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

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.

Hernan AJE 2002Hernan AJE 2002

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

Coronary Heart Disease

Platelet Aggregation

Platelet Aggregation ??

AspirinAspirin

Coronary Heart Disease

Coronary Heart Disease

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

Confounding and Interaction: Part III

• Methods to reduce confounding– during study design:

• Randomization• Restriction• Matching

– during study analysis:• Stratified analysis

– Forming “Adjusted” Summary Estimates– Concept of weighted average

» Woolf’s Method» Mantel-Haenszel Method

– Handling more than one potential confounder– Role of an analysis plan

• Another design technique: Instrumental variables

• Quantitative assessment of unmeasured confounding

• Limitations of stratification

– motivation for multivariable regression

• Limitations of conventional adjustment

– motivation for other “causal” techniques

Effect-Measure Modification

DelayedNot

DelayedSmoking 15 61No Smoking 47 528

Stratified

Delayed Not DelayedSmoking 26 133No Smoking 64 601

Crude

No Caffeine Use

Heavy Caffeine Use

RR crude = 1.7

RRno caffeine use = 2.4

DelayedNot

DelayedSmoking 11 72No Smoking 17 73

RRcaffeine use = 0.7

. cs delayed smoking, by(caffeine) caffeine | RR [95% Conf. Interval] M-H Weight-----------------+------------------------------------------------- no caffeine | 2.414614 1.42165 4.10112 5.486943 heavy caffeine | .70163 .3493615 1.409099 8.156069 -----------------+------------------------------------------------- Crude | 1.699096 1.114485 2.590369 M-H combined | 1.390557 .9246598 2.091201-----------------+-------------------------------------------------Test of homogeneity (M-H) chi2(1) = 7.866 Pr>chi2 = 0.0050

Report interaction; confounding is not relevant

Association Between Smoking and Delayed Conception by Amount of Caffeine Use

Caffeine Use Risk Ratio 95% CI None 2.4* 1.4 to 4.1 Heavy 0.7* 0.35 to 1.4

* test of homogeneity, p = 0.005

Report vs Ignore Effect-Measure Modification?Some Guidelines

Risk Ratios for a Given Exposure and Disease

Potential Effect Modifier Present Absent

P value for heterogeneity

Report or Ignore

Interaction

2.3 2.6 0.45 Ignore

2.3 2.6 0.001 Ignore

2.0 20.0 0.001 Report

2.0 20.0 0.10 Report

2.0 20.0 0.40 Ignore

3.0 4.5 0.30 Ignore

3.0 4.5 0.001 +/-

0.5 3.0 0.001 Report

0.5 3.0 0.20 +/-

Is an art form: requires consideration of clinical, statistical and practical considerations

Does AZT after needlesticks prevent HIV?

HIVNo

HIVAZT 8 40No AZT 16 28

24 68 92

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

OR = 0.0 OR = 0.35

Report or ignore interaction?. cc HIV AZTuse,by(severity)

severity | OR [95% Conf. Interval] M-H Weight-----------------+------------------------------------------------- minor | 0 0 2.302373 1.070588 major | .35 .1344565 .9144599 6.956522-----------------+-------------------------------------------------

Test of homogeneity (B-D) chi2(1) = 0.60 Pr>chi2 = 0.4400

General Framework for Stratification

• Design phase: Create a DAG– Decide which variables to control for

• Implementation phase: measure the confounders (or other variables needed to block path)

• Analysis phase:

Report Effect-Measure Modification? (assess clinical, statistical, and practical considerations)

yesno

Derive summary “adjusted” estimate

Report stratum-specific estimates

Report crude estimate, 95% CI, p value

Decide which variables to adjust for in final estimate

none someReport adjusted estimate, 95% CI, p value

Assuming Interaction is not Present, Form a Summary of the Unconfounded

Stratum-Specific Estimates

• Construct a weighted average– Assign weights to the individual strata– Summary Adjusted Estimate = Weighted

Average of the stratum-specific estimates

– a simple mean is a weighted average where the weights are equal to 1

– which weights to use depends on type of effect estimate desired (OR, RR, RD), characteristics of the data, and goal of research

– e.g., • Woolf’s method• Mantel-Haenszel method• Standardization (see text)

ii

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w

istratuminestimateeffectw )] ([

5)1)(4(

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Forming a Summary Adjusted Estimate for Stratified Data

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

OR = 0.0

HIVNo

HIVAZT 8 40No AZT 16 28

24 68 92

OR = 0.35

How would you weight these strata?

