Analytical epidemiology

Disease frequency Study design: cohorts & case control Choice of a reference group Biases Impact Causal inference

Alain Moren, 2006

Stratification- Effect modification - Confounding

Matching Significance testing Multivariable analysis

Exposure Outcome

Third variable

Two main complications

(1) Effect modifier

(2) Confounding factor

- useful information

- bias

To analyse effect modification

To eliminate confounding

Solution = stratification stratified analysis

Create strata according to categories inside the range of values taken by third variable

Variation in the magnitude of measure of effect across levels of a third variable.

Effect modification is not a bias butuseful information

Effect modifier

Happens when RR or OR is different between strata (subgroups of population)

Effect modifier

• To identify a subgroup with a lower or higher risk

• To target public health action

• To study interaction between risk factors

AR NV - AR VVE = -----------------------------

AR NV

VE = 1 - RR

Vaccine efficacy

Vaccine efficacy

Status Pop. Cases Cases

per 1000 RR

V 301 545 150 0.49 0.28

NV 298 655 515 1.72 Ref.

Total 600 200 665 1.11

VE = 1 - RR = 1 - 0.28

VE = 72%

Vaccine efficacy by age group

Effect modification

Different effects (RR) in different strata (age groups)

VE is modified by age

Test for homogeneity among strata (Woolf test)

Oral contraceptives (OC) and myocardial infarction (MI)

Case-control study, unstratified data

OC MI Controls OR

Yes 693 320 4.8No 307 680 Ref.

Total 1000 1000

Physical activity and MI

*

*

*

**

40 50 60 70 80

1

2

3

4

5

6

Relative risk (RR) of dying from coronary heart disease for smoking physicians, by age groups, England & Wales,

RR

AgeDoll et Hill, 1966

302010

Effect (OR or RR) is a function of the effect modifier

Effect function

Any statistical test to help us?

• Breslow-Day

• Woolf test

• Test for trends: Chi square

Heterogeneity

Confounding

Distortion of measure of effect because of a third factor

Should be prevented

Needs to be controlled for

Simpson’s paradox

Hats Fit Do not fit % fit

Red 17 3 85%

Blue 9 1 90%

Hats Fit Do not fit % fit

Red 1 9 10%

Blue 3 17 15%

Second table

Hats Fit Do not fit % fit

Red 18 12 60%

Blue 12 18 40%

Day 2, one table only

Cases of Down syndroms by birth order

0

20

40

60

80

100

120

140

160

180

1 2 3 4 5

Birth order

Cases per 100 000 live births

Cases of Down Syndrom by age groups

0100200300400500600700800900

1000

< 20 20-24 25-29 30-34 35-39 40+

Age groups

Cases per 100000 live

births

Birthorder

Age ormother

Downsyndrom

0100200300400500600700800900

1000

Cases per 100000

1 2 3 4 5

Birth order

Cases of Down syndrom by birth order and mother's age

Confounding

Exposure Outcome

Third variable

To be a confounding factor, 2 conditions must be met:

Be associated with exposure - without being the consequence of exposure

Be associated with outcome - independently of exposure

To identify confounding

Compare crude measure of effect (RR or OR)

to

adjusted (weighted) measure of effect (Mantel Haenszel RR or OR)

Are Mercedes more dangerous than Porsches?

Type Total Accidents AR % RR

Porsche 1 000 300 30 1.5

Mercedes 1 000 200 20 Ref.

Total 2 000 500 25

95% CI = 1.3 - 1.8

Crude RR = 1.5Adjusted RR = 1.1 (0.94 - 1.27)

Car type Accidents

Confounding factor:Age of driver

Age Porsches Mercedes

< 25 years 550 (55%) 300 (30%)

>= 25 years 450 700

Chi2 = 127.9

Age Accidents No accidents< 25 years 370 (44%) 480

>= 25 years 130 (11%) 1020

Chi2 = 270.7

Exposure OutcomeHypercholesterolaemia Myocardial infarction

Third factorAtheroma

Any factor which is a necessary step in the causal chain is not a confounder

Salt Myocardial infarction

Hypertension

10 - 20 %

Any statistical test to help us?

When is ORMH different from crude OR ?

How to prevent/control confounding?

Prevention– Restriction to one stratum– Matching

Control– Stratified analysis– Multivariable analysis

Mantel-Haenszel summary measure

Adjusted or weighted RR or OR

Advantages of MH

• Zeroes allowed

OR MH = -------------------

kSUM (ai di / ni)

i=1

kSUM (bi cci / ni)

i=1

OR MH = -------------------

kSUM (ai di / ni)

i=1

kSUM (bi cci / ni)

i=1

Examples of stratified analysis

Effect modifierBelongs to natureDifferent effects in different strataSimpleUsefulIncreases knowledge of biological mechanismAllows targeting of PH action

Confounding factorBelongs to study

Weighted RR different from crude RRDistortion of effectCreates confusion in dataPrevent (protocol)

Control (analysis)

How to conduct a stratified analysis

Perform crude analysisMeasure the strength of association

List potential effect modifiers and confounders

Stratify data according topotential modifiers or confounders

Check for effect modification

If effect modification present, show the data by stratum

If no effect modification present, check for confoundingIf confounding, show adjusted dataIf no confounding, show crude data

How to define strata

In each stratum, third variable is no longer a confounder

Stratum of public health interest

If 2 risk factors, we stratify on the different levels of one of them to study the second

Residual confounding ?

Logical order of data analysis

How to deal with multiple risk factors:

Crude analysis

Multivariate analysis

1. stratified analysis

2. modelling

linear regression

logistic regression

A train can mask a second train

A variable can mask another variable

What happened?

Tables

% FittingHatColour

Hat fitting higher in Table I (83%) vs table II (13%)

Blue and red hats not evenly distributed between the 2 tables - table I, 33 % blue - table II, 66 % blue