1 confounding and interaction: part ii confounder vs. intermediary variables factors to be...

1

Confounding and Interaction: Part II

Confounder vs. intermediary variables

Factors to be considered as potential confounders in designing a study

Methods to reduce confounding

– during study design:

» Randomization

» Restriction

» Matching

– during study analysis:

» Stratified analysis

Interaction

– What is it? How to detect it?

– Additive vs. multiplicative interaction

– Comparison with confounding

– Statistical testing for interaction

– Implementation in Stata

2

Exercise and CAD

HDL is associated with exercise

HDL is associated with CAD

When evaluating the relationship between exercise and CAD, is HDL a confounder or an intermediary?

ExerciseExercise

CADCAD

HDLHDL

HDLHDL

3

It depends on the pathway under investigation

If interest is in a pathway other than through HDL, then HDL is a confounder

Here, HDL is extraneous to pathway under study

Confounding factors are extraneous factors

ExerciseExercise

CADCAD

not yet specified

mechanism

not yet specified

mechanismHDLHDL ??

4

Exercise and CAD If pathway under study goes thru HDL, then HDL is

an intermediary variable.

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

Hence, classification of HDL as confounder or intermediary depends upon the biological pathway under investigation and the research question

ExerciseExercise

CADCAD

HDLHDLHDL is not a confounder

here

HDL is not a confounder

here

5

What is NOT a Confounder?

Variables that are the RESULT of the disease, regardless of their association with the exposure are NOT confounders

ConfounderConfounder

DD

6

Lung CA

Lung CA

SmokingSmoking

CoughCough??

Cough is not a confounder.

Do not adjust for it!

Cough is not a confounder.

Do not adjust for it!

7

When Planning a Study, Which Factors Should be Considered as

Potential Confounders?

Any factor for which prior evidence indicates it is a confounder

and

In newer research areas:

– factors known to be associated with the disease and which may be associated with exposure

When in doubt, plan on measuring ALL factors associated with the disease

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

8

Seeking cause of high Marin cancer rates Activists canvass residents to search for trendsSunday, November 10, 2002

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, asking people whether they or anyone in their household has ever been diagnosed with cancer in Marin. The volunteers hope to collect enough money to hire an epidemiologist to analyze the data for use in future studies.

9

Preventing or Managing Confounding

ConfounderConfounder

DD

ANOTHER PATHWAY TO

GET TO THE DISEASE

ANOTHER PATHWAY TO

GET TO THE DISEASE

10

Methods to Prevent or Manage Confounding

DD

DD

oror

11

Methods to Prevent or Manage Confounding

By prohibiting at least one “arm” of the exposure- confounder - disease structure, confounding is precluded

12

Randomization to Reduce Confounding

Definition: random assignment of subjects to exposure (e.g., treatment) categories

All subjects Randomize

One of the most important inventions of the 20th Century!

Exposed

Unexposed

13


DD

14


Definition: random assignment of subjects to exposure (or treatment) categories

All subjects Randomize

Applicable only for intervention (experimental) studies

Special strength of randomization is its ability to control the effect of confounding variables about which the investigator is unaware

Does not, however, eliminate confounding!

Exposed

Unexposed

15

Restriction to Reduce Confounding

AKA Specification

Definition: Restrict enrollment to only those subjects who have a specific value/range of the confounding variable

– e.g., when age is confounder: include only subjects of same narrow age range

16


DD

17


Advantages:

– conceptually straightforward

Disadvantages:

– may limit number of eligible subjects

– inefficient to screen subjects, then not enroll

– “residual confounding” may persist if restriction categories not sufficiently narrow (e.g. “decade of age” might be too broad)

– limits generalizability– not possible to evaluate the relationship of

interest at different levels of the restricted variable (i.e. cannot assess interaction)

18

Matching to Reduce Confounding

Definition: only unexposed/non-case subjects are chosen who match those of the reference group (either exposed or cases) in terms of the confounder in question

– Results in the same distribution of the potential confounder as seen in the exposed/cases

19


Mechanics depends upon study design:

– e.g. cohort study: unexposed subjects are “matched” to exposed subjects according to their values for the potential confounder.

