Sample Actual vote Gallup Poll* *Based on a national survey conducted Oct. 15 -17 in likely voters N = 2263 N = 125,040,818 Obama McCain Other 50% 46%

Sample Actual vote

Gallup Poll*

*Based on a national survey conducted Oct. 15 -17 in likely voters

N = 2263 N = 125,040,818

ObamaMcCain Other

ObamaMcCain Other

50% 46% 4%

50% 46% 4%

53% 46% 1%

53% 46% 1%

Which was present in the sample?

Selection bias�

� Measurement bias

� Sampling error

Perhaps we should conduct our elections by sampling?

Perhaps we should conduct our elections by sampling?

Confounding and Interaction I

Confounding: one of the central problems in observational clinical research

– What is it? What does it do? What is its origin?

– What kind of variables act as confounders?

– Which variables are not confounders (colliders and intermediary variables)?

– Use of causal diagrams (DAGs) to conceptualize confounding and guide us for what to adjust for

» Emphasis on specifying the research question and understanding the underlying biological/clinical/behavioral system

» Confounding is a substantive, not statistical issue

Matches and Lung Cancer

A tobacco company researcher believes that

exposure to matches is a cause of lung cancer

He conducts a large case-control study to test this hypothesis

Exposure odds ratio = (820/180) / (340/660) = disease odds ratio

OR = 8.8

95% CI (7.2, 10.9)

Should we remove matches from the environment?

LungCancer

No LungCancer

Matches 820 340No matches 180 660

Smoking, Matches, and Lung Cancer

Lung Ca No Lung CaMatches 820 340No Matches 180 660

Lung CaNo

Lung CAMatches 810 270No Matches 90 30

Stratified

Crude

Non-SmokersSmokers

OR crude

OR CF+ = ORsmokers OR CF- = ORnon-smokers

Stratification produces two 2-by-2 tables

In each stratum, all subjects are homogeneous with respect to smoking

We have adjusted or controlled for smoking

ORcrude = 8.8 (7.2, 10.9)

ORsmokers = 1.0 (0.6, 1.5)

ORnon-smoker = 1.0 (0.5, 2.0)

ORadjusted = 1.0 (0.5, 2.0)

Lung CaNo

Lung CAMatches 10 70No Matches 90 630

Confounding: Smoking, Matches, and Lung Cancer

Illustrates how confounding can create an apparent effect even when there is no actual true effect

– Can also be opposite: confounding can mask an effect when one is truly present

Proper terminology

– In the relationship between matches and lung cancer, smoking is a confounding factor or a confounder

– Smoking confounds the relationship between matches and lung cancer

In clinical research, confounding has a very specific meaning

Estes continues to be confounding puzzle Ray RATTO

SHAWN ESTES seemed loath to analyze his own performance last night, for fear that people would see the first three innings and use them to obscure the last four.

But that's what made his outing so perfectly Estes-like -- an ongoing argument with himself that he eventually won.

Well, an argument in which he held his own and his teammates won for him in the bottom of the ninth.

Ramon Martinez lined a game-tying single with two outs, and Jeff Kent followed two batters later with a bases-loaded walk off Juan Acevedo to give the Giants a 2-1 victory against Colorado and move them to within 4 1/2 games of division leader Arizona. It was in many ways an eye-opening victory for a team that hadn't had one of this type for a while.

Finding: “After an initial course of post-exposure prophylactic (PEP) medication following a sexual exposure to HIV infection, gay men reported a decrease in the practice of high-risk behavior over the following year.”

Reviewer: “Perhaps the men simply withheld the real amount of high-risk behavior they had in order to be eligible for future courses of PEP. How do you account for this confounding?”

Lung Ca No Lung CaSmoking 900 300No Smoking 100 700

Lung CaNo

Lung CASmoking 810 270No Smoking 10 70

Stratified

Crude

Matches Absent

Matches Present

OR crude

OR CF+ = ORmatches

Lung CaNo

Lung CASmoking 90 30No Smoking 90 630

OR CF+ = OR no matches

ORcrude = 21.0 (16.4, 26.9)

ORmatches = 21.0 (10.7, 41.3)

ORno matches = 21.0 (13.1, 33.6)

The study is not over!