Summary Estimators: Woolf’s Method

• aka Directly pooled or precision estimator• Woolf’s estimate for adjusted odds ratio

– where wi

– wi is the inverse of the variance of the stratum-specific log(odds ratio)

idicibia1111

1

i

i

i

ii

Woolfw

w )]OR (log[

OR log

)(OR logOR WoolfWoolf e

Disease No DiseaseExposed ai bi

Unexposed ci di

Calculating a Summary Effect Using the Woolf Estimator

• e.g., AZT use, severity of needlestick, and HIV

Minor Severity

Major Severity

Crude

Stratified

HIV No HIVAZT 8 131No AZT 19 189

27 320

HIVNo

HIVAZT 0 91No AZT 3 161

3 252 255

ORcrude =0.61

OR = 0.0

HIVNo

HIVAZT 8 40No AZT 16 28

24 68 92

OR = 0.35

281

161

401

81

1

1611

31

911

01

1

)]0.35 log(

281

161

401

81

1[)]0 log(

1611

31

911

01

1[

WoolfOR log

Problem: cannot take log of 0; cannot divide by zero

Summary Adjusted Estimator: Woolf’s Method

• Conceptually straightforward

• Best when:– number of strata is small– sample size within each strata is large

• Cannot be calculated when any cell in any stratum is zero because log(0) is undefined– 1/2 cell corrections have been suggested but

are subject to bias

• Formulae for Woolf’s summary estimates for other measures (e.g., risk ratio, RD) available in texts and software documentation

Summary Adjusted Estimators: Mantel-Haenszel

• Mantel-Haenszel estimate for odds ratios

– ORMH =

– wi =

– wi is inverse of the variance of the stratum-specific odds ratio under the null hypothesis (OR =1)

i

ii

N

cb

i

ii

i

ii

Ncb

Nda

i

ii

i

i

i

i

i

ii

Ncb

dbca

Ncb

*

Disease No DiseaseExposed ai bi

Unexposed ci di

ai+ bi + ci + di = Ni

Summary Adjusted Estimator: Mantel-Haenszel

• Relatively resistant to the effects of large numbers of strata with few observations

• Resistant to cells with a value of “0”

• Computationally easy

• Most commonly used in commercial software

Calculating a Summary Adjusted Effect Using the Mantel-Haenszel Estimator

• ORMH =

• ORMH =

Minor Severity

Major Severity

Crude

Stratified

HIV No HIVAZT 8 131No AZT 19 189

27 320

HIVNo

HIVAZT 0 91No AZT 3 161

3 252 255

ORcrude =0.61

OR = 0.0

HIVNo

HIVAZT 8 40No AZT 16 28

24 68 92

OR = 0.35

i

ii

ii

ii

i

ii

N

cbcb

da

N

cb*

i

ii

i

ii

Ncb

Nda

30.0

921640

255391

92288

2551610

Calculating a Summary Effect in Stata

• To stratify by a third variable:

– cs varcase varexposed, by(varthird variable)

– cc varcase varexposed, by(varthird variable)

• Default summary estimator is Mantel-Haenszel– “ , pool” will also produce Woolf’s method

epitab command - Tables for epidemiologists

Calculating a Summary Effect Using the Mantel-Haenszel Estimator

• e.g. AZT use, severity of needlestick, and HIV

• . cc HIV AZTuse,by(severity) pool• severity | OR [95% Conf. Interval] M-H Weight• -----------------+-------------------------------------------------• minor | 0 0 2.302373 1.070588 • major | .35 .1344565 .9144599 6.956522 • -----------------+-------------------------------------------------• Crude | .6074729 .2638181 1.401432 • Pooled (direct) | . . .• M-H combined | .30332 .1158571 .7941072 • -----------------+-------------------------------------------------• Test of homogeneity (B-D) chi2(1) = 0.60 Pr>chi2 = 0.4400• Test that combined OR = 1:• Mantel-Haenszel chi2(1) = 6.06• Pr>chi2 = 0.0138

