intermediate methods in observational epidemiology 2008 confounding - ii

Intermediate methods in observational epidemiology

2008

Confounding - II

2110750022110500Total

4030752510040065+

18774251010100<65

Mort. (%)

No. dths

Pop. Mort.

(%)No. dths

Pop. Age

Age as a confounding variable

Unexposed Exposed

2110750022110500Total

4030752510040065+

18774251010100<65

Mort. (%)

No. dths

Pop. Mort.

(%)No. dths

Pop. Age


AgeDifferent distributions between the groups

Unexposed Exposed

2110750022110500Total

4030752510040065+

18774251010100<65

Mort. (%)

No. dths

Pop. Mort.

(%)No. dths

Pop. Age


AgeDifferent distributions between the groups

ANDAssociated with mort. (older ages have >mort.)

Unexposed Exposed

2110750022110500Total

4030752510040065+

18774251010100<65

Mort. (%)

No. dths

NMort.

(%)No. dths

N Age


Relative RiskUNADJUSTED= 21% / 22%= 0.95

Unexposed Exposed

Direct Adjustment

• Create a standard population

Standard P

opulation O

ptions

1) Easiest: Sum the number of personsin each stratum

1000500500Total

4757540065+

525425100<65

StandPopExposedUnexp.

Groups

Age

2110750022110500Total

4030752510040065+

18774251010100<65

Mort (%)

No. dths

N Mort (%)

No. dths

N

ExposedUnexposed

Age

144500500Total

[400 x 75]/[400 + 75]= 637540065+

[100 x 425]/[100 + 425]= 81

425100<65

Stand. Pop. (minimum variance)

ExposedUnexp

Groups

Age

Standard Population Options2. Minimum Variance Method: Useful when the sample sizes are small

(variance of adjusted rates is minimized): Wi= [nAi x nBi] / [nAi + nBi]

2110750022110500Total

4030752510040065+

18774251010100<65

Mort (%)

No. dths

N Mort (%)

No. dths

N

ExposedUnexposed

Age


• Replace each population with the standard population.

• Calculate the expected number of events in each age group, using the true age-specific rates and the standard population for each age group.

Direct Adjustment

500500Total

40752540065+

1842510100<65

Mort. (%)

Pop. Mort.

(%)Pop. Age


Unexposed Exposed

144144Total

4063256365+

18811081<65

Mort. (%)

Std pop

Mort.

(%)Std pop

Age


Unexposed Exposed

• Create a standard population • Replace each population with the standard

population.

• Calculate the expected number of events in each age category, using the true age-specific rates and the standard population for each age group.

Direct Adjustment

144144Total

4063 x .40= 25632563 x .25= 166365+

1881 x .18= 15811081 x .10= 881<65

Mort. (%)

Expected No. of deaths

Std pop

Mort. (%)


Std pop

ExposedUnexposed

Age


2110750022110500Total

4030752510040065+

18774251010100<65

Mort (%)

No. dths

N Mort (%)

No. dths

N

ExposedUnexposed

Age


• Replace each group with the standard population

• Calculate the expected number of events in each age group, using the true age-specific rates and the standard population for each age group

• Sum up the total number of events in each age category for each group, and divide by the total standard population to calculate the age-adjusted rates

Direct Adjustment

4014424144Total

4063 x .40= 25632563 x .25= 166365+

1881 x .18= 15811081 x .10= 881<65

Mort. (%)


Std pop

Mort. (%)


Std pop

ExposedUnexposed

Age


Age-Adjusted Mortality Rates Unexposed: [24 / 144] x 100= 16.7%

Exposed: [40 / 144] x 100= 27.8%

Relative Risk= 27.8% / 16.7%= 1.7

Example of direct adjustment when the outcome is continuous

No additive interaction

Example of Calculation of Sunburn Score-Adjusted Mean Number of New Nevi in Each Group

Sunscreen Group Control Group

Sunburn score

Standard Weights

(1)*

Mean No. of New Nevi (2)

Calculation

(2) × (1)

Mean No. of New Nevi

(3)

Calculation

(3) × (1)

Low 230 20 20 × 230=

4 600

50 50 × 230=

11 500

High 228 60 60 × 228=

13 680

90 90 × 228=

20 520

total 458 4 600 + 13 680= 18 280

11 500 + 20 520= 32 020

Sunburn-adjusted

score means

18 280/458= 39.9 32 020/458= 69.9

*Sum of the two groups’ sample sizesDifference

- Crude= 8.5- Adjusted= 30.0

(Szklo M. Arch Dermatol 2000;136:1544-6)

