31/7/20091 Summer Course: Introduction to Epidemiology August 21, 0900-1030 Confounding: control, standardization Dr. N. Birkett, Department of Epidemiology.

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Summer Course:Introduction to Epidemiology

August 21, 0900-1030Confounding: control, standardization

Dr. N. Birkett,Department of Epidemiology &

Community Medicine,University of Ottawa

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Session Overview

• Review methods used to control, prevent or deal with confounding

• Review matching methods

• Present standardization methods both direct and indirect (SMR).

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Confounding (1)• Consider a case-control study relating

alcohol intake to mouth cancer risk.– Crude OR = 3.2 (95% CI: 2.1 to 4.9)– Stratify the data by smoking status

(ever/never):• Ever: OR = 1.2 (95% CI: 0.5 to 2.9)• Never: OR = 1.2 (95% CI: 0.5 to 2.9)

– Best estimate of the ‘true’ OR is 1.2• Adjusted OR (more complex methods used in the

‘real world’).

– This is CONFOUNDING.

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Confounding (2)

Alcohol mouth cancer

Alcohol mouth cancer???

Smoking

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Confounding (3)

• Confounding requires three or more variables.– Two variables 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

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Confounding (4)

• Confounding is a very serious problem in epidemiological research

• Potential confounders are often unknown– OR for leukemia in children living near high

power hydro lines is about 1.3– BUT, could be explained by unknown

confounders (e.g. pesticide application to grass under hydro towers).

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Confounding (5)

• 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 )

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Confounding (6)

• 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

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Confounding (7)

• 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

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Confounding (8)

• 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

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Confounding (9)

• 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

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Confounding (10)

• 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

– Let’s talk more about matching

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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.

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Matching (1a)

• OR =

• Implies no smoking/outcome link and no confounding

Case Control+ve 150 150-ve 50 50

Outcome status

Smoking

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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.

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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

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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.

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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.

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Matching (6)

• Individual matching– My personal view: this method is over-used and

misrepresented• In many apparent cases of individual matching, that isn’t

what is going on.

– Most useful when there is a strong ‘natural’ pairing.• Twins• Body parts

– Analysis uses McNemar method to estimate OR (and to do a chi-square test).

• Unit of analysis is the pair.

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Matching (7)

• 625 pairs of subjects– 201 pairs where both case and control were exposed– 80 pairs where only case was exposed– 43 pairs where only control was exposed– 201 pairs where neither case or control were exposed

+ve - ve+ve 201 80-ve 43 302

Control member

CaseMember

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Matching (8)

• If exposure causes disease, there should be more pairs with only the case exposed then pairs with only the control exposed.

• McNemar OR = 80/43 = 1.86• Ignoring matching would give OR=1.28

• Chi-square =

+ve - ve+ve 201 80-ve 43 302

Control member

CaseMember

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Matching (9)

• McNemar OR = b/c• ‘a’ and ‘d’ pairs contribute no information on OR

(wasteful of interviews).• Make sure table is set-up correctly!!• More sophisticated analysis uses conditional

logistic regression modeling (another course).

+ve - ve+ve a b-ve c d

Control member

CaseMember

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Matching (10)• Frequency matching

– Most commonly used method– Many ways to implement this. Here’s one:

• Case-control study of prostate cancer.• Cases will include all new cases in Ottawa in one

year.– Based on cancer registry data, we know what the age

distribution of cases will be.

• Controls selected at random from the population.• We use the projected distribution of age in the

cases to describe how many controls we need in each age group.

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Matching (11)

• 400 cases & 400 conts• 5% of cases are under

age 60• I want 5% of my

controls to be under 60– 400 * 0.05 = 20

• Similar for other age groups

26065%>70

400400#

12030%60-70

205%<60

ContCase

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Matching (12)

• Frequency matching (cont)– Do you distribute the control recruitment through-out

the case recruitment period?– Analysis must stratify by matching groups or strata– Having too many matching groups is a problem– How do I find the matching controls?

• Only 4% of the population is age 75-84 but about 30% of my cases are in this group. How do I efficiently over-sample this age group?

• Lack of control selection lists in Canada– Mandates use of Random Digit Dialing (RDD) methods.

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Confounding (11)• 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.

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Confounding (12)

• 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 estimate is less ‘valuable’.

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

• Mantel-Haenzel does the same thing with different weights

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Confounding (13)

• 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. This is still commonly used

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Confounding (14)• Analysis options

– Regression modeling• Beyond the scope of this course• 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• Cox models (proportional hazard models) are often

used in cohort studies.