To be complete, you decide to examine the relationship between smoking and lung cancer independent from the use of matches.

Confounding: Smoking, Matches, and Lung Cancer

Interpretation?

What is the effect of matches on the relationship between smoking and lung cancer?

Matches have no effect on the relationshipMatches have no effect on the relationship

Effect of matches could have been predicted based on matches — lung cancer relationship

– Illustrates one important component in the requirements of a confounder

(aka a confounding factor) - A confounder must be causally related to

the outcome

Confounding: Examples of Magnitude and Direction

OR Crude OR CF+ OR CF- Type of Confounding

4.0 2.0 2.0 Positive 4.0 1.0 1.0 Positive 0.2 0.9 0.9 Positive 4.0 4.0 4.0 No confounding 4.0 8.0 8.0 Negative 1.0 3.0 3.0 Negative 0.9 0.2 0.2 Negative 4.0 0.5 0.5 Qualitative (reversal of

effect)

Disease No DiseaseExposedUnexposed



Stratified (adjusted)

Crude (unadjusted)

Potential Confounder

Absent

Potential Confounder

Present

OR crude

OR CF+ OR CF-

Nightlights

Let there be light!Let there be light!

Nightlights and Myopia

Quinn et al. Nature 1999

Prevalence Ratio =

Myopia No MyopiaNight light 79 153No night light 17 155

5.6) to2.1 :CI (95% 4.3

1721723279

Insert picture with nightlight off

Lights are off and the stumbling around begins.

Lights are off and the stumbling around begins.

Nightlights and Myopia

Two subsequent studies found no association and explained the prior result by confounding

– Zadnik et al. and Gwiazda et al. Nature, 2000

Child’s MyopiaChild’s Myopia

Night LightNight Light

??

How might confounding account for this finding?

Child’s MyopiaChild’s Myopia

Night LightNight Light

Parental Myopia

Parental Myopia XX

Positive or negative

confounding?


confounding?

PositivePositive

Insert picture with nightlight on again

Let there be light (again)!Let there be light (again)!

AZT to Prevent HIV After Needlesticks

Case-control study of whether post-exposure AZT use can prevent HIV seroconversion after needlestick (NEJM 1997)

CrudeHIV No HIV

AZT 8 131No AZT 19 189

27 320 347

ORcrude = 0.61

(95% CI: 0.26 - 1.4)

Interpretation?

Could confounding be present?

Interpretation?

Could confounding be present?

HIVHIV

AZT UseAZT Use

??

HIVHIV

AZT UseAZT Use

Severity of

Exposure

Severity of

Exposure

??


confounding?


confounding?

Adjustment for Confounder

Potential confounder: severity of exposure

Minor Severity Major

Severity

Crude

Stratified

HIV No HIVAZT 8 131No AZT 19 189

27 320 347

HIVNo

HIVAZT 0 91No AZT 3 161

3 252 255

ORcrude =0.61

HIVNo

HIVAZT 8 40No AZT 16 28

24 68 92

ORadjusted = 0.30

(95% CI: 0.12 – 0.79)

Negative Confounding

Confounding by Indication

Classification Schemes for Error in Clinical Research

Szklo and Nieto

– Bias

» Selection Bias

» Information/Measurement Bias

– Confounding

– Chance

Other Common Approach

– Bias

» Selection Bias

» Information/Measurement Bias

» Confounding

– Chance

Counterfactuals: Conceptualizing Why Confounding Occurs

Night lights and myopia

Ideal study: evaluate children exposed to night lights for several years and directly compare them to the SAME children not exposed to night lights

– Result (e.g. risk ratio) is called the “Effect Measure” of night lights

– Assuming no measurement error, the “effect measure” must be true.

However, since time has passed and children are older it is impossible to assess them without night lights

Hence, the ideal is “counterfactual” – contrary to the fact. It is unobservable. It cannot happen.