Assumptions when adjusting

• Rates are uniform within each stratum (for example, age category--- i.e, age-specific rates are the same for all ages included in each age category, e.g., 25-29 years). – If assumption not true: residual confounding

• There is a uniform difference (absolute or relative) in the age-specific rates between the groups under comparison. – If assumption not true: interaction

Breast Cancer Incidence Rates, USA, SEER, 1973-77

White women Black Women

AGE Pop’n

(in 1000)

% of total

pop’n

Rate (per

100,000)

Pop’n (in

1000)

% of total

pop’n

Rate (per

100,000) 20-29 7,210 26 4.4 955 32 5.7 30-39 5,268 19 38.9 639 21 49.8 40-49 4,786 17 141.5 527 17 121.4 50-59 4,831 17 212.1 452 15 174.9 60-69 3,543 13 267.5 305 10 209.8 70-79 2,299 8 320.2 148 5 264.2 Total 27,937 100 3,026 100 Crude Rate 129.7 93.7

Age-Adjusted Rate*

108.5 93.7

(*Using Black Women as the Standard Population)

W < B

Breast Cancer Incidence Rates, USA, SEER, 1973-77

White women Black Women

AGEPop’n

(in 1000)

% oftotal

pop’n

Rate(per

100,000)

Pop’n(in

1000)

% oftotal

pop’n

Rate(per

100,000)20-29 7,210 26 4.4 955 32 5.730-39 5,268 19 38.9 639 21 49.840-49 4,786 17 141.5 527 17 121.450-59 4,831 17 212.1 452 15 174.960-69 3,543 13 267.5 305 10 209.870-79 2,299 8 320.2 148 5 264.2Total 27,937 100 3,026 100Crude Rate 129.7 93.7Age-AdjustedRate*

108.5 93.7

(*Using Black Women as the Standard Population) W > B

40

WW

BW

Age (years)

Bre

ast

Can

cer

Inci

denc

e R

ates

Interaction between age and ethnic background

“cross-over”

Adjustment and Interaction

Age A B

N Rate (%)

N Rate (%)

ARexp

RR

<50 100 20 200 10 10% 2.00

50+ 200 50 100 40 10% 1.25

• ARs are the same, butRR’s are different

Multiplicative interaction

When ABSOLUTE differences (ATTRIBUTABLE RISKS IN EXPOSED) are homogeneous, adjusted ARexp is the

same regardless of standard population

Age A B N Rate

(%) N Rate

(%)

ARexp

RR <50 100 20 200 10 10% 2.00 50+ 200 50 100 40 10% 1.25

Standard Populations Age Older Younger Minimum

variance <50 200 1800 66.7 50+ 1800 200 66.7

A B A B A B Adj. Rate 47% 37% 23% 13% 35% 25%

ARexp 10% 10% 10% RR 1.3 1.8 1.4

Adjustment and Interaction

Age A B

N Rate (%)

N Rate (%)

ARexp

RR

<50 100 6 200 3 3% 2.0

50+ 200 30 100 16 15% 2.0

• RRs are the same, butARexp’s are different

Additive interaction

When RELATIVE RISKS are homogeneous, adjusted RR is the same, regardless of standard population

Standard Populations Age Older Younger Minimum

variance <50 200 1800 66.7 50+ 1800 200 66.7

A B A B A B Adj. Rate 27.6% 13.8% 8.4% 4.2% 18% 9%

ARexp 13.8% 4.2% 9.0% RR 2.0 2.0 2.0

Age A B N Rate

(%) N Rate

(%)

ARexp

RR <50 100 6 200 3 3% 2.0 50+ 200 30 100 16 15% 2.0

Mantel-Haenszel Formula for Calculation of Adjusted Odds Ratios

Exposure Cases Controls

Yes ai bi

No ci di

Ni

O R

a dN

b cN

M Hi

i i

i

i i

ii

=

a d

b c

b c

Nb c

N

O R w

w

i i

i i

i i

ii

i i

ii

ii

i

ii

=

b cb c

a dN

b cN

i i

i i

i i

ii

i i

ii

Thus, the ORMHis a weighted average of stratum-specific ORs(ORi), with weights equal to each stratum’s:

