Confounding and effect modification Epidemiology 511 W. A. Kukull November 23 2004.
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Transcript of Confounding and effect modification Epidemiology 511 W. A. Kukull November 23 2004.
Confounding and effect modification
Epidemiology 511W. A. Kukull
November 23 2004
Confounding
• “A function of the complex interrelationships between various exposures and disease”.
• Occurs when the disease - exposure association under study is “mixed” with the effect of another factor
Example(after Rothman, 1998)
• Is frequent beer consumption is associated with rectal cancer ?
• Beer consumption is associated with consumption of pizza
• Is pizza consumption a confounder?– Is pizza, by itself, causally associated with Ca?
• if yes, then its a confounder; otherwise not
Beer and Rectal Ca
Rectal Ca control
Beer 630 770
No Beer 770 630
OR= 0.67 (0.58 - 0.78)
Pizza consumption ?Yes No
Beer
No Beer
Rectal Ca Control Rectal Ca Control
350 700
70 280
280 70
700 350
Confounding(after Rothman, 1998)
• Confounding factor must be risk factor for disease (causally associated)
• Confounding factor must be associated with exposure in the source (study) population
• Confounding factor must not be affected by exposure or disease– it cannot be the result of exposure– it cannot be an intermediate step in causal path
Confounding(after Koepsell & Weiss, 2003)
• A factor that occurs only as a consequence of the exposure cannot distort (confound) the disease-exposure association.
• To be a confounder, the factor would have to give rise to the exposure or be associated with something that did.
• “No matter how strongly a variable is related to exposure status, if it is not also related to the occurrence of the disease in question, it cannot be a confounder.”
Confounder – Exposure – Disease: some finer distinctions (Koepsell & Weiss, 2003)
• A confounder can be an actual cause of disease. • A confounder can be associated with a cause of
disease that, in the context of the study, cannot be measured. (e.g., genotype)
• A variable can be a confounder if it is related to the recognition of the disease even if it has no relationship to the actual occurrence of disease. (e.g., frequency of screening tests for disease)
Exposure
Disease
Confounder
= non causal= causal
Confounding
?
AgeDistribution(conf)
Country (exp)
Mortality
?
GeneralHealth(conf)
Sexual Activity (exp)
Mortality
?
Other Meds(conf)
Ca Channel Blockers (exp)
GI Bleeding
?
Diet, SESLifestyle(conf)
Vitamin CIntake (exp)
Colon Cancer
?
Low Fat Diet (exp)
Cholesterol(conf ?)
Heart disease
?
Consequence of exposure
Weight Loss(conf ?)
Smoking
Lung Ca
?
Consequence of disease
Quetelet Index
Abdominal skinfold(conf ?)
Type IIDiabetes
?
Skinfold is a surrogate measureof body mass
Red Meat diet
Colon Ca
Tax IdNumber(conf ?)
No plausible association with disease
?
Confounder or consequence?
• Studying decreased risk of MI and due to moderate alcohol consumption
• Higher HDL cholesterol is independently associated with lower risk of MI
• HDL increases as a result of moderate alcohol use
• Is HDL a Confounder?
Controlling confounding in the design of a study
• Randomization: ensures known and unknown confounders are evenly distributed in study groups
• Restriction: Limit subjects to one category of a confounder – e.g. if sex confounds, use only men;
• Matching: equalize groups on confounder (must follow matched analysis)
Evaluating Confounder disease and exposure
• Construct tables for – confounder and disease– confounder and exposure
• Examine odds ratios (or effect estimate)– are the associations “strong”– are they likely to be “causal”
Stratification in analysis: adjusting for confounding
• Computing the crude OR from a 2x2 table• Stratification breaks the crude table into
separate 2x2 tables for each level of the confounding factor– analogous to “standardization”– many factors and many levels can cause tables
with empty cells
Is there Confounding?
• Do stratum specific RR estimates differ from Crude estimate?
• Does “adjusted” RR estimate differ from Crude estimate– Mantel-Haenszel – Multivariate modeling
• differences of >10% in RR when factor is included in the model, indicate confounding present
Confounding in stratified analyses
• stratify by the potential confounder• compute stratum-specific OR estimates• If uniform but different from crude OR
then confounding is probably present: – calculate adj. OR (e.g., use Mantel-Haenszel)
• If NOT uniform across strata then “effect modification” (interaction) may be present– Report stratum specific estimates; do not adjust
Is toluene exposure associated with Diabetes?
Diabetes CTRL
Exposedto Toluene
Not Exposed
30 18
70 82
Crude OR = 1.95 (1.0 - 3.8)
Does the Age confound the diabetes – toluene association?<40 > 40
diabetes ctrl diabetes ctrl
Tolu.
Not
Tolu.