Exposed to

night lights

Exposed to

night lights

Unexposed to

night lights

Unexposed to

night lights

timetime


Gender and heart disease

Ideal study: evaluate men for several years for occurrence of heart disease; compare them directly to SAME individuals who are now women

However, you cannot change a man into a woman and you cannot go back in time

The “effect measure” is preposterous. It cannot be observed. It is counterfactual.

menmen

womenwomen

timetime


Nights and Myopia

Because we cannot perform the counterfactual ideal (SAME population studied under 2 conditions), we must evaluate TWO distinct populations (exposed to a night light and unexposed) to study the problem

– Result (e.g. risk ratio): a “measure of association”

The TWO distinct populations may be subject to different influences OTHER than just the night light

If these influences cause the disease under study, any difference in the risk ratio between the SAME population study (effect measure) and the TWO population study (measure of association) is what is known as confounding

Confounding occurs because of a mixing of effects

Exposed to

night lights

Exposed to

night lights

Unexposed to

night lights

Unexposed to

night lights

timetime

Other

influences

Other

influences

Striving for the Counterfactual

In the real (observable) world

All of our strategies in analytic studies are striving to simulate the counterfactual

We strive for our TWO distinct populations (exposed and unexposed) to be “exchangeable”

Whenever the TWO distinct populations are “non-exchangeable”, confounding will be present

Our strategies to manage confounding are attempts to make our populations exchangeable

Back to the Observable (Factual) World: Criteria for Confounding

Confounding occurs because of mixing between exposures of interest and unwanted extraneous effects

Extraneous effects are termed confounders

Criteria for a confounder

– Must be causally associated with the outcome,

or be a surrogate for a causally related variable

– Must be associated with the exposure under

study, but cannot be caused by the exposure

– Must not be on the causal pathway under study

(i.e., must not be an intermediary variable)

CC??

EE

DD

Causal Diagrams -- DAGsCausal Diagrams -- DAGs DAGs = directed acyclic graphs; aka chain graphs

Consist of nodes (variables) and arrows

“Directed”: all arrows have one-way direction and depict causal relationships

“Acyclic”: there is never a complete circle (i.e. no factor can cause itself)

Better than the rough criteria for confounding when planning studies and analyses

Identifies pitfalls of adjusting and not adjusting for certain variables

Frontier of epidemiologic theory

Research Question: Does E cause D?

Research Question: Does E cause D?

Forces investigator to conceptualize system

CC ??

EE

DD

Confounding in a DAGConfounding in a DAG

Confounding occurs if there is a factor C that is a “Common Cause” of both E and D

Confounding occurs if there is a factor C that is a “Common Cause” of both E and D

C is the genesis of a “backdoor path” to E and D

Adjusting/controlling for C closes the backdoor paths; eliminates confounding

Lung CancerLung

Cancer

MatchesMatches

SmokingSmoking

??

Smoking is a “common cause” of matches and lung cancer.

It therefore confounds the relationship (positive CF)

Controlling for smoking blocks the paths and unconfounds relationship

Smoking is a “common cause” of matches and lung cancer.

It therefore confounds the relationship (positive CF)

Controlling for smoking blocks the paths and unconfounds relationship

RQ: Do matches cause lung cancer?

RQ: Do matches cause lung cancer?

Birth DefectsBirth

Defects

Multi-vitamin

Use

Multi-vitamin

Use

History of birth

defects

History of birth

defects ??

Genetic factor is the “common cause” but cannot be measured or adjusted for

Genetic factor is the “common cause” but cannot be measured or adjusted for

Genetic Factor (not measured)


Adjusting for history of birth defects, which can be measured, blocks the path between genetic factor and MVI use, and prevents confounding

Adjusting for history of birth defects, which can be measured, blocks the path between genetic factor and MVI use, and prevents confounding

Threat: negative confounding

Threat: negative confounding

Hernan AJE 2002Hernan AJE 2002

SeriousHead Injury

SeriousHead Injury

Use of Helmets in Motorcyclists

Use of Helmets in Motorcyclists

Safety-oriented

Personality (not

measured)

