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Confounding , stratification based adjustment

Confounding , stratification based adjustment. F.Hosseinpanah , M.D. Explanation Type of association Causal model. Chance Spurious Bias Spurious Effect-cause Real coffee drinking MI

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Confounding , stratification based adjustment

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  1. Confounding , stratification based adjustment F.Hosseinpanah , M.D.

  2. Explanation Type of association Causal model ChanceSpurious Bias Spurious Effect-cause Real coffee drinking MI ConfoundingReal factor x coffee MI Cause-effect Real coffee drinking MI drinking

  3. Confounding variable • An extrinsic factor involved in the association that is the real cause of the outcome. • A variable that is associated with the predictor variable and is a cause of the outcome

  4. Interrelationship • EXPOSURE DISEASE • CONFOUNDING FACTOR

  5. Smoking MI Coffee drinking Real

  6. THE DIFFERENCE BETWEEN BIAS AND CONFOUNDING Bias creates an association that is not true, but confounding describes an association that is true, but potentially misleading.

  7. Confounding Criteria: • Causally associated with the outcome • Noncausally or causally associated with the exposure • not intermediate in exposure/outcome pathway • Confounding can produce either a type 1 or a type 2 error, but we usually focus on type 1 errors.

  8. Overall mortality rates in 1968 for six countries Costa rica 3.8/1000 Venezuela 4.4/1000 Mexico 4.9/1000 Cuba 6.7/1000 Canada 7.3/1000 US 8.7/1000

  9. country ? Age distribution Mortality

  10. Age specific mortality per 1000 Costa rica 3.7 Venezuela 4.6 Mexico 5.0 Cuba 4.0 Canada 3.2 U.S 3.6

  11. Sexual activity ? General Health Mortality

  12. Sexual activity ? General Health Mortality Is it confounder ?

  13. Maternal smoking Low birth weight Perinatal death Doses smoking cause perinatal death ?

  14. Maternal smoking Low birth weight Other mechanisms ? Perinatal death Doses smoking cause perinatal death through mechansms Other than low birth weight ?

  15. Examples of confounding • Demographic factors: age, gender, ethnicity • Lifestyle exposures: smoking, diet, alcohol • Personal characteristics: medical history • Co-occurring occupational or environmental exposures (e.g., solvent mixtures)

  16. Coping with confounders: specification Design phase Matching stratification Analysis phase adjustment

  17. Stratified Analysis ˉ ˉ ˉ D D D ˉ ˉ ˉ E E E LBW D 18 48 30 E ORc = ad/bc = 1.95 NO PRENATALCARE 70 82 152 200 100 100 nonsmokers smoker D D 25 10 35 13 8 5 E E 25 10 35 45 72 117 70 20 50 130 50 80 OR2 = il/kj = 1.0 OR1 = eh/fg = 1.0

  18. Stratified Analysis ˉ ˉ ˉ D D D ˉ ˉ ˉ E E E LBW D 18 48 30 E ORc = ad/bc = 1.95 NO PRENATALCARE 70 82 152 200 100 100 nonsmokers smoker D D 25 10 35 13 8 5 E E 25 10 35 45 72 117 70 20 50 130 50 80 OR2 = il/kj = 1.0 OR1 = eh/fg = 1.0

  19. Stratified Analysis ˉ ˉ ˉ D D D ˉ ˉ ˉ E E E cancer D 18 48 30 E inactivity ORc = ad/bc = 1.95 70 82 152 200 100 100 Age < 40 Age ≥ 40 D D 25 10 35 13 8 5 E E 25 10 35 45 72 117 70 20 50 130 50 80 OR2 = il/kj = 1.0 OR1 = eh/fg = 1.0

  20. Stratified Analysis ˉ ˉ ˉ D D D ˉ ˉ ˉ E E E cancer D 18 48 30 E inactivity ORc = ad/bc = 1.95 70 82 152 200 100 100 Age < 40 Age ≥ 40 D D 25 10 35 13 8 5 E E 25 10 35 45 72 117 70 20 50 130 50 80 OR2 = il/kj = 1.0 OR1 = eh/fg = 1.0

