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Stratification: Confounding , Effect modification

Stratification: Confounding , Effect modification. Third training Module EpiSouth Madrid, 15 th to 19 th June, 2009 Dr D. Hannoun National Institute of Public Health Algeria. Introduction: Generality.

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Stratification: Confounding , Effect modification

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  1. Stratification: Confounding, Effect modification Third training Module EpiSouth Madrid, 15th to 19th June, 2009 Dr D. Hannoun National Institute of Public Health Algeria

  2. Introduction: Generality Aims of analytical studies in epidemiology is to assess the association between two variables • Is the association valid ?  RD – RR – OR … • is it causal ?  Criterion of causality In most case, we have to take in account a third (or more) variable that may affect the relationship studied • Confounding  bias +++ • Effect modification (Interaction)  useful information +++:

  3. Introduction: Generality Exposure Outcome Vaccin efficacy Measle Third variable • No effect: sexe (boy/girl) • Intermediary v.: Antibodies rate • Confounder: Mother education • Effect modifier: Age VE is the same for boy and girl AR is a consequence of Vaccin Effect observed is affected by ME VE is lower for children < 18 months

  4. Introduction: Generality To avoid these complications we have many possibilities at essentially two steps : • Step one in the study design • Randomisation • Restriction • matching • Step two in the analytical phase • Standardization • Stratification +++ • Multivariate analysis

  5. Stratification: Principle Principle : • Create strata according to categories of the third variable • Perfom analysis inside these strata • Conclude about the studied relation inside the strata • Forming «adjusted summary estimate»: concept of weighted average • Assumption: weak variability in the strata Stratification : • To analyse effect modification • To eliminate confounding

  6. Stratification: Principle To perform a stratified analysis, we have 6 steps : • Carry out simple analysis to test the association between the exposure and the disease and to Identify potential confounder • Categorize the confounder and divide the sample in strata, according to the number of categories of the confounder • Carry out simple analysis to test the association between the exposure and the disease in each stratum • Test the presence or absence of effect modification between the variables • If appropriate, check for confounding and calculate a point estimate of overall effect (weighted average measure) • If appropriate, carry out and interpret an overall test for association

  7. Stratification: Step 1 – Example 1 Example 1 : Investigation of the relationship between Vaccin Efficacy and Measle (cohorte study) • Crude analysis: Is there any association between vaccin efficacy and prevention of Measle ? • RR = 0,55 [0,41-0,74] ; p < 10-5  VE = 1-RR = 45% • There is an association between VE and Non occurrence of Measle

  8. Stratification: Step 1 – Example 1 Example 1 : Investigation of the relationship between Vaccin Efficacy and Measle (cohorte study) • Identify potentiel confounder : • Is the association real and valid or could be modify when we take in account a third factor : what about age ? • We were interested in how the effects of a third variable, age at vaccination, may be influencing this relationship

  9. Stratification: Step 2 – Example 1 Categorize the confounder and divide the sample in strata, according to the number of categories of the confounder Example 1: • Number of categories of age : <1 year and 1-4 years • Create strata according to the number of categories

  10. Stratification: Step 3 – Example 1 Perfom analysis inside these strata • In each strate • Calculate the X2 to test the association • Estimate the RRi/ORi RRi = 0,87 [0,54 - 1,40] - VE= 13% p = 0,55 RRi = 0,42 [0,28 - 0,62] – VE= 58% p < 10-8

  11. Stratification: Step 4 – Example 1 Test the presence or absence of interaction between the variables • Appropriate tests • Mantel-Haenszel test +++: the most commonly used • Woolf test • Breslow Day • Tarone … Spss tests

  12. Stratification: Step 4 – Example 1 Test the presence or absence of interaction between the variables • Breslow-Day: Test of homogeneity in strata : • H0 : RR1 = RR2 Or OR1 = OR1 • =Χ2 test compared observed and expected counts • It requires a large sample size within each stratum

  13. Stratification: Step 4 – Example 1 Test the presence or absence of interaction between the variables Two possibilities RR1=RR2orOR1=OR2 RR1RR2orOR1OR2 No Interaction: Third variable isNotan effect modifier Presence of Interaction: Third variable could beeffect modifier Next step:Looking for confoundingTrying to form adjusted measure Stop here:Results only by strate No pooling measure

  14. Stratification: Step 4 – Example 1 Test the presence or absence of interaction … Example 1: Homogeneity test: H0: RR<1year= RR1-4years (RR population) • P < 10-4 statistical interaction +++ • There is interaction between age at vaccination and VE on the risk for Measle • Age at vaccination modifies the effect of VE on the risk for Measle • Age at vaccination is an effect modifier for the relationship between VE and Measle • Not be appropriateto try to summarize these two effects,0,87and 0,42, into one overall number • We should report the two stratum-specific estimatesseparatelyandstop herethe analysis 0,87 ≠ 0,42 ????