Minor Severity

Major Severity

Crude

Stratified

HIV No HIVAZT 8 131No AZT 19 189

27 320

HIVNo

HIVAZT 0 91No AZT 3 161

3 252 255

ORcrude =0.61

OR = 0.0

HIVNo

HIVAZT 8 40No AZT 16 28

24 68 92

OR = 0.35

Calculating a Summary Effect Using the Mantel-Haenszel Estimator

• In addition to the odds ratio, Mantel-Haenszel estimators are also available in Stata for:

– risk ratio

• “cs varcase varexposed, by(varthird variable)”

– rate ratio

• “ir varcase varexposed vartime, by(varthird variable)”

After Confounding is Managed: Confidence Interval Estimation and Hypothesis Testing for the Mantel-

Haenszel Estimator

• e.g. AZT use, severity of needlestick, and HIV

• . cc HIV AZTuse,by(severity) pool• severity | OR [95% Conf. Interval] M-H Weight• -----------------+-------------------------------------------------• minor | 0 0 2.302373 1.070588 • major | .35 .1344565 .9144599 6.956522 • -----------------+-------------------------------------------------• Crude | .6074729 .2638181 1.401432 • Pooled (direct) | . . .

M-H combined | .30332 .1158571 .7941072

• -----------------+-------------------------------------------------• Test of homogeneity (B-D) chi2(1) = 0.60 Pr>chi2 = 0.4400

• Test that combined OR = 1:• Mantel-Haenszel chi2(1) = 6.06• Pr>chi2 = 0.0138

• What does the p value = 0.0138 mean?

Mantel-Haenszel Confidence Interval and Hypothesis Testing

stratumeach in cell a

for the valueexpected theis E

)1(

5.0

eCI %95

;;;

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i

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OR SE(log x (1.96 MH

OR log

1

2

1

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1

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2

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NN

mmnn

Ea

N

cbw

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daR

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cbQ

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where

w

wQ

wR

RQwP

R

RP

k

i ii

iiii

k

i

k

iii

i

iii

i

iii

i

iii

i

iii

k

ii

k

iii

k

i

k

iii

k

iiiii

k

ii

k

iii

Disease No DiseaseExposed ai bi m1i

Unexposed ci di m2i

n1i n2i Ni

Mantel-Haenszel Techniques

• Mantel-Haenszel estimators• Mantel-Haenszel chi-square statistic• Mantel’s test for trend (dose-response)

Spermicides, maternal age & Down Syndrome

•

Down No Down Spermicide use 4 109 No spermicide use 12 1145

Down No Down

Spermici use 3 104 No spermic. 9 1059 1175

Age < 35 Age > 35

Crude

Stratified Down No

Down

Spermic. use 1 5 No spermic. 3 86 95

OR = 3.4 OR = 5.7

OR = 3.5

. cc downs spermici , by(matage) pool

matage | OR [95% Conf. Interval] M-H Weight-----------------+------------------------------------------------- < 35 | 3.394231 .9800358 11.80389 .7965957 >= 35 | 5.733333 0 50.8076 .1578947-----------------+------------------------------------------------- Crude | 3.501529 1.171223 10.49699 Pooled (direct) | 3.824166 1.196437 12.22316 M-H combined | 3.781172 1.18734 12.04142-----------------+-------------------------------------------------Test for heterogeneity (direct) chi2(1) = 0.137 Pr>chi2 = 0.7109Test for heterogeneity (M-H) chi2(1) = 0.138 Pr>chi2 = 0.7105

Test that combined OR = 1: Mantel-Haenszel chi2(1) = 5.81 Pr>chi2 = 0.0159

Which answer should you report as “final”?

What undesired feature has stratification caused?