» e.g. matching on race

One unexposedblack enrolled for each exposedblack

One unexposedasian enrolled for each exposedasian

– e.g. case-control study: non-diseased controls are “matched” to diseased cases

» e.g. matching on age

One controlage 50 enrolled for each caseage 50

One controlage 70 enrolled for each caseage 70

20


DD

DD

oror

21

Advantages of Matching1. Useful in preventing confounding by factors which

would be difficult to manage in any other way

– e.g. “neighborhood” is a nominal variable with multiple values. (complex nominal variable)

– e.g. Cohort study of the effect of stop light cameras in preventing MVA’s

» Exposed: cars going thru stop lights with camera

» Unexposed: cars going thru stop lights without camera

» Potential confounder: ambient driving practices in the neighborhood

» Relying upon random sampling of unexposed cars without attention to neighborhood may result in (especially in a small study) choosing no unexposed cars from some of the neighborhoods seen in the exposed group

» Even if all neighborhoods seen in the exposed group were represented in the unexposed group, adjusting for neighborhood with “analysis phase” strategies are problematic

22

Advantages of Matching

2. By ensuring a balanced number of cases and controls (in a case-control study) or exposed/unexposed (in a cohort study) within the various strata of the confounding variable, statistical precision is increased

23

Smoking, Matches, and Lung Cancer

Lung Ca No Lung CaMatches 820 340No Matches 180 660

Lung CaNo

Lung CAMatches 810 270No Matches 90 30

900 300

B. Controls matched on smoking

A. Random sample of controls

Crude

Non-SmokersSmokers

OR crude = 8.8

OR CF+ = ORsmokers = 1.0 OR CF- = ORnon-smokers = 1.0

ORadj= 1.0 (0.75 to 1.34)

Lung CaNo


100 700

Stratified

Smokers Non-Smokers

OR CF+ = ORsmokers = 1.0 OR CF- = ORnon-smokers = 1.0

ORadj= 1.0 (0.69 to 1.45)

Lung CaNo


900 900

Lung CaNo


100 100

24

Disadvantages of Matching

1. Finding appropriate matches may be difficult and expensive and limit sample size (e.g., have to throw out a case if cannot find a control). Therefore, the gains in statistical efficiency can be offset by losses in overall efficiency.

2. In a case-control study, factor used to match subjects cannot be itself evaluated as a risk factor for the disease. In general, matching decreases robustness of study to address secondary questions.

3. Decisions are irrevocable - if you happened to match on an intermediary, you likely have lost ability to evaluate role of exposure in question.

4. If potential confounding factor really isn’t a confounder, statistical precision will be worse than no matching.

25

Stratification to Reduce Confounding

Goal: evaluate the relationship between the exposure and outcome in strata homogeneous with respect to potentially confounding variables

Each stratum is a mini-example of restriction!

CF = confounding factor

Disease No DiseaseExposedUnexposed

Crude

Dis NoDis

Exp

Unexp

Dis NoDis

Exp

Unexp

Dis NoDis

Exp

Unexp

Stratified

CF Level I CF Level 3CF Level 2

26



Lung CaNo


Stratified

Crude

Non-SmokersSmokersOR crude

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

ORcrude = 8.8

ORsmokers = 1.0

ORnon-smoker = 1.0

Lung CaNo


27

Stratifying by Multiple Potential Confounders

Potential Confounders: Race and Smoking

To control for multiple confounders simultaneously, must construct mutually exclusive and exhaustive strata:

White Black Latino

Smokers Non-smokers

CrudeCAD No CAD

ChlamydiaNo chlamydia

28

Stratifying by Multiple Potential Confounders

Crude

Stratifiedwhite smokers

latino non-smokers

black non-smokers

CAD NoCAD

Chlamydia

NoChlamydia

white non-smokers

black smokers latino 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

29

Summary Estimate from the Stratified Analyses

Goal: Create an unconfounded (“adjusted”) estimate for the relationship in question

– e.g. relationship between matches and lung cancer after adjustment (controlling) for smoking

Process: Summarize the unconfounded estimates from the two (or more) strata to form a single overall unconfounded “summary estimate”

– e.g. summarize the odds ratios from the smoking stratum and non-smoking stratum into one odds ratio

30



Lung CaNo


Stratified

Crude

Non-SmokersSmokersOR crude

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

ORcrude = 8.8 (7.2, 10.9)

ORsmokers = 1.0 (0.6, 1.5)

ORnon-smoker = 1.0 (0.5, 2.0)

Lung CaNo


31

Smoking, Caffeine Use and Delayed Conception

Delayed Not DelayedSmoking 26 133No Smoking 64 601

DelayedNot

DelayedSmoking 15 61No Smoking 47 528

Stratified

Crude

No Caffeine Use

Heavy Caffeine Use

RR crude = 1.7

RRno caffeine use = 2.4

DelayedNot


RRcaffeine use = 0.7

32

Underlying Assumption When Forming a Summary of the Unconfounded

Stratum-Specific Estimates

If the relationship between the exposure and the outcome varies meaningfully (in a clinical/biologic sense) across strata of a third variable, then it is not appropriate to create a single summary estimate of all of the strata

i.e. the assumption is that no statistical interaction is present

33

Statistical Interaction

Definition

– when the magnitude of a measure of association (between exposure and disease) meaningfully differs according to the value of some third variable

Synonyms

– Effect modification

– Effect-measure modification

– Heterogeneity of effect

Proper terminology

– e.g. Smoking, caffeine use, and delayed conception

» Caffeine use modifies the effect of smoking on the risk ratio for delayed conception.

