# Effect Modification & Confounding

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Effect Modification & Confounding
Kostas Danis EPIET Introductory course, Menorca 2012 Lecture notes

Analytical epidemiology
Study design: cohorts & case control & cross-sectional studies Choice of a reference group Biases Impact Causal inference Stratification - Effect modification - Confounding Matching Multivariable analysis

Cohort studies marching towards outcomes

Cohort study Non cases Risk % Total Cases Exposed 100 50 50 50 %
% Not exposed 100 % Risk ratio % / 10% = 5

Cases Controls Source population Exposed Sample Unexposed Controls:
Sample of the denominator Representative with regard to exposure Controls

Controls are non cases Cases Source popn Low attack rate: non-cases likely to represent exposure in source pop Non- cases start end High attack rate: non-cases unlikely to represent exposure in source population Cases Non- cases start end

a/c b/d Case control study Cases Controls Odds ratio a b Exposed
OR= (a/c) / (b/d) = ad / bc Not exposed c d a+c Total b+d Odds of exposure a/c b/d

Who are the right controls?
If we are able of defining the population source of our cases, we still have to decide which one we will choose as a control.

Controls may not be easy to find
Usually it is more complicated to find a control than a case in birds and in humans.

Cross-sectional study: Sampling
Sample Sampling Population When we want to take a sample we first need to define our target population. The target population is the population about which you want information, that you wish to make conclusions about from the results of the study. The study or sampling population is the population from which the sample (sampling frame) is drawn (the population from which you select your sample). It may be a more limited, an accessible population. For example, suppose you want to estimate the prevalence of flu-like symptoms in a country and you conduct telephone interviews; Your target population will be the total population in the country and the study population will be all people with telephones. Or if you want to estimate the vaccination coverage among 6 year old children in Spain and you take a sample of school children; your target population is all 6 year olds in Spain, whereas your sampling population is all first Grammar class school children. Target Population

Cross-sectional study
Non cases Prevalence % Total Cases Exposed 1,000 % Not exposed 1,000 % Prevalence ratio (PR) % / 10% = 5

Should I believe my measurement?
Exposure Outcome RR = 4 True association causal non-causal Chance? Bias? Confounding?

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

Effect modification

Effect modifier Variation in the magnitude of measure of effect across levels of a third variable. Happens when RR or OR is different between strata (subgroups of population)

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

Effect modification Disease Factor A (lung cancer) (asbestos) Factor B
(smoking) Effect modifier = Interaction

Asbestos (As) and lung cancer (Ca)
Case-control study, unstratified data As Ca Controls OR Yes No Ref. Total

Asbestos Lung cancer Smoking

Asbestos (As), smoking and lung cancer (Ca)
As Smoking Cases Controls OR Yes Yes Yes No No Yes No No Ref. 1.5 * 3.0 < * 3.0 * interaction=8.9

Physical activity and MI

Physical Infarction activity
Gender

Vaccine efficacy ARU – ARV VE = ARU VE = 1 – RR

Vaccine efficacy VE = RR = VE = 72%

Vaccine Disease Age

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)

Any statistical test to help us?
Breslow-Day Woolf test Test for trends: Chi square Homogeneity

How to conduct a stratified analysis?
Crude analysis Stratified analysis Do stratum-specific estimates look different? 95% CI of OR/RR do NOT overlap? Is the Test of Homogeneity significant? NO Check for confounding (compare crude RR/OR with MH RR/OR) YES EFFECT MODIFICATION (Report estimates by stratum)

Stratified analysis: Effect Modification

Death from diarrhea according to breast feeding, Brazil, 1980s (Crude analysis)
Diarrhea Controls OR (95% CI) No breast feeding ( ) Breast feeding Ref

No breast Diarhoea feeding Age

Death from diarrhea according to breast feeding, Brazil, 1980s
Infants < 1 month of age Cases Controls OR (95% CI) No breast feeding (6-203) Breast feeding Ref Infants ≥ 1 month of age Cases Controls OR (95% CI) No breast feeding ( ) Breast feeding Ref Woolf test (test of homogeneity):p=0.03

Risk of gastroenteritis by exposure, Outbreak X, Place, time X (crude analysis)
Exposed Exposure Yes No RR† (95% CI‡) n AR (%)* AR(%)* pasta 94 77 7 4.2 18.0 (8.8-38) tuna 49 68 24 2.9 ( ) * AR = Attack Rate † RR = Risk Ratio ‡ 95% CI = 95% confidence interval of the RR

Tuna gastroenteritis Pasta

Risk of gastroenteritis by exposure, Outbreak X, Place, time X (stratified analysis)
Pasta Yes Cases Total AR (%) RR (95% CI) Tuna ( ) No tuna Ref Pasta No Cases Total AR (%) RR (95% CI) Tuna (2.6-46) No tuna Ref Woolf test (test of homogeneity): p=0.0007

Tuna, pasta and gastroenteritis
Tuna Pasta Cases AR(%) RR Yes Yes Yes No No Yes No No Ref. 38 * 12 > * 12 * interaction= 42

