1. Assoc. Prof. Pratap Singhasivanon Faculty of Tropical Medicine, Mahidol University

2. The definitions a situation where the risk or rate of disease in the presence of 2 or more risk factors differs from the rate expected to result from their individual effects rate can be greater than expected - positive interaction or synergism rate can be less than expected - negative interaction or antagonism an interaction (or effect modification) is formed when a third variable modifies the relationship between an exposure and outcome Interactions

3. Interaction When the incidence rate of disease in the presence of two or more risk factors differs from the incidence rate expected to result from their individual effects

4. Interaction The effect can be greater than what we would expect (positive interaction) or less than we would expect (negative interaction)

5. Interaction Interaction (Effect Modification) Represents the phenomenon where the risk associated with the presence of two risk factors exceeds the risk we expect from the combination of the component risk X Y RR1RR1 RR2RR2 X and Y > R 1 and R 2

6. Interaction Interaction (Miettinen 1974) SAMPLE BASED POPULATION BASED (Statistical Interaction) (Effect Modification) (Biological Interaction)

7. Statistical Interaction Model Dependent Depends on deviation from statistical model (not biologic) Additive Model Multiplicative Model

8. R 00 R 01 R 10 R 11 AbsentPresent Absent Present Y X RR 11 = R 11 / R 00 RR 01 = R 01 / R 00 RR 10 = R 10 / R 00 Probability of disease in the presence of factors X and Y Probability of disease in the presence of factors X only Probability of disease in the presence of factors Y only Probability of disease in the absence of both X and Y Background RISK

9. Additive Model 1. In term of excess over “ONE” Stage of “No interaction” on additive scale 2. HOGANS

10. Multiplicative Model Stage of “No interaction” on Multiplicative model

11. Example : 5010 51 asbestos smoke + + - - ID/1000 PY RR 11 = 50/1 (smoking + asbestos) RR 10 = 10/1 (smoking alone) RR 10 = 5/1 (asbestos alone) Additive Model : (50-1)  (10-1) + (5-1) Presence of “Interaction” on Additive model Multiplicative Model : (50) = (10) * (5) Presence of “Interaction” on Multiplicative model

12. Example : 100 9080 60 1020 40 R 11 = 40/100 =.4 R 10 = R 01 = 20/100 =.2 R 00 = 10/100 =.1 RR 11 =.4/.1 = 4 RR 10 =.2/.1 = 2 RR 01 =.2/.1 = 2

13. Multiplicative Model : RR 11 = RR 10 * RR 01 4 = 2 * 2 No interaction on Multiplicative Model Additive Model : (RR 11 -1)  (RR 10 -1)+(RR 01 -1) 3  1 + 1 T = R 11 -R 10 -R 01 +R 00 = 0 =.40 -.20 -.20 +.10 =.10 There is evidence of interaction on Additive Model

14. NOTES : 1.Neither model is right or wrong. They are simply devices for modeling data and may be more or less suitable for a particular application. 2.Most statistical techniques are based on multiplicative model.

15. The presence or absence of interaction pertains to whether or not a particular effect measure (RR, OR) varies in value over categories or strata based on level of some factor(s). Equivalent to an assessment regarding interaction based on multiplicative model

16. 1.For addressing public health concerns regarding disease frequency reduction, deviation from additivity appears to be most relevant 2.Contribution to the understanding of disease etiology  multiplicative model Which of the 2 models we should use :

17. Additive Model (No interaction) smokers Non-smokers Age (X) Blood Pressure (Y) Only change in intercepts no change in slope irrespective of the value of Xi which is being held constant Interactive Model There is change in both intercepts and slope as the level of Xi which is held constant and varied Urban Rural Age (X) Height (Y)

18. Conclude that the non uniformity of the observed OR’s is unlikely to have occurred by chance; thus there is some evidence of interaction. P < 0.005

19. males 1014 19115 20129 2212 15517 17729 females 0.05.483.483-0.05 =.433 (P 1 )(P 2 ).124.414.144-.124 =.290 (P 1 ) (P 2 )

20. MalesFemalesTotal 1.0.4330.290 2. 0.088470.08979 3.113.03111.37224.4 4.4.48.9432.3081.24 5.21.199.3730.56

21. Relative risk of oral cancer according to presence or absence or two exposures : smokingalcohol smoking and alcohol consumption 5.711.23 1.531.00smokingalcohol No Yes

22. Aflatoxin Chronic Hepatitis B infection Relative risk of liver cancer for persons exposed to Aflatoxin and/or Chronic Hepatitis B infection : An example of interaction 59.47.3 3.41.00 Aflatoxin HBs Ag Negative Positive

23. Deaths from lung cancer (per 100,000) among individuals with and without exposure to cigarette smoking and asbestos Cigarette smoking Asbestos Exposure NoYes No11.358.4 Yes122.6601.6

24. Age-Adjusted Odds Ratios Estimated from Logistic Models with and without an Interaction between SMOKING and ORAL CONTRACEPTIVE USE No interaction ModelInteraction Model OC UseOC use Cig/day NoYesNoYes None 1.03.3 (2.0, 5.5)1.03.6 (1.2, 11.1) 1 - 24 3.1 (2.0, 4.6)10.1 (5.2, 19.5)3.3 (2.2, 5.1)3.7 (1.04, 13.0)  25 8.5 (5.6, 12.8)27.8 (14.4, 53.5)8.0 (5.2, 12.4)40.4 (19.4, 84.1)

