2Analytical epidemiology Study design: cohorts & case control &cross-sectional studiesChoice of a reference groupBiasesImpactCausal inferenceStratification- Effect modification - ConfoundingMatchingMultivariable analysis
4Cohort study Non cases Risk % Total Cases Exposed 100 50 50 50 % %Not exposed100%Risk ratio % / 10% = 5
5Cases Controls Source population Exposed Sample Unexposed Controls: Sample of the denominatorRepresentative withregard to exposureControls
6Controls are non casesCasesSource popnLow attack rate: non-cases likely to represent exposure in source popNon- casesstartendHigh attack rate: non-cases unlikely to represent exposure in source populationCasesNon- casesstartend
7a/c b/d Case control study Cases Controls Odds ratio a b Exposed OR= (a/c) / (b/d)= ad / bcNot exposedc da+cTotalb+dOdds ofexposurea/cb/d
8Who 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.
9Controls may not be easy to find Usually it is more complicated to find a control than a case in birds and in humans.
10Cross-sectional study: Sampling SampleSamplingPopulationWhen 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
11Cross-sectional study Noncases Prevalence %TotalCasesExposed1,000%Not exposed1,000%Prevalence ratio (PR) % / 10% = 5
12Should I believe my measurement? Exposure OutcomeRR = 4True associationcausalnon-causalChance?Bias?Confounding?
31Effect modificationDifferent effects (RR) in different strata (age groups)VE is modified by ageTest for homogeneity among strata (Woolf test)
32Any statistical test to help us? Breslow-DayWoolf testTest for trends: Chi squareHomogeneity
33How to conduct a stratified analysis? Crude analysisStratified analysisDo stratum-specific estimates look different?95% CI of OR/RR do NOT overlap?Is the Test of Homogeneity significant?NOCheck for confounding(compare crude RR/ORwith MH RR/OR)YESEFFECT MODIFICATION(Report estimates by stratum)
37Death from diarrhea according to breast feeding, Brazil, 1980s Infants < 1 month of ageCases Controls OR (95% CI)No breast feeding (6-203)Breast feeding RefInfants ≥ 1 month of ageCases Controls OR (95% CI)No breast feeding ( )Breast feeding RefWoolf test (test of homogeneity):p=0.03
38Risk of gastroenteritis by exposure, Outbreak X, Place, time X (crude analysis) ExposedExposureYesNoRR†(95% CI‡)nAR (%)*AR(%)*pasta947774.218.0(8.8-38)tuna4968242.9( )* AR = Attack Rate† RR = Risk Ratio‡ 95% CI = 95% confidence interval of the RR
40Risk of gastroenteritis by exposure, Outbreak X, Place, time X (stratified analysis) Pasta YesCases Total AR (%) RR (95% CI)Tuna ( )No tuna RefPasta NoCases Total AR (%) RR (95% CI) Tuna (2.6-46)No tuna RefWoolf test (test of homogeneity): p=0.0007
41Tuna, pasta and gastroenteritis Tuna Pasta Cases AR(%) RRYes YesYes NoNo YesNo No Ref.38 * 12 > * 12 * interaction= 42
42Risk of HIV by injecting drug use (idu), surveillance data, Spain, 1988-2004 Cases Total AR (%) RR (95% CI)Idu , ( )No idu , Ref
44Risk of HIV by injecting drug use (idu), Spain, 1988-2004 (stratified analysis) MalesCases Total AR (%) RR (95% CI)idu (14-28)No idu , RefFemalesCases Total AR (%) RR (95% CI) idu , ( )No idu , RefWoolf test (test of homogeneity): p=
45Idu, gender and hiv Idu Male Cases AR(%) RR Yes Yes 86 12.4 3.0 Yes NoNo YesNo No Ref.0.14 * 2.2 > * 2.2 * interaction= 3.0
56Confounding Exposure Outcome Third variable To be a confounding factor, 2 conditions must be met:ExposureOutcomeThird variableBe associated with exposure- without being the consequence of exposureBe associated with outcome- independently of exposure
57Exposure Outcome Third factor Hypercholesterolaemia Myocardial infarctionThird factorAtheromaAny factor which is a necessary step in the causal chain is not a confounder
