneous (no multiplicative interaction).

=

Mantel-Haenszel Formula for Calculation of Adjusted Odds RatiosThus, the ORMHis a weighted average of stratum-specific ORs

(ORi), with weights equal to each stratum’s:

Stratum-specific odds ratios: 2.5, 2.6, 4.0

Average= ORMH 2.83

There is an analogous procedure to obtain an adjusted Rate Ratio from stratified data in a prospective study (see Kahn & Sempos, pp. 219-221)

Mortality of Individuals with High and Low Vitamin C/Beta-Carotene Intake Index, by Smoking Status, Western Electric Company Study(Pandey et al, Am J Epidemiol 1995;142:1269-78)

Formulas for calculating confidence intervals for the ORMH are available (Schlesselman, p. 184, Szklo & Nieto, Appendix A.8)

If ORPooled

(ORZ=1

ORZ=2

~

~

~

~

~

~

~

~

~

~

ORZ=3, …)

If ORPooled

(ORZ=1

ORZ=2

#

ORZ=3, …

If

ORZ=1

ORZ=2

#

#

Z is not a confounder:

report crude OR (ORPooled)

Z is a confounder:

report ORPooledand adjusted OR

Z is an effect modifier. Do not

adjust: report Z-specific ORs

Correspondence between the “matched” odds ratios and the Mantel-Haenszel method

OR??

OR= 45/23= 1.96

(Adapted from Heinone et al, Lancet 2:675, 1974)

Reserpine Use and Breast Cancer

OR= 45/23= 1.96

Stratification Methods

- Advantages
- Easy to understand and compute
- Allow simultaneous assessment of interaction
- Disadvantages
- Cannot handle a large number of variables (zero cells are problematic in direct adjustment)
- Each calculation requires a rearrangement of tables

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