1. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 1/50 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

2. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 2/50 Generality 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. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 3/50 Generality Introduction: Generality ExposureOutcome Vaccin efficacyMeasle Third variable No effect: sexe (boy/girl) Intermediary v.: Antibodies rate Confounder: Mother education Effect modifier: Age VE is lower for children < 18 months VE is the same for boy and girl AR is a consequence of Vaccin Effect observed is affected by ME

4. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 4/50 Generality 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. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 5/50 Principle 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. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 6/50 Principle Stratification: Principle To perform a stratified analysis, we have 6 steps : 1.Carry out simple analysis to test the association between the exposure and the disease and to Identify potential confounder 2.Categorize the confounder and divide the sample in strata, according to the number of categories of the confounder 3.Carry out simple analysis to test the association between the exposure and the disease in each stratum 4.Test the presence or absence of effect modification between the variables 5.If appropriate, check for confounding and calculate a point estimate of overall effect (weighted average measure) 6.If appropriate, carry out and interpret an overall test for association

7. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 7/50 Step 1 – Example 1 Stratification: Step 1 – Example 1 Example 1 : Investigation of the relationship between Vaccin Efficacy and Measle (cohorte study) 1.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 Measle+Measle - Vaccinated7279773 No vaccinated11671039

8. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 8/50 Step 1 – Example 1 Stratification: Step 1 – Example 1 Example 1 : Investigation of the relationship between Vaccin Efficacy and Measle (cohorte study) 2.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. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 9/50 Step 2 – Example 1 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: 1.Number of categories of age : <1 year and 1-4 years 2.Create strata according to the number of categories <1 year Measle+Measle - Vaccinated3835587 Not Vaccinated3024345 1 - 4 years Measle+Measle - Vaccinated3444186 No vaccinated8646694

10. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 10/50 Step 3 – Example 1 Stratification: Step 3 – Example 1 Perfom analysis inside these strata 1.In each strate Calculate the X 2 to test the association Estimate the RR i /OR i <1 year Measle+Measle - Vaccinated3835587 Not Vaccinated3024345 1 - 4 years Measle+Measle - Vaccinated3444186 No vaccinated8646694 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. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 11/50 Step 4 – Example 1 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. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 12/50 Step 4 – Example 1 Stratification: Step 4 – Example 1 Test the presence or absence of interaction between the variables Breslow-Day:Test of homogeneity in strata : H0 : RR 1 = RR 2 OrOR 1 = OR 1 =Χ 2 test compared observed and expected counts It requires a large sample size within each stratum

13. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 13/50 Step 4 – Example 1 Stratification: Step 4 – Example 1 Test the presence or absence of interaction between the variables Two possibilities RR 1 = RR 2 or OR 1 = OR 2 RR 1  RR 2 or OR 1  OR 2 No Interaction: Third variable is Not an effect modifier Presence of Interaction: Third variable could be effect modifier Next step: Looking for confounding Trying to form adjusted measure Stop here: Results only by strate No pooling measure

14. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 14/50 Step 4 – Example 1 Stratification: Step 4 – Example 1 Test the presence or absence of interaction … Example 1: Homogeneity test: H 0 : RR <1year = RR 1-4years (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 appropriate to try to summarize these two effects, 0,87 and 0,42, into one overall number We should report the two stratum-specific estimates separately and stop here the analysis 0,87 ≠ 0,42 ????

15. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 15/50 Step 1 – Example 2 Stratification: Step 1 – Example 2 Example 2 : Investigation of Effectiveness of AZT in preventing HIV seroconversion after a needlestick (case control study) 1.Crude analysis: Is there any association between AZT and prevention of HIV seroconversion after a needlestick in health care workers ? OR crude = 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 HIV+HIV- AZT +8130 AZT -19189

16. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 16/50 Steps 2 and 3 – Example 2 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 … 1.Categories of severity of needlestick : minor and major severity 2.Create strata according to the number of categories 3.In each strate test the association and Estimate the RD i /RR i /OR i Minor severity HIV+HIV - AZT +190 AZT -3161 Major severity HIV+HIV - AZT +740 AZT -1628 OR minor = 0,60 [0.06-5,81] – p = 1 No association OR major = 0,31 [0,11- 0,84] – p =0,02 Presence of association

17. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 17/50 Step 4 – Example 2 Stratification: Step 4 – Example 2 Test the presence or absence of interaction between the variables Test of homogeneity in strata : H 0 : OR minor = OR major ? 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  Construct a weighted average estimate Go to step 5

18. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 18/50 Step 5 – Example 2 Stratification: Step 5 – Example 2 If appropriate, check for confounding Two steps Forming adjusted summary estimate Compare adjusted summary estimate to crude estimate

19. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 19/50 Step 5 – Example 2 Stratification: Step 5 – Example 2 If appropriate, check for confounding 1.Forming an adjusted summary estimate It is the first step to assess the presence of confounding Properties: Summary measure = weigthed average measure of the effect of exposure: RD i - RR i - OR i … 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. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 20/50 Strate i of F Dis+Dis - E +aiai bibi n oi E -cici didi n 1i m oi m 1i nini Step 5 – Example 2 Stratification: Step 5 – Example 2 If appropriate, check for confounding 1.Estimation of RR a : Follow up study

21. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 21/50 Strate i of F Dis+Dis - E +aiai bibi n oi E -cici didi n 1i m oi m 1i nini Step 5 – Example 2 Stratification: Step 5 – Example 2 If appropriate, check for confounding 1.Estimation of OR a : Case control study OR MH =  a i d i  b i c i n i n i w i OR i w i Avec w i = b i c i / n i OR MH =  w i OR i /  w i Avec w i = b i c i / n i

22. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 22/50 Step 5 – Example 2 Stratification: Step 5 – Example 2 If appropriate, check for confounding 2.Identify confounding Compare the crude measure of effect to Adjusted measure of effect: H 0 : RR MH = RR crude orOR MH = OR crude No statistical test to help us Confounding can be judged present when adjusted RR MH or OR MH is different from crude effect  = (OR MH - OR crude ) / OR crude Arbitrary cut-off:>15-20 %or >20-30 % Interpretation

23. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 23/50 Step 5 – Example 2 Stratification: Step 5 – Example 2 If appropriate, check for confounding Two possibilities  < 15-20 %  > 15-20 % No confoundingPresence of confounding Use RR crude or OR crude To measure the relation Use RR MH or OR MH To measure the relation

24. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 24/50 Step 5 – Example 2 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: RR i or OR i are homogenous among strata And if we have detected confounding

25. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 25/50 Step 5 – Example 2 Stratification: Step 5 – Example 2 Example 2: Effectiveness of AZT in preventing HIV seroconversion after a needlestick in health care workers 1.Estimation of OR a adjusted n i = 255 ; OR = 0,60 n i = 92 ; OR = 0,31 Minor severity HIV+HIV - AZT +190 AZT -3161 Major severity HIV+HIV - AZT +840 AZT -1628 OR MH = 0,34 [0,14 – 0,87]

26. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 26/50 Step 5 – Example 2 Stratification: Step 5 – Example 2 Example 2: Effectiveness of AZT in preventing HIV seroconversion after a needlestick in health… 2.Identify confounding Compare the OR MH = 0,34With OR crude = 0,61  = (OR MH - OR crude ) / OR crude = 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 summary measure to use is the adjusted OR MH = 0,34

27. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 27/50 Step 6 – Example 2 Stratification: Step 6 – Example 2 If appropriate, carry out and interpret an overall test for association 1.Verify the relationship between the exposure and the outcome after adjusting on a third variable H 0 : RR MH = 1orOR MH = 1 Statistical test  Mantel-Haenszel it follows a chi-square distribution of 1 ddl, regardless of the number of strata 2.Intervalle estimates of of RR a or OR a adjusted

28. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 28/50 Step 6 – Example 2 Stratification: Step 6 – Example 2 Example 2: Effectiveness of AZT in preventing HIV seroconversion after a needlestick in health care workers 1.Verify the relationship between the AZT and the HIV seroconversion after adjusting on the severity of needlestick H 0 : OR MH = 1 p = 0,036  Mantel-Haenszel test is significant Conclusion: After adjustement for severity of needlestick, we have an association between AZT and HIV When we have adjusted for severity of needlestick the OR decreased from 0,61 to 0,34 but became significant

29. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 29/50 : Definition Confounding : Definition = Stratum specific-estimates are  from the crude estimate = Distortion of measure effect because of a third factor Due to differences in the distribution of an extraneous factor in the exposed and unexposed group Example: Individuals who are vaccinated tend to be healthier than individuals who are not vaccinated  Overestimation of the vaccin efficacy Influenza Vaccine in elderly subjects ARI death Health status: 58% 74,7%

30. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 30/50 : Definition 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: 1.Health status confonds the estimation of vaccine efficacy on ARI death 2.Needlestick confonds the estimation of AZT in preventing HIV seroconversion

31. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 31/50 : Definition 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. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 32/50 Criteria Confounding: Criteria To be a confounding factor, The variable must be: 1.Associated with the outcome independently of exposure= risk factor for the disease even in 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 cohort study In case control study OR CD/Ē  1

33. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 33/50 Criteria Confounding: Criteria To be a confounding factor, The variable must be: 2.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 Confounder: Severity of needlestick OR CE  1 In cohort study In case control study OR CE/ Ḋ  1

34. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 34/50 Criteria Confounding: Criteria To be a confounding factor, The variable must be: 3.Not an intermediate link in the causal pathway between the exposure and the disease Exposure: AZT Confounder: Severity of needlestick Outcome: HIV

35. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 35/50 Criteria Confounding: Criteria To be a confounder, the variable must be presented the three criteria Exposure: AZT Outcome: HIV Confounder: Severity of needlestick

36. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 36/50 How to identify confounder Confounding : How to identify confounder Compare : Crude effect of measure association : RD - RR - OR To adjusted measure of effect : RD A - RR MH - OR MH How ? Take in account only  = (OR MH - OR crude ) / OR crude If  > 15-20 %  Presence of confounding If  < 15-20 %  No confounding Statistical test must be avoided to identify confounding

37. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 37/50 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. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 38/50 Interaction/synergism Effect modification: Interaction/synergism  Synergism= action of separates substances that in combination produce an effect greater than any component taken alone Interaction quantitative relationship not necessarily related to basic biologic mechanisms Is a characteristic of the OBSERVED data is model-dependent Effect modification Estimate depends on the presence/absence of another factor Is a characteristic of the POPULATION from the data came is effect measure-dependent  The two factors act at different levels of the processus

39. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 39/50 Additive/multiplicative Effect modification: Additive/multiplicative Remarks: Absence of interaction, when we use risk DIFFERENCE: RA AB = RA A + RA B  Interaction, in this case, is called  Additive interaction OR Absence of interaction, when we use risk RATIO: RR AB = RR A * RR B  Interaction, in this case, is called  Multiplicative interaction OR RD AB > RD A + RD B RR AB > RR A * RR B RR AB < RR A * RR B

40. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 40/50 Additive/multiplicative Effect modification: Additive/multiplicative exposed unexposed 0,05 0,15 0,45 RR = 3 Risk of disease 0,05 0,15 RR = 3 – RD = 0,1 0,25 0,15 RR = 1,7 – RD = 0,1 Additive interaction No multiplicative interaction Multiplicative interaction No additive interaction Third variable present Third variable absent unexposedexposed RD = 0,3 RD = 0,1

41. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 41/50 Additive/multiplicative Effect modification: 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. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 42/50 Properties 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. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 43/50 Properties Effect modification : Properties 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 To target public health action Example 1 :Influenza Vaccination is recommanded for : Old person, Person with cardiac and pulmonary disease Diabetus …

44. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 44/50 : How to assess it ? Effect modification : How to assess it ? 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 size of the study

45. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 45/50 Report effect modification or not ? What is the decision ? Potential effect modifier present Potential effect modifier absent P value for heterogeneity test Report or ignore interaction 4,24,50,40 4,34,60,001 4,025,00,001 425,00,10 Ignore Report

46. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 46/50 Effect modification/Confounding 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 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

47. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 47/50 Effect modification/Confounding Effect modification Not Could be controlled only if we have take in account in the study design phase Statistical test for interaction Confounding Be prevented in the study design Be controlled in the analytical phase No statistical test for confounding Both confounding and effect modification must be interpreted and take in account according to the knowledge of physiopathologic mechanism Determination is dependent on choice of effect measure : RD – RR – OR … Effect modification and confounding can exist separately or together

48. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 48/50 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. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 49/50 Crude analysis Specific estimates  among strata Yes = Effect modification No = No effect modification Estimate adjusted estimate  Crude estimate Yes = ConfoundingNo = No Confounding Report stratum- specific estimates – No pooled measure Report adjusted estimate, 95% CI, p value of χ2 MH Report crude estimate, 95% CI, p value Stratification Specific estimates in each strata

50. Third Training Module, EpiSouth: Stratification, 15 th to 19 th June 2009 50/50 Conclusion 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