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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 but useful 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 = RR

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Vaccine efficacy VE = RR = 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 No Ref. Total

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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 6 * 5 4 3 * 2 * * 1 * 10 20 30 40 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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Simpson’s 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 Exposure Outcome Third variable**

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 =

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Crude RR = 1.5 Adjusted RR = 1.1 ( )

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Car type Accidents Confounding factor: Age of driver

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Age Porsches Mercedes < 25 years 550 (55%) 300 (30%) >= 25 years Chi2 = 127.9 Age Accidents No accidents < 25 years 370 (44%) 480 >= 25 years 130 (11%) 1020 Chi2 = 270.7

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**Exposure Outcome Third factor**

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 ? %

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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 OR MH = k SUM (ai di / ni) i=1 SUM (bi cci / ni)

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

k SUM (ai di / ni) i=1 SUM (bi cci / ni)

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**Examples of stratified analysis**

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**Weighted RR different from crude RR**

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 analysis Measure the strength of association List potential effect modifiers and confounders Stratify data according to potential modifiers or confounders Check for effect modification If effect modification present, show the data by stratum If no effect modification present, check for confounding If confounding, show adjusted data If 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 % Fitting Colour**

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

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