» There is interaction between caffeine use and smoking in the risk ratio for delayed conception.

» Caffeine is an effect modifier in the relationship between smoking and delayed conception.

34

No Interaction

0.05

0.150.15

0.45

0.01

0.1

1

10

Unexposed Exposed

Ris

k o

f D

ise

as

e

Third Variable Present

Third Variable Absent

Interaction

0.05

0.150.08

0.9

0.01

0.1

1

10

Unexposed Exposed

Ris

k o

f D

ise

as

e



35

Qualitative Interaction

0.180.13

0.08

0.2

0.01

0.1

1

10

Unexposed Exposed

Ris

k o

f D

ise

as

e



36

Interaction is likely everywhere

Susceptibility to infections

– e.g.,

» exposure: sexual activity

» disease: HIV infection

» effect modifier: chemokine receptor phenotype

Susceptibility to non-infectious diseases

– e.g.,

» exposure: smoking

» disease: lung cancer

» effect modifier: genetic susceptibility to smoke

Susceptibility to drugs

» effect modifier: genetic susceptibility to drug

But in practice to date, difficult to document

37

Smoking, Caffeine Use and Delayed Conception:

Additive vs Multiplicative Interaction


DelayedNot


Stratified

Crude

No Caffeine Use

Heavy Caffeine Use

RR crude = 1.7

RD crude = 0.07


RDno caffeine use = 0.12

DelayedNot



RDcaffeine use = -0.06

RD =

Risk Difference = Risk exposed - Risk Unexposed

38


Assessment of whether interaction is present depends upon the measure of association

– ratio measure (multiplicative interaction) or difference measure (additive interaction)

– Hence, the term effect-measure modification

Absence of multiplicative interaction typically implies presence of additive interaction

0.05

0.150.15

0.45

0.01

0.1

1

Unexposed Exposed

Ris

k o

f D

ise

as

e

Additive interaction present

39


Absence of additive interaction typically implies presence of multiplicative interaction

0.05

0.150.150.25

0.01

0.1

1

Unexposed Exposed

Ris

k o

f D

ise

as

e

Multiplicative interaction present

40


Presence of multiplicative interaction may or may not be accompanied by additive interaction

0.1

0.20.2

0.6

0.01

0.1

1

Unexposed Exposed

Ris

k o

f D

ise

as

e

0.1

0.2

0.05

0.15

0.01

0.1

1

Unexposed Exposed

Ris

k o

f D

ise

as

e

Additive interaction present

No additive interaction

41


Presence of additive interaction may or may not be accompanied by multiplicative interaction

0.1

0.20.2

0.6

0.01

0.1

1

Unexposed Exposed

Ris

k o

f D

ise

as

e

0.1

0.3

0.05

0.15

0.01

0.1

1

Unexposed Exposed

Ris

k o

f D

ise

as

e Multiplicative interaction absent

Multiplicative interaction present

42


Presence of qualitative multiplicative interaction is always accompanied by qualitative additive interaction

Qualitative Interaction

0.18

0.13

0.08

0.2

0.01

0.1

1

Unexposed Exposed

Ris

k o

f D

ise

as

e



43

Additive vs Multiplicative Scales

Additive measures (e.g., risk difference):

– readily translated into impact of an exposure (or intervention) in terms of number of outcomes prevented

» e.g. 1/risk difference = no. needed to treat to prevent (or avert) one case of disease

or no. of exposed persons one needs to take the exposure away from to avert one case of disease

– gives “public health impact” of the exposure

Multiplicative measures (e.g., risk ratio)

– favored measure when looking for causal association

44

Additive vs Multiplicative Scales

Causally related but minor public health importance

– RR = 2

– RD = 0.0001 - 0.00005 = 0.00005

– Need to eliminate exposure in 20,000 persons to avert one case of disease

Causally related but major public health importance

– RR = 2

– RD = 0.2 - 0.1 = 0.1

– Need to eliminate exposure in 10 persons to avert one case of disease

Disease No DiseaseExposed 10 99990Unexposed 5 99995

Disease No DiseaseExposed 20 80Unexposed 10 90

45

Smoking, Family History and Cancer:


Cancer No CancerSmoking 50 150No Smoking 25 175

CancerNo

CancerSmoking 10 90No Smoking 5 95

Stratified

Crude

Family History Absent

Family History Present

RRno family history = 2.0

RDno family history = 0.05

CancerNo

CancerSmoking 40 60No Smoking 20 80

RRfamily history = 2.0

RDfamily history = 0.20

• No multiplicative interaction but presence of additive interaction

• If goal is to define sub-groups of persons to target:

- Rather than ignoring, it is worth reporting that only 5 persons with a family history have to be prevented from smoking to avert one case of cancer

46

Confounding vs Interaction

Confounding

– An extraneous or nuisance pathway that an investigator hopes to prevent or rule out

Interaction

– A more detailed description of the “true” relationship between the exposure and disease

– A richer description of the biologic system

– A finding to be reported, not a bias to be eliminated

47

When Assessing the Association Between an Exposure and a Disease,

What are the Possible Effects of a Third Variable?

EM+

_Confounding:

ANOTHER PATHWAY TO

GET TO THE DISEASE

Confounding:

ANOTHER PATHWAY TO

GET TO THE DISEASE

Effect Modifier (Interaction):

MODIFIES THE EFFECT OF THE EXPOSURE

D

I C Intermediary

Variable

No Effect

48

Smoking, Caffeine Use and Delayed Conception


DelayedNot


Stratified

Crude

No Caffeine Use

Heavy Caffeine Use

RR crude = 1.7


DelayedNot



RR adjusted = 1.4 (95% CI= 0.9 to 2.1)

Here, adjustment is contraindicated!

49

Chance as a Cause of Interaction?

Down’s No Down’sSpermicide Use 4 109No Spermicide 12 1145

Down’sNo

Down’sSpermicide 3 104No Spermicide 9 1059

Stratified

Crude

Age > 35Age < 35

OR crude = 3.5

ORage >35 = 5.7

Down’sNo

Down’sSpermicide 1 5No Spermicide 3 86

ORage <35 = 3.4

50

Statistical Tests of Interaction: Test of Homogeneity (heterogeneity)

Null hypothesis: The individual stratum-specific estimates of the measure of association differ only by random variation

– i.e., the strength of association is homogeneous across all strata

– i.e., there is no interaction

A variety of formal tests are available with the general format, following a chi-square distribution:

where:

– effecti = stratum-specific measure of assoc.

– var(effecti) = variance of stratum-specifc m.o.a.

– summary effect = summary adjusted effect

– N = no. of strata of third variable

For ratio measures of effect, e.g., OR, log transformations are used:

The test statistic will have a chi-square distribution with degrees of freedom of one less than the number of strata

i i

iN effect

effectsummaryeffectsquarechi

)var(

) ( 2

1

51

Interpreting Tests of Homogeneity

If the test of homogeneity is “significant”, this is evidence that there is heterogeneity (i.e. no homogeneity)

– i.e., interaction may be present

The choice of a significance level (e.g. p < 0.05) is somewhat controversial.

– There are inherent limitations in the power of the test of homogeneity

» p < 0.05 is likely too conservative

– One approach is to declare interaction for p < 0.20

» i.e., err on the side of assuming that interaction is present (and reporting the stratified estimates of effect) rather than on reporting a uniform estimate that may not be true across strata.

52

Tests of Homogeneity with Stata

1. Determine crude measure of association

e.g. for a cohort study

“cs outcome-variable exposure-variable”

for smoking, caffeine, delayed conception:

-exposure variable = smoking

-outcome variable = delayed

-third variable = caffeine

“cs delayed smoking”

2. Determine stratum-specific estimates by levels of third variable

“cs outcome-var exposure-var, by(third-variable)”

e.g. cs delayed smoking, by(caffeine)

54

Declare vs Ignore Interaction?

Relative Risks for aGiven Exposure and

Disease

Potential Effect ModifierPresent Absent

P value forheterogeneity

Declare orIgnore

Interaction

2.3 2.6 0.45 Ignore

2.3 2.6 0.001 Ignore

2.0 20.0 0.001 Declare

2.0 20.0 0.20 Declare

2.0 20.0 0.30 +/-

3.0 4.5 0.30 Ignore

3.0 4.5 0.001 +/-

0.5 3.0 0.001 Declare

0.5 3.0 0.20 Declare

0.5 3.0 0.30 +/-

1 confounding and interaction: part ii confounder vs. intermediary variables factors to be...

Documents

exercise hdl

exercise cad hdl slide

disease slide

confounding confounder

confounding d d d d

exposure confounder

study confounding factors

classification of hdl