Effect of Adjustment on Precision (Variance)

• Adjustment can increase or decrease standard errors (and CI’s) depending upon:– Nature of outcome (interval scale vs. binary)– Measure of association desired– Method of adjustment (Woolf vs M-H vs MLE)– Strength of association between potential

confounding factor and exposure/disease

• Complex and difficult to memorize

• Good news: adjustment for strong confounders removes bias and often improves precision

• Bad news: adjustment for less-than-strong confounders can often (but not always) worsen precision

Effect of Adjustment on Precision

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

Lung CaNo

Lung CASmoking 90 30No Smoking 90 630

OR crude = 21.0

(95% CI: 16.4 - 26.9)

ORmatches = 21.0 OR no matches = 21.0

OR adj = 21.0

(95% CI: 14.2 - 31.1)

Whether or not to accept the “adjusted” summary estimate instead

of the crude?• Methodologic literature is inconsistent on this

– Bias-variance tradeoff

• Scientifically most rigorous approach is to:– Create the DAG and identify potential confounders– Prior to adjustment, create two lists of potential

confounders• “A” List: Those factors for which you will accept

the adjusted result no matter how small the difference from the crude.

– Factors strongly believed to be confounders

• “B” List: Those factors for which you will accept the adjusted result only if it meaningfully differs from the crude (with some pre-specified difference, e.g., 5 to 10%).

– “Change-in-estimate” approach– Factors you are less sure about

• For some analyses, may have no factors on A list. For other analyses, no factors on B list.

• Always putting all factors on A list may seem conservative, but not necessarily the right thing to do in light of penalty of statistical imprecision

Bias control paramount

Need for tradeoffs

Choosing the crude or adjusted estimate?

• Assume all factors are on B list and a 10% change-in-estimate rule is in place

Risk Ratios Crude Third

Factor Present

Third Factor Absent

Adjusted

Crude or Adjusted?

4.1 1.9 2.1 2.0 Adjusted

4.0 1.2 1.0 1.1 Adjusted

0.2 0.7 0.9 0.8 Adjusted

4.0 3.8 4.2 4.1 Crude

4.0 8.2 7.7 7.9 Adjusted

1.0 3.1 2.7 3.0 Adjusted

1.9 1.6 1.9 1.8 Crude

0.9 0.1 0.2 0.1 Adjusted

4.0 0.4 0.6 0.5 Adjusted

No Role for Statistical Testing for Confounding

• Testing for statistically significant differences between crude and adjusted measures is inappropriate

– e.g., examining an association for which a factor is a known confounder (say age in the association between hypertension and CAD)

– if the study has a small sample size, even large differences between crude and adjusted measures may not be statistically different

• yet, we know confounding is present• therefore, the difference between crude and adjusted

measures cannot be ignored as merely chance. • bias must be prevented and hence adjusted estimate

is preferred• we must live with whatever effects we see after

adjustment for a factor for which there is a strong a priori belief about confounding

– the issue of confounding is one of bias, not of sampling error.

• Other than in RCTs, we’re not concerned that sampling error is causing confounding and therefore we don’t have to worry about testing for role of chance

Spermicides, maternal age & Down Syndrome

•

Down No Down Spermicide use 4 109 No spermicide use 12 1145

Down No Down

Spermici use 3 104 No spermic. 9 1059 1175

Age < 35 Age > 35

Crude

Stratified Down No

Down

Spermic. use 1 5 No spermic. 3 86 95

OR = 3.4 OR = 5.7

OR = 3.5

. cc downs spermici , by(matage) pool

matage | OR [95% Conf. Interval] M-H Weight-----------------+------------------------------------------------- < 35 | 3.394231 .9800358 11.80389 .7965957 >= 35 | 5.733333 0 50.8076 .1578947-----------------+------------------------------------------------- Crude | 3.501529 1.171223 10.49699 Pooled (direct) | 3.824166 1.196437 12.22316 M-H combined | 3.781172 1.18734 12.04142-----------------+-------------------------------------------------Test for heterogeneity (direct) chi2(1) = 0.137 Pr>chi2 = 0.7109Test for heterogeneity (M-H) chi2(1) = 0.138 Pr>chi2 = 0.7105

Test that combined OR = 1: Mantel-Haenszel chi2(1) = 5.81 Pr>chi2 = 0.0159

Which answer should you report as “final”?