  15. Stratification: Step 1 – Example 2 Example 2 : Investigation of Effectiveness of AZT in preventing HIV seroconversion after a needlestick (case control study) • Crude analysis: Is there any association between AZT and prevention of HIV seroconversion after a needlestick in health care workers ? • ORcrude = 0,61 [0,26-1,44] ; p = 0,25 • No evidence of a benefit from AZT • the authors stratified by the severity of the needlestick

  16. Stratification: Steps 2 and 3 – Example 2 Divide the sample in strata, according to the number of categories of the confounder and perfom analysis inside … • Categories of severity of needlestick : minor and major severity • Create strata according to the number of categories • In each stratetest the association and Estimate the RDi/RRi/ORi • ORminor = 0,60 [0.06-5,81] – p = 1 • No association • ORmajor = 0,31 [0,11- 0,84] – p =0,02 • Presence of association

  17. Stratification: Step 4 – Example 2 Test the presence or absence of interaction between the variables • Test of homogeneity in strata : H0 : ORminor = ORmajor ? • p = 0,59  Breslow-Day test is not significant  No statistical interaction  Paradoxal result ? • We assume there is no effect modification between severity of needlestick and AZT on the risk of HIV • We could try to summarize these two effects, 0,60 and 0.31, into one overall number  Constructa weighted average estimate • Go to step 5

  18. Stratification: Step 5 – Example 2 If appropriate, check for confounding • Two steps • Forming adjusted summary estimate • Compare adjusted summary estimate to crude estimate

  19. Stratification: Step 5 – Example 2 If appropriate, check for confounding • Forming an adjusted summary estimate • It is the first step to assess the presence of confounding • Properties: • Summary measure • = weigthed average measureof the effect of exposure: RDi - RRi - ORi … according to the size of each stratum • Weight depends upon a lot of factors: • measure of association: RD – RR – OR… • nature of data: qualitative, quantitative • purpose of the analysis: follow-up study, case control study… • Methods: • Mantel-Haenszel+++ • Woolf, Miettinen RR/OR

  20. Stratification: Step 5 – Example 2 If appropriate, check for confounding • Estimation of RRa : Follow up study

  21. Stratification: Step 5 – Example 2 If appropriate, check for confounding • Estimation of ORa : Case control study ORMH =  ai di bi ci nini ORMH =  wiORi/ wiAvec wi = bi ci / ni

  22. Stratification: Step 5 – Example 2 If appropriate, check for confounding • Identify confounding • Compare the crude measure of effect to Adjusted measure of effect: • H0 : RRMH = RRcrude or ORMH = ORcrude • No statistical testto help us • Confounding can be judged present when adjusted RRMH or ORMHisdifferent from crude effect •  = (ORMH - ORcrude ) / ORcrude • Arbitrary cut-off: >15-20 % or >20-30 % • Interpretation

  23. Stratification: Step 5 – Example 2 If appropriate, check for confounding Two possibilities  <15-20 %  >15-20 % Noconfounding Presence of confounding UseRRcrudeorORcrude To measure the relation UseRRMHorORMH To measure the relation

  24. Stratification: Step 5 – Example 2 If appropriate, check for confounding Be careful! We should report the adjusted measure: Only if we haven’t detected interaction: RRi or ORi are homogenous among strata And if we have detected confounding

  25. Stratification: Step 5 – Example 2 Example 2: Effectiveness of AZT in preventing HIV seroconversion after a needlestick in health care workers • Estimation of ORa adjusted ni = 255 ; OR = 0,60 ni = 92 ; OR = 0,31 • ORMH = 0,34 [0,14 – 0,87]

