Dr. N. Birkett, Department of Epidemiology & Community Medicine, University of Ottawa

11/2009 1

EPI 5240:Introduction to EpidemiologyConfounding: concepts and general approaches

November 9, 2009

Dr. N. Birkett,Department of Epidemiology & Community

Medicine,University of Ottawa

11/2009 2

• Earlier session introduced confounding• THERE MUST BE THREE VARIABLES!!!• ‘Usual approach’ is based on ‘causation triad’

– Related to exposure– Related to outcome– Not part of the causal pathway

• These criteria aren’t ‘quite’ right• No-one actually uses this approach in real

research• We will introduce new ideas and expand on the

triad.

11/2009 3

Confounding (1) Dementia

Yes No Total

Yes 400 600 1,000

No 100 900 1,000

500 1,000 1,000

Diabetes

Risk in exposed: = 400/1000 = 0.4Risk in Non-exposed = 100/1000 = 0.1

Risk ratio (RR) = 0.4/0.1 = 4.0

CRUDEtable

11/2009 4

Confounding (2)

Dementia Yes No Total

Yes 21 79 100

No 79 821 900

100 900 1,000


Risk ratio (RR) = 0.21/0.088 = 2.39

45-79


Risk ratio (RR) = 0.42/0.21 = 2.01


Yes 379 521 900

No 21 79 100

400 600 1,000

80-99

Best ‘guess’ of RR would be about 2.2, not 4.0!!

11/2009 5

Confounding (3)

• Previous example is confounding– The estimate of the effect of an exposure is

distorted or confounded by a third factor.– We’ll come to ‘why’ in a minute.– Tables in previous slide are called stratified

tables (here, age stratified).

• Let’s consider a new situation based on the same crude table.

11/2009 6

Confounding (4)


Yes 5 95 100

No 95 805 900

100 900 1,000


Risk ratio (RR) = 0.05/0.106 = 0.47

45-79


Risk ratio (RR) = 0.44/0.05 = 8.78


Yes 395 505 900

No 5 95 100

400 600 1,000

80-99

What is best ‘guess’ of RR? It depends on age.There is no single answer!

11/2009 7

Confounding (5)

• Previous example is effect modification– The effect of an exposure on an outcome depends

on the level of a third variable– In this example:

• For people under age 79, it looks like diabetes protects against dementia

• For people over age 80, it looks like diabetes increases the risk of getting dementia,

• No single number or statement is an appropriate summary when this pattern occurs.

– Links statistically to interactions.• Gene-environment interactions are a ‘hot’ topic of study.

11/2009 8

Confounding (5A)

• We’re not going to talk more about effect modification today.

11/2009 9

Confounding (6)

• Why was there confounding?– Numerical/mathematical answer can be given

but let’s talk more conceptually.

• Does heavy alcohol drinking cause mouth cancer?– A case-control study was done which found

an OR of 3.2 (95% CI: 2.1 to 4.9).– Does this prove the case?– Consider the following situations.

11/2009 10

Confounding (7)

Alcohol mouth cancer

• This is what we are trying to prove.

• But, we know that smoking can cause mouth cancer.

• And, people who drink heavily tend, in general, to be heavy smokers.

• So, we might have:

11/2009 11

Confounding (8)

Alcohol mouth cancer???

Smoking

• The association between alcohol and mouth cancer is explained away by the link to smoking.

• Adjusted OR is 1.1 (95% CI: 0.6 to 2.0).

11/2009 12

Confounding (9)

• Confounding requires three or more variables.– Two variables, each with multiple levels,

cannot produce confounding.

• Three requirements for confounding– Confounder relates to outcome– Confounder relates to exposure– Confounder is not part of causal pathway

between exposure and outcome

11/2009 13

Confounding (9A)

• Requirements aren’t this simple

• For case-control study, you need:– Confounder is related to exposure in the

control group (OR≠1.)– Confounder is related to the outcome in the

unexposed group (OR≠1.)

11/2009 14

Confounding (10)

• In our initial dementia example, we have:– OR relating age and dementia in people

without diabetes = 2.8 – OR relating age and diabetes in people

without dementia = 68.5 – There is no suggestion that diabetes causes

dementia because people are getting older.

11/2009 15

Confounding (11)

• In ‘real’ research, these three ‘rules’ are not applied to identify confounding.– Inefficient and prone to false negatives

• Instead, we compute an adjusted RR or OR and compare this to the crude RR or OR [Change of Estimate method].– If these differ enough to ‘matter’, then we say

there is confounding.• Usual guideline is a 10% change.

11/2009 16

Confounding (12) Dementia

Yes No Total

Yes 400 600 1,000

No 100 900 1,000

500 1,000 1,000

Diabetes


Risk ratio (RR) = 0.4/0.1 = 4.0

CRUDEtable

11/2009 17

Confounding (13)


Yes 21 79 100

No 79 821 900

100 900 1,000


Risk ratio (RR) = 0.21/0.088 = 2.39

45-79


Risk ratio (RR) = 0.42/0.21 = 2.01


Yes 379 521 900

No 21 79 100

400 600 1,000

80-99

How to ‘adjust’ the OR?

11/2009 18

Confounding (14)

• How to adjust?– Topic for later class

• Basic idea is that a good ‘guess’ is in the middle between the two strata-specific OR’s

• Take an average BUT weight the average in some way– USE board to explain weighted average.

11/2009 19

Confounding (15)

• Confounding can be complex and controversial– Presence of confounding can depend on analysis

scale• Multiplicative vs. additive

• Works best for simple situations (e.g. only three variables)

• The basic idea is to look for the independent effect of each variable

• BUT, suppose the etiology is more complex?