Stratifying by Multiple Potential Confounders

Crude

Stratified

<40 smokers

>60 non-smokers40-60 non-smokers

CAD NoCAD

Chlamydia

NoChlamydia

<40 non-smokers

40-60 smokers >60 smokers

CAD No CADChlamydiaNo chlamydia

CAD NoCAD

Chlamydia

NoChlamydia

CAD NoCAD

Chlamydia

NoChlamydia

CAD NoCAD

Chlamydia

NoChlamydia

CAD NoCAD

Chlamydia

NoChlamydia

CAD NoCAD

Chlamydia

NoChlamydia

The Need for Evaluation of Joint Confounding

• Variables that evaluated alone show no confounding may show confounding when evaluated jointly

Crude

Stratified by Factor 1 alone

by Factor 2 alone

by Factor 1 & 2

Disease No DiseaseExposed 12 4Unexposed 30 22

OR = 2.2

F1 +Disease

NoDisease

Exposed 6 2Unexposed 15 11

OR = 2.2

F1+F2+Disease

NoDisease

Exposed 1 1Unexposed 10 10

OR = 1.0

F1-F2+Disease

NoDisease

Exposed 5 1Unexposed 5 1

OR = 1.0

F1+F2-Disease

NoDisease

Exposed 5 1Unexposed 5 1

OR = 1.0

F1-F2-Disease

NoDisease

Exposed 1 1Unexposed 10 10

OR = 1.0

F1 -Disease

NoDisease

Exposed 6 2Unexposed 15 11

OR = 2.2

F2 +Disease

NoDisease

Exposed 6 2Unexposed 15 11

OR = 2.2

F2 -Disease

NoDisease

Exposed 6 2Unexposed 15 11

OR = 2.2

Murray et al. Population Health Metrics 2003

WHO Causal Model of Coronary Heart Disease

Approaches for When More than One Potential Confounder is Present

• Backward vs forward variable selection strategies

– relevant both for stratification and multivariable regression modeling (“model selection”)

• Backwards Strategy

– initially evaluate all potential confounders together (i.e., look for joint confounding)

– preferred because in nature variables act together

– Procedure:

• with all potential confounders considered, form adjusted estimate. This is the “gold standard”

• Of variables on the B list, one variable can then be dropped and the adjusted estimate is re-calculated (adjusted for remaining variables)

• if the dropping of the first variable results in a non-meaningful (eg < 5 or 10%) change compared to the gold standard, it can be eliminated

• continue until no more variables can be dropped (i.e. all remaining variables are relevant)

– Problem:

• With many potential confounders and multiple stratified analyses, p values (too small) & confidence intervals (too narrow) lose their nominal interpretation

– Active area of methodologic interpretation

• With many potential confounders, cells become very sparse and many strata provide no information

Approaches for When More than One Potential Confounder is Present

• Forward Strategy– start with the variable that has the biggest

“change-in-estimate” impact when evaluated individually

– then add the variable with the second biggest impact

– keep this variable if its presence meaningfully changes the adjusted estimate

– procedure continues until no other added variable has an important impact

– Advantage:• avoids the initial sparse cell problem of

backwards approach

– Problem:• does not evaluate joint confounding effects

of many variables • Multiple analyses again lead to problems in

interpreting p values and CI’s

An Analysis Plan

• Available methods often arbitrary and invite fishing for desired answers

• Solution: Analysis plan

• Written before the data are analyzed

• Content– Detailed description of the techniques to be used to

analyze data, step by step– Forms the basis of “Statistical Analysis” section in

manuscripts– Parameters/rules/logic to guide key decisions:

• which variables will be assessed for interaction and for adjustment?

• what p value will be used to guide reporting of interaction?

• what is a meaningful change-in-estimate threshold between two estimates (e.g., 10%) to determine model selection?

• Utility: A plan helps to keep the analysis:– Focused– Transparent– Reproducible– Honest (avoids p value shopping)

Instrumental Variables to Manage Confounding

C1C1 ??

EE

DD

Unmeasured C

Unmeasured C

Instrumental variable (IV)

Instrumental variable (IV)

C2C2

IV must be related to E but nothing else

IV must be related to E but nothing else

Assess association between IV and D to estimate E-D relationship

Assess association between IV and D to estimate E-D relationship

??Length of stayLength of stay

Neonatal outcomes

Neonatal outcomes

Unmeasured C

Unmeasured C

Hour of birthHour of birth

Prenatal complications

Prenatal complications

Malkin et al. Heath Serv. Res., 2000

RQ: Does length of stay determine neonatal outcomes?

RQ: Does length of stay determine neonatal outcomes?