  26. Stratification: Step 5 – Example 2 Example 2: Effectiveness of AZT in preventing HIV seroconversion after a needlestick in health… • Identify confounding • Compare the ORMH = 0,34 With ORcrude = 0,61 •  = (ORMH - ORcrude ) / ORcrude = 44 % •  > 15-20 %  We conclude that severity of needlestick is a confounder • After adjusting for severity of needlestick, we obtain a reduction of the magnitude of the relation between AZT and prevention of the HIV seroconversion • Conclusion : The good summarymeasure to use is theadjusted ORMH= 0,34

  27. Stratification: Step 6 – Example 2 If appropriate, carry out and interpret an overall test for association • Verify the relationship between the exposure and the outcome after adjusting on a third variable • H0 : RRMH = 1 or ORMH = 1 • Statistical test  Mantel-Haenszel • it follows a chi-square distribution of 1 ddl, regardless of the number of strata • Intervalle estimates of of RRa or ORa adjusted

  28. Stratification: Step 6 – Example 2 Example 2: Effectiveness of AZT in preventing HIV seroconversion after a needlestick in health care workers • Verify the relationship between the AZT and the HIV seroconversion after adjusting on the severity of needlestick • H0 : ORMH = 1 • p = 0,036  Mantel-Haenszel test is significant • Conclusion: • After adjustement for severity of needlestick, we havean associationbetweenAZT and HIV • When we have adjusted for severity of needlestick theOR decreasedfrom 0,61 to 0,34 butbecame significant

  29. Confounding: Definition = Stratum specific-estimates are  from the crude estimate = Distortion of measure effect because of a thirdfactor • Due to differencesin the distribution of an extraneous factor in the exposedand unexposed group Example: • Individuals who are vaccinated tend to be healthier than individuals who are not vaccinated  Overestimationof the vaccin efficacy 74,7% Influenza Vaccine in elderly subjects ARIdeath Healthstatus: 58%

  30. Confounding: Definition Be careful! • Confounding is a concept • Factor responsible for confounding is called a confounder or a confounding variable • Confounder factor confounds the association of interest: It confounds an estimate Examples: • Health status confonds the estimation of vaccine efficacy on ARI death • Needlestickconfonds the estimation of AZT in preventing HIV seroconversion

  31. Confounding: Definition When we have confounding: • The observed association between exposure and disease can be attributed totally or in part to the effect of confounder • Overestimation of the true association between exposure and disease occurs: • Underestimation of the true association between exposure and disease occurs: • Direction of observed effect could change Crude effect > Adjusted Effect Crude effect < Adjusted Effect

  32. Confounding: Criteria To be a confounding factor, The variable must be: • Associated with the outcomeindependently of exposure= risk factorfor the disease evenin the absence of exposure • e.g. needlestick is asociated with the risk of HIV independently of exposure (prescription of AZT) Exposure:AZT Outcome:HIV Confounder:Severity of needlestick In cohortstudy In case control study • ORCD/Ē 1 • ORCD/Ē 1

  33. Confounding: Criteria To be a confounding factor, The variable must be: • Associated with the exposure in the study population without being the consequence of exposure= Different distribution of the third variable in the exposed and unexposed group • occurrence of needlestick is associated with the prescription of AZT • Individuals with minor needlestich have lower probability to take AZT Exposure:AZT Outcome:HIV In case control study In cohortstudy Confounder:Severity of needlestick • ORCE/Ḋ 1 • ORCE 1

  34. Confounding: Criteria To be a confounding factor, The variable must be: • Not an intermediate linkin the causal pathway between the exposure and the disease Confounder:Severity of needlestick Exposure:AZT Outcome:HIV

  35. Confounding: Criteria To be a confounder, the variable must be presented the three criteria Exposure:AZT Outcome:HIV Confounder:Severity of needlestick

  36. Confounding : How to identifyconfounder Compare : Crude effect of measure association : RD - RR-OR To adjusted measure of effect : RDA - RRMH - ORMH How ? Take in account only  = (ORMH - ORcrude ) / ORcrude If  > 15-20 %  Presence of confounding If  < 15-20 %  No confounding Statistical test must be avoided to identify confounding

  37. Effect modification = Variation in the magnitude of measure of effect across levels of a third variable • Tetracycline discolours teeth in children but not in adults Tetracyclines Age: children/adults Vocabulary: • Effect modification is a concept, also called effect measure modification, interaction or heterogeneity of effect • Factor responsible for effect modification is called an effect modifier it modifies the effect of exposure on the outcome Teeth coloration