Safety-oriented

Personality (not

measured)

??Safe

Driving Practices

Safe Driving

Practices

Threat: positive confounding

Threat: positive confounding

Adjusting for safe driving practices, which can (theoretically) be measured, blocks path from safety-oriented personality to head injury

Adjusting for safe driving practices, which can (theoretically) be measured, blocks path from safety-oriented personality to head injury

Attraction of DAGs Abstract: The Criteria

– Must be causally associated with the outcome, or be a surrogate for a causally related variable

– Must be associated with the exposure under study, but cannot be caused by the exposure

– Must not be on the causal pathway under study (i.e. must not be an intermediary variable)

More tangible: DAGs

– Draw the system

– Look for “common causes” of exposure and disease

Birth DefectsBirth Defects

Multi-vitamin

Use

Multi-vitamin

Use

??



History of birth

defects

History of birth

defects

The Challenge

DAGs provide the framework

However, to identify the confounders, you need to be a subject matter expert

Sexual Activity

?

Mortality

RQ: Does sexual activity cause greater lifespan?


Self-reported General Health

Unknown biologic factor(s)

(not measured)

Sexual Activity

?

Mortality



Ca channel Blockers

GI Bleeding

?

RQ: Do Calcium channel blockers cause GI bleeding?


Coronary Artery

Disease

Other Meds (e.g.,

aspirin)

Ca channel Blockers

GI Bleeding

?



Birth DefectsBirth

Defects

Folate Intake

Folate Intake

??

What should we do with stillbirths (spontaneous

abortions)?

What should we do with stillbirths (spontaneous

abortions)?

RQ: Does lack of folate cause birth defects?RQ: Does lack of folate cause birth defects?

Stillbirths are associated with folate intake, even among infants without birth defects: OR = 0.50

Stillbirths are associated with birth detects: OR = 15.22

Stillbirths are not on the causal pathway between folate and birth defects

In the past, other investigators have commonly adjusted for stillbirths in analyses, or have limited analyses to live births.

Should we adjust for stillbirths here?

Slone Epidemiology Unit Birth Defects Study


Adjustment for Stillbirths

Stillbirth No stillbirth

Crude

Stratified

Defect No Defect Good folate 43 239 Low folate 194 704 237 943 1180

ORcrude = 0.65

(95% CI 0.45 – 0.95)

ORadjusted = 0.80

(95% CI: 0.53 – 1.2)

Apparent positive confounding

Public health implication: No reason for women to supplement diet with folate

Defect

No Defect

Good folate 19 8 Low folate 100 46 119 54 173

Defect

No Defect

Good folate 24 231 Low folate 94 658 118 889 1007

Slone Epidemiology Unit Birth Defects Study


Birth DefectsBirth

Defects

Folate Intake

Folate Intake

StillbirthsStillbirths ??

RQ: Does lack of folate intake cause birth defects?

RQ: Does lack of folate intake cause birth defects?

Use of DAGs to Identify What is Not Confounding

Stillbirths are a “common effect” of both the exposure and disease – not a common cause.

Common effects are called “colliders”

Adjusting for colliders OPENS paths. Will actually result in bias. It is harmful.

Stillbirths are a “common effect” of both the exposure and disease – not a common cause.

Common effects are called “colliders”

Adjusting for colliders OPENS paths. Will actually result in bias. It is harmful.


Birth DefectsBirth

Defects

Multi-vitamin

use

Multi-vitamin

use

Maternal Weight Gain

Maternal Weight Gain ??

No common causes for exposure and disease

No common causes for exposure and disease

DAGs to Identify What is Not Confounding

Maternal weight gain is a collider

Adjusting for colliders will OPEN the path. Will actually result in bias. It is harmful.

Maternal weight gain is a collider

Adjusting for colliders will OPEN the path. Will actually result in bias. It is harmful.