Residual Confounding

Four Mechanisms• Categorization of confounder too broad

– e.g., Association between natural menopause and prevalent CHD

Szklo and Nieto, 2007

Method of age adjustment OR 95% CI Crude 4.54 2.67-7.85 2 categories: 45-54, 55-64 3.35 1.60-6.01 4 categories: 45-49, 50-54, 55-59, and 60-64

3.04 1.37-6.11

Continuous variable 2.47 1.31-4.63

• Misclassification of confounders – Can be differential or non-differential

with respect to exposure and disease– If non-differential, will lead to adjusted

estimates somewhere in between crude and true adjusted

– If differential, can lead to a variety of unpredictable directions of bias

Residual Confounding

Mechanisms – cont’d

• Variable used for adjustment is imperfect surrogate for true confounder

CRP level

CRP level ??

Periodontal disease

Periodontal disease

CADCAD

Inflammatory

Predisposition

Inflammatory

Predisposition

• Unmeasured confounders

AgeAge??

E E

DD

Unmeasured C

Unmeasured C

Quantitative Analysis of Unmeasured Confounding

• Can back calculate to determine how a confounder would need to act in order to spuriously cause any apparent odds ratio. Example: OR= 2.0

Prevalence of “high” level of unmeasured confounder

Association between unmeasured confounder and disease (risk ratio)

Ass

ocia

tion

betw

een

unm

easu

red

conf

ound

er a

nd

expo

sure

(pr

eval

ence

rat

io)

A (low prevalence scenario) = 7 B (high prevalence scenario) = 3.4

Winkelstein et al., AJE 1984

Stratification to Manage Confounding

• Advantages– straightforward to implement and comprehend– easy way to evaluate interaction

• Limitations– Requires continuous variables to be discretized

• loses information; possibly results in “residual confounding”

• Discretizing often brings less precision– Deteriorates with multiple confounders

• e.g., suppose 4 confounders with 3 levels– 3x3x3x3=81 strata needed– unless huge sample, many cells have “0”’s

and strata have undefined effect measures– Solution:

• Mathematical modeling (multivariable regression)– e.g.

» linear regression» logistic regression» proportional hazards regression

Limitation of Conventional Stratification (and Regression)

• RQ: Does coffee use cause CAD?

??

CoffeeCoffee

CADCAD

Cholesterol level

Cholesterol level

Behavioral factors (unmeasured)

Behavioral factors (unmeasured)

• RQ: Does HAART prevent AIDS/Death?

Simultaneous desire to control for cholesterol/CD4 to manage confounding and NOT to control because they are intermediary variables

AIDSAIDS

HAART HAART

CD4 countCD4 count

Severity of HIV (unmeasured)

Severity of HIV (unmeasured)

??

When factors are simultaneously confounders and intermediaries, conventional techniques fail and

“causal methods” are needed

Causal methods: g-estimation, structural nested models, marginal structural models

Cole et al, AJE 2003

Regression is ahead but don’t forget about the simple

techniques …..• “Because of the increased ease and availability of

computer software, the last few years have seen a flourishing of the use of multivariate analysis in the biomedical literature. These highly sophisticated mathematic models, however, rarely eliminate the need to examine carefully the raw data by means of scatter diagrams, simple n x k table, and stratified analyses.” Szklo and Nieto 2007

• “The widespread availability and user-friendly nature of computer software make the method accessible to some data analysts who may not have had adequate instruction in its appropriate applications. When they are misapplied, multivariate techniques have the potential to contribute to incorrect model development, misleading results, and inappropriate interpretation of the effect of hypothesized confounders.”

Friis and Sellers, 2009• “Statistical software is like raising the gas pedal in a

car for a 4 year old.” Peter Bachetti (UCSF), date unknown

• Next Tuesday (12/9/08) – 8:45 to 10:15: Journal Club

– 1:30 to 3:00 pm: Mitch Katz• “Conceptual approach to

multivariable regression”• Note chapters in his textbook

– 3:15 to 4:45: Last Small Group Section• Web-based course evaluation• Bring laptop

– Distribute Final Exam (on line)• Exam due 12/16 in hands of Olivia by

4 pm by email (olivia@epi.ucsf.edu) or China Basin 5700