Third variable

What is a third variable? How to interpret third variable in observational studies?

1. What is a third variable ? How to interpret third variable in observational studies Dr Rukman Mecca Manapurath Assistant Scientist CHRD SAS New Delhi

2. X/exposure Y / outcome Z/Third variable ?

3. Coffee drinking Pancreatic cancer

4. Confounder Coffee drinking Pancreatic cancer Any variable?

5. Effect modifier Coffee drinking Pancreatic Ca ?

6. Mediator Coffee drinking ? Pancreatic Ca

7. Concept – Confounder A third variable that distorts the observed relation between exposure and the outcome. Also associated with both exposure & outcome .

8. Concept – Effect modifier Effect of exposure on a disease outcome is modified by presence of another third variable

9. How will you assess? Make a crude 2* 2 table Calculate RR Calculate RR for each strata Test If RR similar Possible that 3 rd variable is a confounder If different, effect modification Stratify by third variable

10. Confounding Criteria Whether in the causal pathway of the exposure- outcome -using biological and clinical knowledge 2. Associated with both exposure and outcome 3. Unequally distributed among population

11. How to identify? First, to find out if the assumed confounding variable is associated with both outcome variable and exposure variable Second, to compare the associations before and after adjusting for that confounding factor.

12. Coffee n(%) drinking Pancreatic Controls Cancer n(%) Total Yes 30 (63) 18 (37) 48 No 70 (46) 82 (54) 152 Total 100 100 200 Unadjusted RR = 30*82/70*18 = 1.95 Lets consider the third variable – age

13. Step 1- If variable is associated with exposure & outcome Age Ca Pancreas Controls < 40 yrs 50 80 > 40 yrs 50 20 100 100 Age Total Coffee Non Coffee Drinkers drinkers % exposure < 40 yrs 130 13 117 10 > 40 yrs 70 35 35 50 100 100 Age is related to having Pancreatic Ca Age is related to being a coffee drinker RR =2.5 RR = 5

14. Age Coffee drinking Ca Pancreas Controls Relative risk <40 yrs Yes 5 8 1 No 45 72 Total 50 80 >40 yrs Yes 25 10 1 No 25 10 Total 50 20 Here age is a confounder Limitations- using this stratification, we cannot check multiple confounders at one time. Step 2- Find adjusted RR & compare it with unadjusted RR

15. Control at design stage Matching Matching involves pairing the study groups for potential confounding factors, such as smoking, age or sex; thus assuring even distribution of potential confounders

16. Control at analysis stage Stratified analyses Multivariate analyses. the estimation of the effect of an exposure variable on a given outcome variable after controlling for the cofounding effect of other included variable

17. Effect modifier Exposure Outcome ?

18. Association of exposure on an outcome differs depending on the presence of third variable Here exposure and outcome differ in strata of population

19. Example Coffee drinkers & Pancreatic Ca - RR of 2.8 (95% CI: 2.5–3.1) After stratifying for gender, RR of 1.3 (95% CI: 1.1–1.5) among females Inference?? Gender variable has made some modifications of the pathway by increasing the risk of pancreatic cancer among coffee drinkers

20. How will you represent effect modifier By strata of population based on third variable

21. Summarize If an observed association is uniform across stratified groups, it is called as confounding variable. Whereas, if it is different across different stratified groups, it is effect modifier. If we miss EM sub group pattern will be missed Confounding Bias occurs

22. For data representation Do a crude analysis & estimate the measure of association List potential confounders & modifiers Stratify data based on these variables Check for Effect modifier Yes Present by strata No Check for confounding Yes Present adjusted Data No Present crude Data

23. Thank you Refer to Leon Gordis for further concepts Read more on how to represent effect modifier and confounder in a observational studies Read third variable - mediator