Behavioral factors (not measured)

Behavioral factors (not measured)




DAGs Force Investigators to First Conceptualize the System

Study of sunlight exposure & melanoma

A college intern is given a dataset and asked to estimate relationship between sunlight exposure and melanoma – adjusted for “everything”

He analyzes the data and finds that gum chewing is associated with melanoma and associated with sunlight exposure

After adjusting for gum chewing there is an appreciable difference between the crude and adjusted measure of association

Should gum chewing be controlled for?

No. Just by chance alone there can be the appearance of confounding

Based on our a priori understanding of the role of gum chewing (in melanoma), it is more likely that chance – as opposed to truth -- is causing appearance of confounding

Controlling for a variable should only be done if there is a strong subject matter evidence.

i.e. If it is not in your DAG, don’t control for it.

Rules for Reading DAGs

A path is blocked if

– a collider (“common effect”) is present, which has not been adjusted for (by stratification, mathematical regression or other techniques)

Or

– a non-collider (“common cause”) is adjusted for

To prevent confounding, block all of the paths

FolateFolate

Birth defects

Birth defects


NightlightsNightlights

Child’s Myopia

Child’s Myopia

Parental Myopia

Parental Myopia

??

Rules for Reading DAGs

A path is open if

– A collider (“common effect”) is adjusted for

Or

– a non-collider (“common cause”) is not adjusted for

Open paths produce bias

FolateFolate

Birth defects

Birth defects


NightlightsNightlights

Child’s Myopia

Child’s Myopia

Parental Myopia

Parental Myopia

??

What other variables are NOT Confounders? “Must not be on the causal pathway under study

(i.e. must not be an intermediary variable)”

A variable that you are conceiving as an intermediate step in the causal path under study between the exposure in question and the disease is not a confounding variable.

EE

DD

factor Ifactor I

Despite being associated with both exposure and outcome,

Factor I is not a confounder

It is on the pathway under

study.

It is an intermediary

variable

Despite being associated with both exposure and outcome,

Factor I is not a confounder

It is on the pathway under

study.

It is an intermediary

variable

CCR5 and HIV Disease Progression

CCR5 (receptor)

defect

CCR5 (receptor)

defect

AIDSAIDS

How should CD4 count be handled in assessing the association between CCR5 defect status and progression in HIV disease to AIDS?


??

CCR5: the human cellular receptor for HIV –found on CD4 cells

Genetic defects in CCR5 now described

CD4 count potent predictor of time-to-AIDS




CD4 count

CD4 count

CCR5 and HIV Disease Progression

CCR5 (receptor)

defect

CCR5 (receptor)

defect

AIDSAIDS



CD4 countCD4 count







It depends upon the research question

CCR5 defectCCR5 defect

? [Other mechanisms]

? [Other mechanisms]

? [CD4 count]? [CD4 count]

AIDSAIDS

#1: Do CCR5 defects reduce progression to AIDS, irrespective of mechanism?

#1: Do CCR5 defects reduce progression to AIDS, irrespective of mechanism?


Low CD4 countLow CD4 count

AIDSAIDS

Do not adjust for CD4 count !

Do not adjust for CD4 count !

AIDS No AIDS Defect No defect



High CD4 countHigh CD4 count

CD4 countCD4 count

Do Adjust ! Do Adjust !

#2: Do CCR5 defects reduce progression to AIDS, independent of CD4 count?

#2: Do CCR5 defects reduce progression to AIDS, independent of CD4 count?

RQ 1: What if you did adjust for CD4 count?


AIDSAIDS

#1: Is CCR5 associated with progression to AIDS, irrespective of mechanism?

#1: Is CCR5 associated with progression to AIDS, irrespective of mechanism?

Low CD4 countLow CD4 count




High CD4 countHigh CD4 count

If “via CD4 count” was only pathway, no effect for CCR5 would be observed after stratification

If “via CD4 count” was only pathway, no effect for CCR5 would be observed after stratification

? [CD4 count]? [CD4 count]

Taylor et al. JAIDS 2003


Other mechanism

Other mechanism

#2 #2

??

CD4 countCD4 count

AIDSAIDS

#1#1


??