25. Conceptual Framework of the definition of interaction based on comparing expected and observed joint effects A. When there is no interaction, the joint effect of risk factors A and Z equals the sum of their independent effects : A A A + Z Z Z Expected Observed

26. Conceptual Framework of the definition of interaction based on comparing expected and observed joint effects B. When there is positive interaction (synergism). The observed joint effect of risk factors A and Z is greater than that expected on the basis of summing the independent effects of A and Z : A A + Z Z Expected Observed   Excess due to positive interaction

27. Conceptual Framework of the definition of interaction based on comparing expected and observed joint effects C. When there is negative interaction (antagonism), the observed joint effect of risk factors A and Z is smaller than that expected on the basis of summing the independent effects of A and Z : A + Z Expected Observed * * “Deficit” due to negative interaction A Z

28. BLBLBLBL BL A ZZ A Z A I Baseline + excess due to A Baseline + excess due to Z Expected Joint OR based on adding absolute independent excesses due to A and Z* Observed joint OR> Expected OR. Excess due to I (Interaction) is not explainable on the basis of excess due to A and Z (1) OR = 1.0 (2) OR = 2.0 (3) OR = 3.0 (4) OR = 4.0 (5) OR = 7.0 * Note that when the independent relative odds for A and Z are added, the baseline is added twice; thus, it is necessary to subtract 1.0 from the joint expected OR: that is, Expected OR A+Z+ =(Excess due to A + baseline) + (Excess due to Z + baseline) – baseline = OR A+Z- + OR A-Z+ - 1.0. Schematic representation of the meaning of the formula, Expected OR A+Z+ =Observed OR A+Z- +Observed OR A-Z+ -1.0.

29. 3.09.0 15.0 3.09.0 15.021.0 Factor A Factor B + _ + _ + _ Factor B Factor A Incidence Rates + _ 3.09.0 15.021.0 + _ Factor B Factor A Incidence Rates + _ 06 12 + _ Factor B Factor A Attributable Rates + _ 06 1218 + _ Factor B Factor A Attributable Rates + _

30. Evans County Study  Prospective cohort study of CVD and Cerebro vascular disease  Logistic regression analysis of 10-year mortality among the members of this cohort (1904)  9 variables were considered for inclusion of the model

31. Example of Logistic Regression Analysis of a prospective cohort study adapted from Evans County Study 1960-72 VariableVariable range Variable coefficient Standard error of coefficient P value Age40-69 years0.086520.01153< 0.001 Gender0 = male ; 1 = female1.499760.967230.121 Age X GenderMales : 0 ; Females : 40-69-0.042960.016990.011 Race0 = white ; 1 = black1.593820.963550.098 SBP88-310 mmHg0.019430.00208< 0.001 Diabetes0 = no or suspect ; 1 = yes1.123250.26134< 0.001 Cigarette Smoking 0 = never smoke ; 1 = present or past smoker 0.317390.156820.043 Cholesterol94-546 mg/100 ml0.003110.001520.041 Quelet index X 1002.107 – 8.761-1.064150.431580.014 SBP = systolic blood pressure Quelet index = weight in pounds divided by the square of height in inches

32. Use of Logistic Regression Coefficient for calculation of the probability of dying over a ten-year period for a hypothetical individual Variable Coefficient (log Odds for 1 unit) Value for hypothetical individual Product Age0.08652504.32600 Gender1.4997600.00000 Age X Gender-0.0429600.00000 Race1.593821 SBP0.019431803.49740 Diabetes1.123251 Cigarette Smoking0.317391 Cholesterol0.003113501.08850 Quelet index X 100-1.064153.2653-3.47477 Intercept -6.37626

33. Maximum Likelyhood estimates of logistic parameters (seven risk factors of coronary heart disease) VariableParameterEstimate ( ) Standard Error of X 0 interce0pt 00 -13.2573 X 1 age (yr) 11.1216.0473 X 2 cholesterol (mg/dl) 22.0070.0025 X 3 systolic BP (mm Hg) 33.0068.0060 X 4 relative Weight 44.0257.0091 X 5 hemoglobin (g%) 55 -.0010.0098 X 6 cigarettes 66.4223.1031 X 7 ECG Abnormality 77.7206.4009 X 4 = relative weight (100 x actual weight / median for sex-height group) X 6 = cigarettes per day (coded 0=never, 1=less than one pack, 2= one pack, 3= more than one pack) X 7 = ECG (coded  0=normal, 1=abnormal)

34. Maternal Age Affected Babies per 1000 Live Births Prevalence of Down syndrome at Maternal Age

35. Birth Order Affected Babies per 1000 Live Births Prevalence of Down syndrome at birth by birth order

38. Example No.Type of ConfoundingUnadjusted Relative Risk Adjusted Relative Risk 1Positive3.51.0 2Positive3.52.1 3Positive0.30.7 4Negative1.03.2 5Negative1.53.2 6Negative0.80.2 7Qualitative2.00.7 8Qualitative0.61.8 Hypothetical Examples of Unadjusted and Adjusted Relative Risks According to Type of confounding (Positive or Negative)