66Crude data Malaria Total AR% RR Radio set 80 520 15 0.7 Incidence of malaria according to the presence of a radio set, Kahinbhi PradeshCrude data Malaria Total AR% RRRadio setNo radio RefRR: 0.7; 95% CI: ; p < 0.0295% CI =
69To identify confounding Compare crude measure of effect (RR or OR)toadjusted (weighted) measure of effect(Mantel Haenszel RR or OR)
70Any statistical test to help us? When is ORMH different from crude OR ?%
71Mantel-Haenszel summary measure Adjusted or weighted RR or ORAdvantages of MHZeroes allowedS (ai di) / niOR MH =S (bi ci) / ni
72Mantel-Haenszel summary measure Mantel-Haenszel (adjusted or weighted) ORa1b1c1d1CasesControlsExp+Exp-OR MH =SUM (ai di / ni)SUM (bi ci / ni)n1CasesControls(a1 x d1) / n1 +ORMH =(a2 x d2) / n2Exp+a2b2(b1 x c1) / n1 +(b2 x c2) / n2Exp-d2c2n2
73How to conduct a stratified analysis? Crude analysisStratified analysisDo stratum-specific estimates look different?95% CI of OR/RR do NOT overlap?Is the Test of Homogeneity significant?NOCheck for confounding(compare crude RR/ORwith MH RR/OR)YESEFFECT MODIFICATION(Report estimates by stratum)
74Risk of gastroenteritis by exposure, Outbreak X, Place, time X (crude analysis) ???
77Weighted RR different from crude RR Effect modifierBelongs to natureDifferent effects in different strataSimpleUsefulIncreases knowledge of biological mechanismAllows targeting of PH actionConfounding factorBelongs to studyWeighted RR different from crude RRDistortion of effectCreates confusion in dataPrevent (protocol)Control (analysis)
79How to conduct a stratified analysis Perform crude analysis Measure the strength of associationList potential effect modifiers and confoundersStratify data according to potential modifiers or confoundersCheck for effect modificationIf effect modification present, show the data by stratumIf no effect modification present, check for confounding If confounding, show adjusted data If no confounding, show crude data
80How 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 factorStratum of public health interestFor two risk factors:stratify on one to study the effect of the second on outcomeTwo or more exposure categories:each is a stratumResidual confounding ?
81Logical order of data analysis How to deal with multiple risk factors:Crude analysisMultivariable analysis1. stratified analysis2. modellinglinear regressionlogistic regression
82Multivariate analysis Mathematical modelSimultaneous adjustment of all confounding and risk factorsCan address effect modification
83A train can mask a second train A variable can mask another variable
86Risk factors for Salmonella enteritidis infections, France, 1995 Delarocque-Astagneau et al Epidemiol. Infect 1998:121:561-7
87Cases of Salmonella enteritidis gastroenteritis according to egg storage and season SummerCasesControlsOR(95%CI)Duration of storage>= 2 weeks1227.4( )< 2 weeks5264Other seasons732.6( )3236All seasons1954.5(1.5 – 16.1)84100
89Cases of Salmonella enteritidis gastroenteritis according to egg storage and season Summer(A)“Long” storage(B)CasesControlORYes122ORAB6.8No5264ORA0.973ORB2.63236Ref
90Advantages & Disadvantages of Stratified Analysis straightforward to implement and comprehendeasy way to evaluate interactionDisadvantagesonly one exposure-disease association at a timerequires continuous variables to be groupedLoss of information; possible “residual confounding”deteriorates with multiple confounderse.g. suppose 4 confounders with 3 levels3x3x3x3=81 strata neededunless huge sample, many cells have “0”’ and strata have undefined effect measures