  21. PROCESS TO IDENTIFY A CONFOUNDER • CALCULATE the appropriate CRUDE measure of association between exposure and outcome (RR or OR) • CALCULATE RR’s or OR’s for the association when the data has been STRATIFIED according to levels of the 3rd variable (potential confounder) - one for each level • Investigate OR level 1= OR level 2...‡ OR crude • CONFIRM that 3rd variable is associated with exposure and with outcome independently

  22. PROCESS TO IDENTIFY A CONFOUNDER KEY ELEMENT…. If you have a confounder your stratum specific OR or RR must all be EQUAL and they must all be different from your crude OR or RR OR 1 = OR 2 = OR 3 = OR 4 -- all same! BUT… OR stratum specific ‡ OR crude or overall

  23. THE BRESLOW DAY TEST Knowing that an important part of your definition of a confounder rests on the fact that your stratum specific OR or RR must all be EQUAL... ...the Breslow Day test for homogeneity of the OR’s confirms this statistically HO: OR 1 = OR 2 = OR 3 = OR 4 -- all same! HA: OR 1 ‡ OR 2 ‡ OR 3 ‡ OR 4 -- at least one NOT same!

  24. THE BRESLOW DAY TEST • the test statistic: where i =stratum (i=1,2…I) BD chi sq = Σ [ai - E(ai ׀crude OR)]2 var (ai ׀crude OR) • it has a chi-square distribution with I-1 degrees of freedom • can be used to test H0: OR1 = OR2 • can be used to test H0: OR1 = ORcrude I i=1

  25. IDENTIFYING A CONFOUNDER - an example Calculate crude measure of association… smokers nonsmokers CHD 305 58 363 no CHD 345 292 637 650 350 1000 RR = a/(a+b) c/(c+d) RR = 2.8

  26. IDENTIFYING A CONFOUNDER - an example Calculate stratum-specific measures of association... STRATUM 1: MEN smkrs nonsmkrs CHD 300 50 350 NO CHD 300 150 450 600 200 800 STRATUM 2: WOMEN smkrs nosmkrs CHD 5 8 13 NO CHD 45 142 187 50 150 200 RR = 2.0 RR = 1.9

  27. IS THERE A CONFOUNDER? • CRUDE RR for smoking and CHD =2.8 • STRATUM-SPECIFIC RR for smoking and CHD with gender as a potential confounder... MEN RR = 2.0 WOMEN RR = 1.9 • Do Breslow- Day tests(if difference is clinically significant) • Gender confounds the association between smoking and CHD because the crude RR of 2.8 is NOT the same as the stratum-specific RR’s of approx. 2.0 roughly the same

  28. IS THERE A CONFOUNDER? • THE 10% RULE as a rule of thumb • We assert that gender confounds the association between smoking and CHD because the crude RR of 2.8 is NOT the same as the stratum-specific RR’s of 2.0 or 1.9 • the 10% rule is a good rule of thumb for assessing whether there is confounding present Is 2.0 and 1.9 more than 10% different from 2.8? 10% of 2.8 = .28 and the difference between our stratum specific RR’s and the crude RR is greater than .28 Not a replacement for a statistical test- simply a way to initially judge whether something is a potentially confounding factor

  29. Using the Mantel Haenszel Method to Report Adjusted OR’s • Can only use with confounders because we assume that ORs are constant across stratum • GENERAL FORMULA: where i = strata and N=total MH OR = Σ ai di Ni Σ bi ci Ni • this technique generates a summary measure across strata by removing the effect of the confounder

  30. Example of the Mantel Haenszel Method…. STRATUM 1:Pre-Menopause OR=1.19 Stroke No Stroke MH OR = 1.29 Fm Hsty 1647 63 16 x 7 + 24 x 33 NO Fm Hsty 27 9 72 128 18 54 722x 47 + 13 x 58 72 128 STRATUM 2: Post-Menopause OR=1.05 Stroke No Stroke Fm Hsty 2413 37 NO Fm Hsty 58 33 91 82 46 128

