Analytical epidemiology

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Analytical epidemiology

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

• Stratification
• - Effect modification - Confounding
• Matching
• Significance testing
• Multivariable analysis

Alain Moren, 2006
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Exposure Outcome
Third variable
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Two main complications

• (1) Effect modifier
• (2) Confounding factor

- useful information - bias
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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


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Effect modifier
Variation in the magnitude of measure of effect
across levels of a third variable. Effect
modification is not a bias butuseful information
Happens when RR or OR is different between
strata (subgroups of population)
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Effect modifier

• To identify a subgroup with a lower or higher
  risk
• To target public health action
• To study interaction between risk factors

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Vaccine efficacy
AR NV
-

AR V
VE
-----------------------------

AR NV
VE 1 - RR
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Vaccine efficacy
VE 1 - RR 1 - 0.28 VE 72
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Vaccine efficacy by age group
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Effect modification

• Different effects (RR) in different strata (age
  groups)
• VE is modified by age
• Test for homogeneity among strata (Woolf test)

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Oral contraceptives (OC) and myocardial
infarction (MI)
Case-control study, unstratified data
OC MI Controls OR Yes 693
320 4.8 No 307 680 Ref. Total 1000
1000
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Physical activity and MI
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Effect function
Effect (OR or RR) is a function of the effect
modifier
Relative risk (RR) of dying from coronary heart
disease for smoking physicians, by age groups,
England Wales,
RR
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5
4
3

2


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40
30
20
10
50
60
70
80
Age
Doll et Hill, 1966
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Any statistical test to help us?

• Breslow-Day
• Woolf test
• Test for trends Chi square

Heterogeneity
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Confounding

• Distortion of measure of effect because of a
  third factor
• Should be prevented
• Needs to be controlled for

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Simpsons paradox
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Second table
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Day 2, one table only
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Birth order
Down syndrom
Age or mother
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Confounding
To be a confounding factor, 2 conditions must be
met
Exposure
Outcome
Third variable
Be associated with exposure - without
being the consequence of exposure
Be associated with outcome -
independently of exposure
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To identify confounding

• Compare crude measure of effect (RR or OR)
• to
• adjusted (weighted) measure of effect
• (Mantel Haenszel RR or OR)

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Are Mercedes more dangerous than Porsches?
95 CI 1.3 - 1.8
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Crude RR 1.5 Adjusted RR 1.1 (0.94 - 1.27)
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Car type
Accidents
Confounding factor Age of driver
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Age Porsches Mercedes lt 25 years 550 (55) 3
00 (30) gt 25 years 450 700 Chi2 127.9
Age Accidents No accidents lt 25 years 370
(44) 480 gt 25 years 130
(11) 1020 Chi2 270.7
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Exposure
Outcome Hypercholesterolaemia
Myocardial infarction
Third factor Atheroma
Any factor which is a necessary step in the
causal chain is not a confounder
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Salt
Myocardial
infarction
Hypertension
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Any statistical test to help us?

• When is ORMH different from crude OR ?

10 - 20
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How to prevent/control confounding?

• Prevention
• Restriction to one stratum
• Matching
• Control
• Stratified analysis
• Multivariable analysis

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Mantel-Haenszel summary measure

• Adjusted or weighted RR or OR
• Advantages of MH
• Zeroes allowed

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Examples of stratified analysis
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• Effect modifier
• Belongs to nature
• Different effects in different strata
• Simple
• Useful
• Increases knowledge of biological mechanism
• Allows targeting of PH action
• Confounding factor
• Belongs to study
• Weighted RR different from crude RR
• Distortion of effect
• Creates confusion in data
• Prevent (protocol)
• Control (analysis)

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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

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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 ?

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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

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A train can mask a second train
A variable can mask another variable
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What happened?
Hat Colour
Fitting
Blue and red hats not evenly distributed between
the 2 tables - table I, 33 blue - table
II, 66 blue
Hat fitting higher in Table I (83) vs table
II (13)
Tables