wb cNii i

i

CHD No CHD

Post-menopausal 118 3 606 ORPOOLED = 4.5

Pre-menopausal 17 2 361

Stratum 1 Post 3 141 OR1= 2.5

Ages 45-49 Pre 10 1 428

1 612


Ages 50-54 Pre 6 757

1 461

Stratum 3 Post 37 1 408 OR3= 4.0

Ages 55-59 Pre 1 153

1 599

Stratum 4 Post 64 1 343 OR4= 1.2*

Ages 60-64 Pre 0 23

1 430

CHD No CHD

Post-menopausal 118 3 606 ORPOOLED = 4.5

Pre-menopausal 17 2 361

*1.0 was added to each cell

Variable to be adjusted for in

the outside stubMain

varia

ble

of in

tere

st in

the

inside

stub


Ages 45-49 Pre 10 1 428

1 612


Ages 50-54 Pre 6 757

1 461


Ages 55-59 Pre 1 153

1 599

Stratum 4 Post 64 1 343 OR4= 1.2*

Ages 60-64 Pre 0 23

1 430*1.0 was added to each cell


Ages 45-49 Pre 10 1 428

1 612


Ages 50-54 Pre 6 757

1 461


Ages 55-59 Pre 1 153

1 599

Stratum 4 Post 64 1 343 OR4= 1.2*

Ages 60-64 Pre 0 23

1 430

O R M H

3 1 4 2 81 6 1 2

1 4 7 5 71 4 6 1

3 7 1 5 31 5 9 9

6 4 2 31 4 3 0

1 7 1 1 01 6 1 2

6 8 4 61 4 6 1

1 4 0 8 11 5 9 9

1 3 4 3 01 4 3 0

3 0 4.



Ages 45-49 Pre 10 1 428

1 612


Ages 50-54 Pre 6 757

1 461


Ages 55-59 Pre 1 153

1 599

Stratum 4 Post 64 1 343 OR4= 1.2*

Ages 60-64 Pre 0 23

1 430

O R M H

3 1 4 2 81 6 1 2

1 4 7 5 71 4 6 1

3 7 1 5 31 5 9 9

6 4 2 31 4 3 0

1 7 1 1 01 6 1 2

6 8 4 61 4 6 1

1 4 0 8 11 5 9 9

1 3 4 3 01 4 3 0

3 0 4.

ORMZ = Weighted average= 3.04

Is this weighted average

representative of the OR in this stratum?



Ages 45-49 Pre 10 1 428

1 612


Ages 50-54 Pre 6 757

1 461


Ages 55-59 Pre 1 153

1 599

Report the OR separately for age group 60-64

Stratum 4 Post 64 1 343 OR4= 1.2*

Ages 60-64 Pre 0 23

1 430

Calculate the MH-adjusted OR for these 3 (relatively) homogeneous age groups and…

O R M H

3 1 4 2 8

1 6 1 2

1 4 7 5 7

1 4 6 1

3 7 1 5 3

1 5 9 91 7 1 1 0

1 6 1 2

6 8 4 6

1 4 6 1

1 4 0 8 1

1 5 9 9

2 8 3.


Men Cases Controls

Exposed 20 5 OR= 4.75

Unexposed 80 95

100 100 200

Women

Exposed 10 25 OR= 0.33

Unexposed 90 75

100 100 200

O R M H

2 0 9 5

2 0 0

1 0 7 5

2 0 08 0 5

2 0 0

9 0 2 5

2 0 0

1 0.

Does an ORMH= 1.0 properly characterize the relationship of the exposure to the disease in this study population? NO

A MORE DRAMATIC EXAMPLE

Stratification Methods

• Advantages

– Easy to understand and compute

– Allow simultaneous assessment of interaction

• Disadvantages

– Cannot handle a large number of variables

– Each calculation requires a rearrangement of tables

Main Variable of Interest: Menopausal Status

Age Menopausal?

Cases Contls

45-49 Pre

Post

50-54 Pre

Post

55-59 Pre

Post

60-64 Pre

Post

Main Variable of Interest: Age

Menopausal? Age Cases Contls

Pre 45-49

50-54

55-59

60-64

Post 45-49

50-54

55-59

60-64

Types of confounding

• Positive confoundingWhen the confounding effect results in an overestimation

of the magnitude of the association (i.e., the crude OR estimate is further away from 1.0 than it would be if confounding were not present).

• Negative confoundingWhen the confounding effect results in an

underestimation of the magnitude of the association (i.e., the crude OR estimate is closer to 1.0 than it would be if confounding were not present).

10.1 10

Odds Ratio

3.0

2.0

0.40.3

3.00.7

0.40.7

Type of confounding:Positive Negative

3.0TRUE, UNCONFOUNDED

5.0OBSERVED, CRUDE

x

x

x

x

x ? QUALITATIVE CONFOUNDING

1/3.3=1/2.5=

Confounding is not an “all or none” phenomenon

A confounding variable may explain the whole or just part of the observed association between a given exposure and a given outcome.