AIDSAIDS

CD4 not adjusted

for

CD4 not adjusted

for

CD4 countCD4 count

CD4 adjusted for

CD4 adjusted for

Crude (unadjusted) association:

- rate ratio: 0.71

Crude (unadjusted) association:

- rate ratio: 0.71

Stratified (adjusted) by CD4 count

-rate ratio: 0.93;

-Conclude: no mechanism other than via CD4

Stratified (adjusted) by CD4 count

-rate ratio: 0.93;

-Conclude: no mechanism other than via CD4

Hep B and C virus

infection

Hep B/C are not “common causes” but they do form another extraneous path from IDU to mortality; adjusting for Hep B/C blocks the path

IDU

Early Mortality

? [via bacterial infections]

RQ: Does injection drug use (IDU) cause earlier mortality independent of its effect on hepatitis infections?

RQ: Does injection drug use (IDU) cause earlier mortality independent of its effect on hepatitis infections?

Poor Diet

Poverty

Mortality

? [access to care]

RQ: Does poverty cause early mortality independent of effects on diet?

RQ: Does poverty cause early mortality independent of effects on diet?

Adjust for diet to

remove the extraneous

pathway

Adjust for diet to

remove the extraneous

pathway

Exercise and Coronary Heart Disease

When evaluating the relationship between exercise and CHD, what should be done with HDL cholesterol?

ExerciseExercise

Coronary Heart

Disease

Coronary Heart

Disease

??HDL

cholesterol

HDL cholesterol

RQ: Does exercise prevent coronary heart disease?

It depends on the pathway under investigation

If interest is in a pathway other than through HDL, then HDL should be adjusted for

Termed the “direct effect, independent of HDL”

ExerciseExercise

CADCAD

[not yet specified

mechanism]

[not yet specified

mechanism]HDLHDL ??

Adjust for HDL to remove the

extraneous pathway

Adjust for HDL to remove the

extraneous pathway

Exercise and CAD

If no particular mechanistic pathway is being studied

e.g., Does exercise influence CAD risk in a newly studied population (elderly Asians)?

Here, HDL as well as a variety of other mechanistic explanations are on the pathway in question

Therefore, HDL is an intermediary variable.

ExerciseExercise

CADCAD

Do not adjust for

HDL

Do not adjust for

HDL [HDL . .+. . other mechanisms][HDL . .+. . other mechanisms]

DAGs point out special issue when estimating direct effects

RQ: Does aspirin prevent CHD in a pathway other than through platelet aggregation

– Assumes no common cause of platelet agg. and D

Would be correct to adjust

But if

– Assume common cause (e.g., genetic component)

– Need other statistical methods to resolve

AspirinAspirin

Coronary Heart Disease


Platelet Aggregation

Platelet Aggregation ??

AspirinAspirin



Platelet Aggregation

Platelet Aggregation ??

Genetic factors (not measured)

Genetic factors (not measured)

Would be incorrect to

adjust OR not to adjust for

platelet aggregation

Would be incorrect to

adjust OR not to adjust for

platelet aggregation

Cole and Hernan IJE 2002Cole and Hernan IJE 2002

When Planning a Study, Which Factors Should be Measured as Potential

Confounders or Extraneous Pathways?

Draw a DAG

With previously studied exposures-diseases:

– consider/measure any factor for which prior evidence indicates is a confounder

» e.g., effect of diet on CAD?

must deal with smoking as potential confounder

When studying new exposures for which little is known:

– plan on measuring ALL factors associated with the disease

– i.e. If you don’t, you may regret it later

Confounding can be dealt with in the analysis phase of a study but NOT if the factor is not measured

Seeking cause of high Marin cancer rates Activists canvass residents to search for trends

Thousands of volunteers scattered across Marin County under baleful skies Saturday in an unprecedented grassroots campaign against the region's soaring cancer rate.

Armed with surveys, some 2,000 volunteers went door to door in every neighborhood in the county . . . . The volunteers hope to collect enough money to hire an epidemiologist . . .

Documents

Sample Actual vote Gallup Poll* *Based on a national survey conducted Oct. 15 -17 in likely voters N = 2263 N = 125,040,818 Obama McCain Other 50% 46%