Confounding stratification based adjustment F Hosseinpanah M D
Confounding , stratification based adjustment F. Hosseinpanah , M. D.
Explanation Type of association Chance Spurious Bias Spurious Effect-cause Real Confounding Real Causal model coffee drinking MI factor x coffee drinking Cause-effect Real coffee drinking MI MI
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
Interrelationship • EXPOSURE • DISEASE CONFOUNDING FACTOR
Smoking MI Coffee drinking Real
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.
Study design RCT Approach Random allocation Example A=vaccine B=placebo Random differences Source of confounding Observational Prospective study Nonrandom allocation A=smokers B=nonsmokers Random differences and factors associated with the exposure of interest
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.
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
country Age distribution ? Mortality
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
Sexual activity General Health ? Mortality
Sexual activity General Health ? Mortality Is it confounder ?
Maternal smoking Low birth weight Perinatal death Doses smoking cause perinatal death ?
Maternal smoking Low birth weight Other mechanisms ? Perinatal death Doses smoking cause perinatal death through mechansms Other than low birth weight ?
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)
Coping with confounders: specification Design phase Matching stratification Analysis phase adjustment
Stratified Analysis LBW NO PRENATALCARE D ˉ D E 30 18 48 Eˉ 70 82 152 100 200 D ˉ D E 5 8 13 Eˉ 45 72 117 80 130 nonsmokers 50 D ˉ D E 25 10 35 Eˉ 25 10 35 50 20 70 smoker OR 1 = eh/fg = 1. 0 ORc = ad/bc = 1. 95 OR 2 = il/kj = 1. 0
Stratified Analysis LBW NO PRENATALCARE D ˉ D E 30 18 48 Eˉ 70 82 152 100 200 D ˉ D E 5 8 13 Eˉ 45 72 117 80 130 nonsmokers 50 D ˉ D E 25 10 35 Eˉ 25 10 35 50 20 70 smoker OR 1 = eh/fg = 1. 0 ORc = ad/bc = 1. 95 OR 2 = il/kj = 1. 0
Stratified Analysis cancer inactivity D ˉ D E 30 18 48 Eˉ 70 82 152 100 200 D ˉ D E 5 8 13 Eˉ 45 72 117 80 130 Age < 40 50 D ˉ D E 25 10 35 Eˉ 25 10 35 50 20 70 Age ≥ 40 OR 1 = eh/fg = 1. 0 ORc = ad/bc = 1. 95 OR 2 = il/kj = 1. 0
Stratified Analysis cancer inactivity D ˉ D E 30 18 48 Eˉ 70 82 152 100 200 D ˉ D E 5 8 13 Eˉ 45 72 117 80 130 Age < 40 50 D ˉ D E 25 10 35 Eˉ 25 10 35 50 20 70 Age ≥ 40 OR 1 = eh/fg = 1. 0 ORc = ad/bc = 1. 95 OR 2 = il/kj = 1. 0
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 3 rd variable (potential confounder) - one for each level • Investigate OR level 1= OR level 2. . . ‡ OR crude • CONFIRM that 3 rd variable is associated with exposure and with outcome independently
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
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!
THE BRESLOW DAY TEST • the test statistic: where i =stratum (i=1, 2…I) I BD chi sq = Σ [ai - E(ai ׀ crude OR)]2 i=1 var (ai ׀ crude OR) • it has a chi-square distribution with I-1 degrees of freedom • can be used to test H 0: OR 1 = OR 2 • can be used to test H 0: OR 1 = ORcrude
IDENTIFYING A CONFOUNDER - an example Calculate crude measure of association… CHD no CHD smokers nonsmokers 305 58 363 345 292 637 650 350 1000 RR = a/(a+b) c/(c+d) RR = 2. 8
IDENTIFYING A CONFOUNDER - an example Calculate stratum-specific measures of association. . . STRATUM 1: MEN smkrs CHD NO CHD 300 600 nonsmkrs 50 150 200 350 450 800 RR = 2. 0 STRATUM 2: WOMEN smkrs CHD NO CHD nosmkrs 5 45 8 142 50 13 187 200 RR = 1. 9
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 roughly the same 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
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 whethere 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
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 b i ci Ni • this technique generates a summary measure across strata by removing the effect of the confounder
Example of the Mantel Haenszel Method…. STRATUM 1: Pre-Menopause OR=1. 19 Stroke Fm Hsty NO Fm Hsty 16 2 18 MH OR = 1. 29 No Stroke 47 7 54 63 9 72 STRATUM 2: Post-Menopause OR=1. 05 Stroke Fm Hsty NO Fm Hsty 24 58 82 No Stroke 13 33 46 37 91 128 16 x 7 + 24 x 33 72 128 2 x 47 + 13 x 58 72 128
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)
---- Interaction • Definition “Interaction is present when the incidence rate of disease in the presence of two or -- from the incidence more risk factors differs rate expected to result from their individual effects. ”
The definition… INTERACTIONS • 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
The definition… INTERACTIONS • 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
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 3 rd variable - one for each level • Use Breslow Day to test OR level 1 ‡ OR level 2. . . ‡ OR crude
IDENTIFYING AN INTERACTION - an example Calculate crude measure of association… smkrs nonsmkrs MI 32 15 47 no MI 168 185 353 200 400 OR = ad bc OR = 2. 35
IDENTIFYING AN INTERACTION - an example Calculate stratum-specific measures of association… STRATUM 1: Dietary fat consumption <30% of calories MI smkrs nonsmkrs 14 10 24 no. MI 126 130 256 140 280 OR = 1. 45 STRATUM 2: Dietary fat consumption > 30% of calroies smkrs nonsmkrs MI no. MI 18 5 42 55 60 60 23 97 120 OR = 4. 71
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 NOT THE SAME! 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 stratumspecific OR’s show this association differs by level of DFC
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 3 rd variables in study)
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
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
Stratification Advantages • Easily understood • Flexible and reversible: can choose which variables to stratify upon after data collection Disadvantages • 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
Approach to Interaction and Confounding Is there interaction? Yes No Report separate measures for levels of covariate Is there confounding? Yes No Adjust for confounder No need for adjustment
Approach to bias, Confounding Interaction, chance and… Internal validity bias breslow Stratify regression interaction confounding chance causality DESIGN Selection information CI
• Researchers report findings Coffee drinking causes Myocardial Infarction + MI + Coffee - Coffee 90 - MI 60 60 90 150 OR=2. 25
• Researchers report findings Coffee drinking causes Myocardial Infarction + MI + Coffee - Coffee 90 - MI 60 60 90 150 OR=2. 25
MI + No MI coffee No coffee Smokers 120 30 Nonsmokers 30 120 OR = 16
MI + No MI coffee No coffee Smokers 120 30 Nonsmokers 30 120 OR = 16
Coffee + No coffee MI No MI Smokers 100 50 Nonsmokers 50 100 OR = 4
Coffee + No coffee MI No MI Smokers 100 50 Nonsmokers 50 100 OR = 4
+ Coffee - Coffee + MI - MI 90 60 60 90 150 + MI - MI 80 40 20 10 Smokers OR =1 OR=2. 25 150 + MI - MI 10 20 40 80 Non-Smokers OR =1
+ Coffee - Coffee + MI - MI 90 60 60 90 150 + MI - MI 80 40 20 10 Smokers OR =1 OR=2. 25 150 + MI - MI 10 20 40 80 Non-Smokers OR =1
Adjusted OR ? ORMH= Σ ai di Ni Σ bi ci Ni
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