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Standardization (1)

• Crude prostate cancer incidence rates (fictional):– Canada (2000): 100/100,000– Canada (1940): 50/100,000

• Does this mean that prostate cancer is twice as common in 2000 (RR = 2.0)?– Yes, the rate is twice as high– BUT: answer is too simplistic if it is taken to

mean that people in 2000 are at higher risk of developing prostate cancer.

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Standardization (2)

• Concern is that the population in Canada is older in 2000 than in 1950. Also, prostate cancer incidence increases with age.

• Sound familiar?

Age

Calendartime

Prostatecancer

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Standardization (3)

• Changes in the age distribution of the Canadian population could confound any change in incidence over time.– Will make it appear that the population is at higher

risk when it really isn’t

• This is really a type of confounding.– For historical reasons, this issue is usually taught as a

separate topic, often before confounding is introduced.

• Approached through direct standardization or age adjustment.

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Standardization (4)

• Remember stratified analysis?– Divide the sample into strata– Within each stratum, compute the OR/RR/etc– Produce an average of the strata-specific

estimates to adjust for the confounder.

• Roughly, the same process is used for direct standardization.

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Standardization (5)

Direct Standardization• Select a reference population (can be anything)• Compute age-specific incidence in each study

group.• Multiply the age-specific incidence by the # of

people in the reference population in that age stratum ‘expected’ number of cases

• Add up the ‘expected’ number and divide by the total size of the reference population.

Age-adjusted rate for the study group.• Let’s look at an example

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Standardization (6)

# cases Pop size Incidence

Area ‘A’ 380 16,000 0.0238

Area ‘B’ 825 16,000 0.0516RR = 2.35

Mean age: Area A = 49.7 yrsArea B = 63.4 yrs

Standardization (7)

Age group

cases pop incid cases Pop incid

35-50 100 10000 0.01 15 2000 0.0075

50-65 80 4000 0.02 60 4000 0.015

>65 200 2000 0.10 750 10000 0.075

380 16000 825 16000

Area A Area B

RR in each age stratum (B vs A) = 0.75 not 2.35

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Standardization (8)

• Why the difference?– Area ‘A’ is a lot younger than area ‘B’.– Incidence increases with age. confounding by age.

• Direct standardization

• First, select reference population– We will take combined population of area ‘A’

and area ‘B’.

Standardization (9)

1110148032000

9000.07512000.1012000>65

1200.0151600.02800050-65

900.00751200.011200035-50

exprateexprateRef Pop

Age group

Area A Area B

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Standardization (10)

Ref pop Exp Exp

32000 1480 1100

Area A Area B

Area A adjusted incidence = 1480/32000 = 0.0463Area B adjusted incidence = 1100/32000 = 0.0347

The adjusted RR (area B to A) = 0.75

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Standardization (11)

• Adjustment has rendered the rates comparable by eliminating the confounding due to age.

• There are more complex ways of doing this but this approach gives the basic ideas.

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Standardization (11)

• Does it always work? – If the rate is higher in one area for younger

age groups but lower for higher ones, adjustment can give a misleading picture.

• Do NOT treat adjusted rates as ‘real’ rates.– To estimate the burden of illness, you must

use unadjusted rates.

• What if the group has very few events?– SMR & indirect standardization.

NO!!

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Standardization (12)

Indirect Standardization• Used when the study group has few cases so

the age-specific rates will be unstable (subject to wide chance variation).

• Does not produce adjusted estimates.• Is used to compare study population to rates

expected based on a large general population or reference population.

• Rate taken from reference pop (unlike direct standardization).

• Main statistic produced is the SMR (standardized mortality rate)

Standardization (13)

3876

204020000.01> 65

81640000.00250-65

1020100000.00135-50

Exp events

Obs events

# peopleRef rateAge group

SMR = # obs cases/# exp cases= 76/38= 2.0 (or 200)

Standardization (14)

Indirect Standardization (cont)

• SMR does not depend on the number of observed events in each age stratum. That is why it is useful when the number of cases is small.

• Interpret an SMR similar to an RR or OR:– < 1.0 protection– 1.0 null value (no effect)– > 1.0 increased risk

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Summary

• Confounding is a very common problem

• Try to prevent it through:– Restriction– Matching

• Use statistical methods to adjust for it:– Stratified analysis– Matched analysis– Regression modeling