Risk of HIV by injecting drug use (idu), surveillance data, Spain, 1988-2004
Cases Total AR (%) RR (95% CI) Idu , ( ) No idu , Ref

idu hiv gender

Risk of HIV by injecting drug use (idu), Spain, 1988-2004 (stratified analysis)
Males Cases Total AR (%) RR (95% CI) idu (14-28) No idu , Ref Females Cases Total AR (%) RR (95% CI) idu , ( ) No idu , Ref Woolf test (test of homogeneity): p=

Idu, gender and hiv Idu Male Cases AR(%) RR Yes Yes 86 12.4 3.0
Yes No No Yes No No Ref. 0.14 * 2.2 > * 2.2 * interaction= 3.0

Confounding

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

Confounding Skate- boarding Chlamydia Age
Age not evenly distributed between the 2 exposure groups - skate-boarders, 90% young - Non skate-boarders, 20% young

Exposure Outcome (coffee) (Lung cancer) Third variable (smoking)

Grey hair stroke Age

Birth order Down syndrom Age or mother

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

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

Salt Myocardial infarction
Hypertension

The nuisance introduced by confounding factors
May simulate an association May hide an association that does exist May alter the strength of the association Increased Decreased Confounding factor

Apparent association Ethnicity Pneumonia Crowding

Altered strength of association
Crowding Pneumonia Malnutrition

How to prevent/control confounding?
Prevention Randomization (experiment) Restriction to one stratum Matching Control Stratified analysis Multivariable analysis

Are Mercedes more dangerous than Porsches?
95% CI =

Car type Accidents Confounding factor: Age of driver

Crude RR = 1.5 Adjusted RR = 1.1 ( )

Crude data Malaria Total AR% RR Radio set 80 520 15 0.7
Incidence of malaria according to the presence of a radio set, Kahinbhi Pradesh Crude data Malaria Total AR% RR Radio set No radio Ref RR: 0.7; 95% CI: ; p < 0.02 95% CI =

Radio Malaria Confounding factor: Mosquito net

Crude RR = 0.7 Adjusted RR = 1.01

To identify confounding
Compare crude measure of effect (RR or OR) to adjusted (weighted) measure of effect (Mantel Haenszel RR or OR)

Any statistical test to help us?
When is ORMH different from crude OR ? %

Mantel-Haenszel summary measure
Adjusted or weighted RR or OR Advantages of MH Zeroes allowed S (ai di) / ni OR MH = S (bi ci) / ni

Mantel-Haenszel summary measure
Mantel-Haenszel (adjusted or weighted) OR a1 b1 c1 d1 Cases Controls Exp+ Exp- OR MH = SUM (ai di / ni) SUM (bi ci / ni) n1 Cases Controls (a1 x d1) / n1 + ORMH = (a2 x d2) / n2 Exp+ a2 b2 (b1 x c1) / n1 + (b2 x c2) / n2 Exp- d2 c2 n2

How to conduct a stratified analysis?
Crude analysis Stratified analysis Do stratum-specific estimates look different? 95% CI of OR/RR do NOT overlap? Is the Test of Homogeneity significant? NO Check for confounding (compare crude RR/OR with MH RR/OR) YES EFFECT MODIFICATION (Report estimates by stratum)

Risk of gastroenteritis by exposure, Outbreak X, Place, time X (crude analysis)
???

Stratified Analysis > 10-20%

Examples of stratified analysis

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)

Analyzing a third factor

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

How to define the strata?
Strata defined according to third variable: ‘Usual’ confounders (e.g. age, sex, socio-economic status) Any other suspected confounder, effect modifier or additional risk factor Stratum of public health interest For two risk factors: stratify on one to study the effect of the second on outcome Two or more exposure categories: each is a stratum Residual confounding ?

Logical order of data analysis
How to deal with multiple risk factors: Crude analysis Multivariable analysis 1. stratified analysis 2. modelling linear regression logistic regression

Multivariate analysis
Mathematical model Simultaneous adjustment of all confounding and risk factors Can address effect modification

A train can mask a second train
A variable can mask another variable

Back-up slides

Risk factors for Salmonella enteritidis infections, France, 1995
Delarocque-Astagneau et al Epidemiol. Infect 1998:121:561-7

Cases of Salmonella enteritidis gastroenteritis according to egg storage and season
Summer Cases Controls OR (95%CI) Duration of storage >= 2 weeks 12 2 7.4 ( ) < 2 weeks 52 64 Other seasons 7 3 2.6 ( ) 32 36 All seasons 19 5 4.5 (1.5 – 16.1) 84 100

Duration Salmonellosis
of storage Season

Cases of Salmonella enteritidis gastroenteritis according to egg storage and season
Summer (A) “Long” storage (B) Cases Control OR Yes 12 2 ORAB 6.8 No 52 64 ORA 0.9 7 3 ORB 2.6 32 36 Ref