  31. HOW TO REPORT DATA WITH CONFOUNDERS IF YOU HAVE A CONFOUNDER…. • DO NOT report crude OR or RR (you know it’s wrong) • GOOD: Report stratum-specific OR or RR • BEST: Report summary measures such as a Mantel-Haenszel OR (this is like compling stratum-specific OR’s)

  32. Interaction ---- • Definition “Interaction is present 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.” --

  33. INTERACTIONS The definition… • a situation where the 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 relation between an exposure and outcome

  34. INTERACTIONS The definition… • a situation where the 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 relation between an exposure and outcome

  35. PROCESS TO INDENTIFY AN INTERACTION • CALCULATE the appropriate CRUDE measure of association between exposure and outcome (RR or OR) • CALCULATE RR’s or OR’s for the association when the data has been STRATIFIED according to levels of the 3rd variable - one for each level • Use Breslow Day to test OR level 1 ‡ OR level 2...‡ OR crude

  36. IDENTIFYING AN INTERACTION - an example Calculate crude measure of association… MI no MI smkrs 32 168 200 nonsmkrs 15 185 200 47 353 400 OR = ad bc OR = 2.35

  37. IDENTIFYING AN INTERACTION - an example Calculate stratum-specific measures of association… STRATUM 1: Dietary fat consumption <30% of calories MI noMI smkrs 14 126 140 nonsmkrs 10 130 140 24 256 280 STRATUM 2: Dietary fat consumption > 30% of calroies MI noMI smkrs 18 42 60 nonsmkrs 5 55 60 23 97 120 OR = 1.45 OR = 4.71

  38. IS THERE AN INTERACTION? • CRUDE OR for smoking and MI =2.35 • STRATUM-SPECIFIC OR for smoking and MI with Dietary fat consumption as a potential interacting variable... DFC<30% OR = 1.45 DFC>30% OR = 4.71 • therefore, dietary fat levels modify (by interaction) the association between smoking and MI because the crude OR of 2.35 is NOT the same as the stratum-specific OR’s AND the different stratum-specific OR’s show this association differs by level of DFC NOT THE SAME!

  39. HOW TO CONTROL FOR INTERACTION • IN STUDY DESIGN… • MAINTAIN adequate sample size to potentially evaluate your data in terms of interaction • RESTRICTION of subjects according to potential interactive terms (i.e. simply don’t include those 3rd variables in study)

  40. HOW TO CONTROL FOR INTERACTION • IN DATA ANALYSIS… • STRATIFIED ANALYSIS yet do not create a summary measure like the Mantel Haenszel • RESTRICTION is still possible at the analysis stage but you are throwing away data!!! • MODEL FITTING using regression techniques

  41. HOW TO REPORT DATA WITH INTERACTIONS IF YOU HAVE A INTERACTION…. • DO NOT report crude OR or RR (you KNOW its wrong!) • DO NOT Report summary measures such as a Mantel-Haenszel OR as they are NOT valid when stratum-specific OR’s differ (a defining quality of an interaction) • Only: Report stratum-specific OR or RR

  42. Easily understood Flexible and reversible: can choose which variables to stratify upon after data collection Number of strata limited by sample size needed for each stratum Few covariables can be considered Few strata per covariable leads to less complete control of confouding Relevant covariables must have been measured Stratification Advantages Disadvantages

  43. Is there interaction? No Yes Is there confounding? Report separate measures for levels of covariate Yes No Adjust for confounder No need for adjustment Approach to Interaction and Confounding

  44. Approach to bias, Confounding Interaction,chance and… Internal validity Selection information bias interaction breslow Stratify regression confounding chance CI causality DESIGN

  45. Researchers report findings Coffee drinking causes Myocardial Infarction + MI - MI + Coffee - Coffee OR=2.25 150 150

  46. Researchers report findings Coffee drinking causes Myocardial Infarction + MI - MI + Coffee - Coffee OR=2.25 150 150

  47. MI + No MI OR = 16

  48. MI + No MI OR = 16

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