  38. Effect modification: Interaction/synergism Synergism= action of separates substances that in combinationproducean effectgreaterthanany component takenalone The two factors actat different levelsof the processus • Effect modification • Estimatedepends on the presence/absence of another factor • Is a characteristic of the POPULATION from the data came • is effect measure-dependent • Interaction • quantitative relationship not necessarily related to basic biologic mechanisms • Is a characteristic of the OBSERVEDdata • is model-dependent

  39. Effectmodification:Additive/multiplicative Remarks: • Absence of interaction, when we use risk DIFFERENCE: RAAB = RAA + RAB Interaction, in this case, is called Additive interaction OR • Absence of interaction, when we use risk RATIO: RRAB = RRA * RRB Interaction, in this case, is called Multiplicative interaction OR RDAB > RDA + RDB RDAB > RDA + RDB RRAB< RRA * RRB RRAB > RRA * RRB

  40. Effect modification: Additive/multiplicative RR = 3 RD = 0,3 0,45 0,15 Third variable present Additive interaction No multiplicative interaction Risk of disease 0,15 Third variable absent RR = 3 RD = 0,1 0,05 unexposed exposed RR = 1,7 – RD = 0,1 0,25 0,15 Multiplicative interaction No additive interaction Risk of disease 0,15 RR = 3 – RD = 0,1 0,05 unexposed exposed

  41. Effectmodification:Additive/multiplicative Remarks: • Assessment of interaction depends of the measure association usedeffect measure modification • When you talk about intercation always precise the measure of association used • When we have an effect, absence of multiplicative interaction implies presence of additive interaction and vice versa

  42. Effect modification : Properties Effect modification is not a bias but useful information • Identification of subgroups with a lower or higher risk • Targeting public health action • Better understand of the disease: biological mechanism

  43. Effect modification : Properties • To target public health action • Example 1 : Influenza • Vaccination is recommanded for : • Old person, • Person with cardiac and pulmonary disease • Diabetus … To identify a subgroup with a lower or higher risk • Example 1 : Influenza : • Important complications for old people, for person with cardiac and pulmonary disease or diabetus… • The risk of complication is more higher for these categories of people • Age and comorbidity are effect modifiers for influenza

  44. Effect modification : How to assessit ? Any statistical test to help us in assessing effect modification ? • Yes: many tests to verify the homogeneity of the strata +++ • But not sufficient • Clinical/biological decision rather than statistical • Taking in account the magnitude of the effect modification • Statistical tests depend on the sizeof the study

  45. Report effect modification or not ? What is the decision ? Ignore Ignore Report Report

  46. Effect modification/Confounding Confounding Belongs to study Frequent • Specific effects ≠ crude measure • Should report an adjusted weighted estimate • Distorsion of effect: bias • Creates confusion in data • ≠ distribution of the conf. in the exposed and unexposed group Effect modification Belongs to nature Rare ≠ effects in ≠ strata Must report stratum-specific estimates separately Useful information • ↗knowledge of biological mechanism • Allows targeting of public health action

  47. Effect modification/Confounding Confounding Be prevented in the study design Be controlled in the analytical phase No statistical test for confounding Effect modification Not Couldbecontrolledonly if we have take in account in the study design phase Statistical test for interaction • Bothconfounding and effect modification • must beinterpreted and take in accountaccording to the knowledge of physiopathologicmechanism • Determinationisdependent on choice of effectmeasure : RD – RR – OR … • Effect modification and confoundingcanexistseparately or together

  48. General framework for stratification In the study design phase: • Decide which variables to control for In the implementation phase: • Measure the confounders or other variables needed to block path In the analytical phase: • Assess clinical, statistical and practical consideration

  49. Crudeanalysis Stratification Specificestimates in eachstrata Specificestimatesamongstrata Yes = Effect modification No = No effect modification Estimateadjustedestimate Crudeestimate Yes = Confounding No = No Confounding Report stratum-specificestimates – No pooledmeasure Report adjustedestimate, 95% CI, p value of χ2MH Report crudeestimate, 95% CI, p value

  50. Stratification: Conclusion • Stratification is useful tool to assess the real effect of exposure on the disease • But, its have some limits: • Possibility of insufficient data when we have several strata • Tool developped only for categorical variable • Precision of the adjusted summary measure could be affected with overcontrolled • Only possible to adjust for a limited number of confounders simultaneously •  Necessity of other tools

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