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

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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

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Cohort studies marching towards outcomes

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

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

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

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

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Who are the right controls?

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Controls may not be easy to find

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Cross-sectional study: Sampling Sample Target Population Sampling Population

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Exposed Not exposed Cases Non cases Prevalence % Cross-sectional study % % Prevalence ratio (PR) 50% / 10% = 5 Total 1,000

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

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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 modification

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Variation in the magnitude of measure of effect across levels of a third variable. Effect modifier 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 ratio To target public health action To study interaction between risk factors

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Effect modification Factor A (asbestos) Disease (lung cancer) Factor B (smoking) Effect modifier = Interaction 19

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

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Asbestos Lung cancer Smoking

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

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Physical activity and MI

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Physical Infarction activity Gender

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

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Vaccine efficacy VE= 1 - RR = VE = 72%

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Vaccine Disease Age

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

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How to conduct a stratified analysis? Crude analysis Stratified analysis 1.Do stratum-specific estimates look different? 2.95% CI of OR/RR do NOT overlap? 3.Is the Test of Homogeneity significant? 33 YES EFFECT MODIFICATION (Report estimates by stratum) NO Check for confounding (compare crude RR/OR with MH RR/OR)

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Stratified analysis: Effect Modification

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

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No breast Diarhoea feeding Age

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Infants < 1 month of age Cases Controls OR (95% CI) No breast feeding (6-203) Breast feeding 7 68 Ref Infants 1 month of age Cases Controls OR (95% CI) No breast feeding ( ) Breast feeding Ref Death from diarrhea according to breast feeding, Brazil, 1980s Woolf test (test of homogeneity):p=0.03

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Exposed Exposure Yes No RR (95% CI ) nAR (%) * n pasta (8.8-38) tuna ( ) RR = Risk Ratio* AR = Attack Rate 95% CI = 95% confidence interval of the RR Risk of gastroenteritis by exposure, Outbreak X, Place, time X (crude analysis)

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Tuna gastroenteritis Pasta

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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= Risk of gastroenteritis by exposure, Outbreak X, Place, time X (stratified analysis)

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Tuna, pasta and gastroenteritis Tuna Pasta Cases AR(%) RR Yes Yes Yes No No Yes No No 3 2 Ref. 38 * 12 > * 12 * interaction= 42

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Risk of HIV by injecting drug use (idu), surveillance data, Spain, Cases Total AR (%)RR (95% CI) Idu 268 2, ( ) No idu , Ref

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idu hiv gender

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Males Cases Total AR (%) RR (95% CI) idu (14-28) No idu 52 8, Ref Females Cases Total AR (%) RR (95% CI) idu 182 2, ( ) No idu , Ref Woolf test (test of homogeneity): p= Risk of HIV by injecting drug use (idu), Spain, (stratified analysis)

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

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Confounding

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

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

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

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51 Grey hair stroke Age

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Birth order Age or mother Down syndrom

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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

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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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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

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Ethnicity Pneumonia Crowding Apparent association

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Crowding Pneumonia Malnutrition Altered strength of association

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

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Are Mercedes more dangerous than Porsches? 95% CI =

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Car type Accidents Confounding factor: Age of driver

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Crude RR = 1.5 Adjusted RR = 1.1 ( )

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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 < % CI =

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Radio Malaria Confounding factor: Mosquito net

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Crude RR = 0.7 Adjusted RR = 1.01

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

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Mantel-Haenszel summary measure Adjusted or weighted RR or OR Advantages of MH Zeroes allowed (a i d i ) / n i OR MH = (b i c i ) / n i

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Mantel-Haenszel summary measure Mantel-Haenszel (adjusted or weighted) OR OR MH = SUM (a i d i / n i ) SUM (b i c i / n i ) n1n1 a1a1 b1b1 c1c1 d1d1 CasesControls Exp+ Exp- b2b2 c2c2 d2d2 CasesControls Exp+ Exp- n2n2 a2a2 (a 1 x d 1 ) / n 1 + OR MH = (a 2 x d 2 ) / n 2 (b 2 x c 2 ) / n 2 (b 1 x c 1 ) / n 1 +

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How to conduct a stratified analysis? Crude analysis Stratified analysis 1.Do stratum-specific estimates look different? 2.95% CI of OR/RR do NOT overlap? 3.Is the Test of Homogeneity significant? 73 YES EFFECT MODIFICATION (Report estimates by stratum) NO Check for confounding (compare crude RR/OR with MH RR/OR)

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

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75 Stratified Analysis > 10-20%

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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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Analyzing a third factor

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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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80 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 ?

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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

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

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

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Back-up slides

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

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87 SummerCasesControls OR (95%CI) Duration of storage >= 2 weeks ( ) < 2 weeks5264 Other seasons Duration of storage >= 2 weeks732.6 ( ) < 2 weeks3236 All seasons >= 2 weeks (1.5 – 16.1) < 2 weeks84100 Cases of Salmonella enteritidis gastroenteritis according to egg storage and season

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88 Duration Salmonellosis of storage Season

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89 Summer (A) Long storage (B) CasesControlOR Yes 122OR AB 6.8 YesNo5264OR A 0.9 NoYes73OR B 2.6 No 3236Ref Cases of Salmonella enteritidis gastroenteritis according to egg storage and season

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90 Advantages & Disadvantages of Stratified Analysis Advantages –straightforward to implement and comprehend –easy way to evaluate interaction Disadvantages –only one exposure-disease association at a time –requires continuous variables to be grouped Loss of information; possible residual confounding –deteriorates with multiple confounders e.g. suppose 4 confounders with 3 levels –3x3x3x3=81 strata needed –unless huge sample, many cells have 0 and strata have undefined effect measures

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