11/2009 20

Web of Causation sample

11/2009 2113/7/2008 21

Confounding (16)

• How do we deal with confounding?– Prevention

• You need to ‘break’ one of the links between the confounder and the exposure or outcome

– ‘Treatment’ (analysis)• Stratified analysis (like my simple example)• Standardization (we’ll discuss this later)• Regression modeling methods (covered in a

different course )

11/2009 2213/7/2008 22

Confounding (17)

• Prevention– Randomization

• One of the big advantages of an RCT

– Restriction• Limits the subject to one level of confounder (e.g.

study effect of alcohol on mouth cancer ONLY in non-smokers)

– Matching• Ensures that the distribution of the exposure is the

same for all levels of confounder

11/2009 2313/7/2008 23

Confounding (18)

• Randomization– Exposure <=> treatment– Subjects randomly assigned to each treatment

without regard to other factors.– On average, distribution of other factors will be the

same in each treatment group• Implies no confounder/exposure correlation no confounding.

– Issues• Small sample sizes• Chance imbalances• Infeasible in many situations• Stratified allocation

11/2009 2413/7/2008 24

Confounding (19)

• Restriction– Limit the study to people who have the same

level of a potential confounder.• Study alcohol and mouth cancer only in non-

smokers.

– Lack of variability in confounder means it can not ‘confound’

• There is only one 2X2 table in the stratified analysis

– Relatively cheap

11/2009 2513/7/2008 25

Confounding (20)

• Restriction (cont)– ISSUES

• Limits generalizibility• Cannot study effect of confounder on risk• Limited value with multiple potential confounders• Continuous variables?• Can only study risk in one level of confounder

– exposure X confounder interactions can’t be studied

• Impact on sample size and feasibility

– Alternative: do a regular study with stratified analysis• Report separate analyses in each stratum

11/2009 2613/7/2008 26

Confounding (21)

• Matching– The process of making a study group and a

comparison group comparable with respect to some extraneous factor.

• Breaks the confounder/exposure link– Most often used in case-control studies.– Usually can’t match on more than 3-4 factors in one

study• Minimum # of matching groups: 2x2x2x2 = 16

– We’ll talk more about matching on Nov. 30– KEY POINT: in a case control study, matching does

not ‘fix’ confounding – you still have to use stratified analyses.

11/2009 2727

Matching (1)

• Example study (case-control)– Identify 200 cases of mouth cancer from a

local hospital.– As each new case is found, do a preliminary

interview to determine their smoking status.– Identify a non-case who has the same

smoking status as the case

• If there are 150 cases who smoke, there will also be 150 controls who smoke.

11/2009 2828

Matching (1a)

• OR =

• Implies no smoking/outcome link and no confounding

Case Control+ve 150 150-ve 50 50

Outcome status

Smoking

11/2009 2929

Matching (2)

• Two main types of matching– Individual (pair)

• Matches subjects as individuals• Twins• Right/left eye

– Frequency• Ensures that the distribution of the matching

variable in cases and controls is similar but does not match individual people.

11/2009 3030

Matching (3)

• Matching by itself does not fully eliminate confounding in a case-control study!– You must use analytic methods as well

• Matched OR• Stratified analyses• Logistic regression models

• In a cohort study, you don’t have to use these methods although they can help.– But, matching in cohort studies is uncommon

11/2009 3131

Matching (4)

• Advantages– Strengthens statistical analysis, especially

when the number of cases is small.– Increases study credibility for ‘naive’ readers.– Useful when confounder is a complex,

nominal variable (e.g. occupation).• Standard statistical methods can be problematic,

especially if many levels have very few subjects.

11/2009 3232

Matching (5)

• Disadvantages– You can not study the relationship of matched

variable to outcome.– Can be costly and time consuming to find matches,

especially if you have many matching factors.– Often, some important predictors can not be matched

since you have no information on their level in potential controls before doing interview/lab tests

• Genotype• Depression/stress

– If matching factor is not a confounder, can reduce precision and power.

11/2009 3333

Confounding (22)• Analysis options

– Stratified analysis• Divide study into strata based on levels of potential

confounding variable(s).• Do analysis within each strata to give strata-

specific OR or RR.• If the strata-specific values are ‘close’, produce an

adjusted estimate as some type of average of the strata-specific values.

• Many methods of adjustment of available. Mantel-Haenzel is most commonly used.

11/2009 3434

Confounding (23)

• Stratified analysis (cont)– Strata specific OR’s are: 2.3, 2.6, 3.4– A ‘credible’ adjusted estimate should be between 2.3

and 3.4.• Simple average is: 2.8

– Ignores the number of subjects in the strata. If one group has very few subjects, its OR should contribute less information

• Weight by # of subjects in each group, e.g.:

• Mantel-Haenzel does the same thing with different weights

11/2009 3535

Confounding (24)

• Stratified analysis (cont)– This approach limits the number of variables which

can be controlled or adjusted.– Also hard to apply it to continuous confounders– But, gives information about strata-specific effects

and can help identify effect modification.– Used to be very common. Now, no longer widely

used in research with case-control studies.– Stratified analysis methods can be applied to cohort

studies with person-time.

11/2009 3636

Confounding (25)• Analysis options

– Regression modeling• The most common approach to confounding• Can control multiple factors (often 10-20 or more)• Can control for continuous variables• Logistic regression is most popular method for

case-control studies– Discussed in last class

• Cox models (proportional hazard models) are often used in cohort studies.

11/2009 37

Summary: Confounding

• Confounding occurs when a third factor explains away an apparent association

• This is a major problem with epidemiological research– If you measure a confounder, you can adjust

for it in the analysis– Many potential confounders are not measured

in study and so can not be controlled [Unmeasured confounders]

Documents

Dr. N. Birkett, Department of Epidemiology & Community Medicine, University of Ottawa