• Crude OR=3.0 … Adjusted OR=1.0• Crude OR=3.0 … Adjusted OR=2.0

The confounding variable may reflect a “constellation” of variables/characteristics

– E.g., Occupation (SES, physical activity, exposure to environmental risk factors)

– Healthy life style (diet, physical activity)

Directions of the Associations of the Confounder with the Exposure and the Disease, and Expectation of Change of Estimate with Adjustment (Assume a Direct Relationship Between the Exposure and the Disease,

i.e., Odds Ratio > 1.0 (in Case-Based Control Studies), or Relative Risk > 1.0 (in Case-Cohort Studies)

Association of Exposure with Confounder is

Association of Confounder with Disease is

Type of confounding

Expectation of Change from Unadjusted to Adjusted OR

Direct* Direct* Positive# Unadjusted > Adjusted

Direct* Inverse** Negative## Unadjusted < Adjusted

Inverse** Direct* Positive# Unadjusted > Adjusted

Inverse** Inverse** Negative## Unadjusted < Adjusted

*Direct association: presence of the confounder is related to an increased odds of the exposure or the disease**Inverse association: presence of the confounder is related to a decreased odds of the exposure or the disease#Positive confounding: when the confounding effect results in an unadjusted odds ratio further away from the null hypothesis than the adjusted estimate##Negative confounding” when the confounding effect results in an unadjusted odds ratio closer to the null hypothesis than the adjusted estimate

CONFOUNDING EFFECT IN CASE-CONTROL STUDIES

(Szklo M & Nieto FJ, Epidemiology: Beyond the Basics, Jones & Bartlett, 2nd Edition, 2007, p. 176)

Residual confounding

Controlling for one of several confounding variables does not guarantee that confounding be completely removed.

Residual confounding may be present when:

- The variable that is controlled for is an imperfect surrogate of the true confounder,

- Other confounders are ignored,

- The units of the variable used for adjustment/stratification are too broad

- The confounding variable is misclassified

Residual Confounding: Relationship Between Natural Menopause and

Prevalent CHD (prevalent cases v. normal controls), ARIC Study, Ages 45-64 Years,

1987-89Model Odds Ratio (95% CI)

1 Crude 4.54 (2.67, 7.85)

2 Adjusted for age: 45-54 Vs. 55+ (Mantel-Haenszel)

3.35 (1.60, 6.01)

3 Adjusted for age:

45-49, 50-54, 55-59, 60-64 (Mantel-Haenszel)

3.04 (1.37, 6.11)

4 Adjusted for age: continuous (logistic regression)

2.47 (1.31, 4.63)

CONTROLLING FOR CONFOUNDING WITHOUT ADJUSTMENT

Men: Years of Age Women: Years of Age

30-49 50-62 30-49 50-62

Serum Cholesterol

(mg/dL) Incidence Rates per 1,000 Individuals

< 190 38.2 105.7 11.1 155.2

190-219 44.1 187.5 9.1 88.9

220-249 95.0 201.1 24.3 96.3

250+ 157.5 267.8 50.4 121.5

(Truett et al, J Chronic Dis 1967;20:511)


30-49 50-62 30-49 50-62

Serum Cholesterol


< 190 38.2 105.7 11.1 155.2

190-219 44.1 187.5 9.1 88.9

220-249 95.0 201.1 24.3 96.3

250+ 157.5 267.8 50.4 121.5


How to control (“adjust”) with no calculations?- Examine the effect of varying one variable, holding all

other variables “constant” (fixed).

Relationship Between Serum Cholesterol Levels and Risk of Coronary Heart Disease by Age and Sex, Framingham Study, 12-year Follow-up


30-49 50-62 30-49 50-62

Serum Cholesterol


< 190 38.2 105.7 11.1 155.2

190-219 44.1 187.5 9.1 88.9

220-249 95.0 201.1 24.3 96.3

250+ 157.5 267.8 50.4 121.5


Examine the effect of varying one variable, holding allother variables “constant” (fixed). Example: effect of sex,

holding serum cholesterol and age constant


30-49 50-62 30-49 50-62

Serum Cholesterol


< 190 38.2 105.7 11.1 155.2

190-219 44.1 187.5 9.1 88.9

220-249 95.0 201.1 24.3 96.3

250+ 157.5 267.8 50.4 121.5


Examine the effect of varying one variable, holding allother variables “constant” (fixed). Example: effect of

serum cholesterol, holding sex and age constant


30-49 50-62 30-49 50-62

Serum Cholesterol


< 190 38.2 105.7 11.1 155.2

190-219 44.1 187.5 9.1 88.9

220-249 95.0 201.1 24.3 96.3

250+ 157.5 267.8 50.4 121.5


Examine the effect of varying one variable, holding allother variables “constant” (fixed). Example: effect of age,

holding sex and serum cholesterol constant.

intermediate methods in observational epidemiology 2008 confounding - ii

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