Not
5
45
8
72
25
25
10
10
OR(1) = 1.0 (0.3 - 3.1)
OR(2) = 1.0 (0.4 - 2.8)
Why? Age confounds because it is associated with diabetes, regardless of toluene exposure
Toluene exposed
No Toluene
Diab Ctrl Diab Ctrl
>40
<40
>40
<40
25 10
5 8
25 10
45 72
OR = 4.0 (1.1 - 14.7)
OR = 4.0 (1.8 - 9.0)
Stratification example 1
• Crude OR = 1.95• OR in each age group is 1.0
– when the strata OR’s are the roughly equal --but different from the Crude OR-- it indicates confounding
• Age is a confounder • We should adjust for Age in the analysis
– Mantel-Haenszel adjusted OR (you will not need to memorize the formula)
ETOH and MIMI No MI
AlcoholYes
No
71 52
29 48
OR= 2.26 {1.26 - 4.04}
non smokers smokersMI Ctrl MI Ctrl
ETOHYes
No
Yes
No
8 16
22 44
63 36
7 4
OR=1.0 (0.38 - 2.65)
OR = 1.0 (0.29 - 3.45)
Stratify by smoking
Physical Activity and StrokeStroke No Stroke
P. A. High
Low
190 266
176 157
OR= 0.64 {0.48 - 0.85}
Men WomenStroke Ctrl Stroke Ctrl
P.A.
Hi
Lo
Hi
Lo
141 208
144 112
49 58
32 45
OR= 0.53 (0.38 - 0.73)
OR = 1.19 (0.65 - 2.16)
Stratify by Gender
Controlling Confounding in the Analysis: Adjusted odds ratio
• Stratified analysis (examine strata OR)– Mantel-Haenszel adjusted OR : a weighted
average of stratum specific OR’s
(ad / N) divided by (bc / N) = ORmh
– Where N= total subjects in each sub table
a bc d N1
a bc d N2
Mantel-HaenszelAdjusted OR
(a1d1)/N1 + (a2d2)/N2 + . . .
(b1c1)/N1 + (b2c2)/N2 +. . .OR mh =^
Trisomy 21 and spermicide use:Case-Control Study
4 109
12 1145
1270
Down’s Ctrl
Sp +
Sp -
OR=
Stratify by Maternal Age<35 35+
Down Ctrl Down Ctrl
Sp +
Sp -
Sp +
Sp -
3
9
104
1059
1
3
5
86
OR= OR=
1175 95
Mantel-HaenszelAdjusted OR
(a1d1)/N1 + (a2d2)/N2 + . . .
(b1c1)/N1 + (b2c2)/N2 +. . .OR mh =^
[(3)(1059) / (1175)] + [(1)(86) / (95)]
[(9)(104) / (1175)] + [(3)(5) / (95)]=
= 3.8
Multivariate Statistics
Linear: y = b0 + b1x1 + b2x2 +. . . bkxk
Logistic: exp (b) gives you adjusted ORlog(odds) = b0 + b1x1 + b2x2 +. . . bkxk
for b1 coded as a [0,1] variable, the ORx1= eb1 (adjusted for all other xi )
Cox : exp (b) gives you adjusted RRlog(haz) = b0 + b1x1 + b2x2 +. . . bkxk
Logistic RegressionCoding Variables
• Continuous x causes b to be interpreted as: increase in log odds per unit change in x
• Interaction of two variables is represented by a single product term: x1x2 (with only one b)– interpretation of models which include
interaction and continuous terms can be tricky– Consult a friendly Biostatistician
Recognizing Confounding in logistic regression models
• Logistic Regression:– ln[Y/(1-Y)] = a + b1X1 + b2X2 + … bnXn
– e(bi) = OR(xi) (per unit change in Xi)
– does bxi change when Xk factor(s) are added?– Does crude OR differ from adjusted OR?– does model “log-likelihood” change (score
test)
Logistic coefficients and OR’s
Variable (x) Coefficient (b) Odds Ratio
intercept -4.56 ----
gender(1=m,0=F)
1.31 3.71
smoking(1=yes,0=no)
0.70 2.01
HTN(1=yes,0=no)
0.51 1.67
eb = OR
Interaction (Effect Modification)
• Statistical, Biological and Social semantic meanings differ.
• Does the RR estimate “differ” at each level of a third variable? Homogeneity of RR
• Biological reasoning: is there something about the third factor that changes the way the Exposure-Disease association works?
Stratification Example:Crude tableCrude table
Hepatocellular carcinoma
Case ControlHepatitis CVirus infection
Yes
No
63
102
24
357
Crude OR = 9.2 (5.5 - 15.4)
Stratify by HBV infectionAre the stratum specific odds ratios statistically
different?HBV-
HepC+
-
HepC+
-
Case Ctrl Case Ctrl
HBV+
37
40
1
28
26
62
23
329
OR(1)= 25.9 (4.2 - * ) OR(2)= 6.0 (3.2 - 11.1)
M-H“adjusted odds ratio” OR= 8.1
ORs are not statistically different: should we adjust or report strata ORs???
Stratification Example 2:HBV, HepC and Liver Ca
• The OR’s in the HBV strata look quite different– Does this indicate “effect modification”?– Effect modification is a finding in the data
that needs to be elaborated; it is a natural phenomena that exists independently
– Confounding is a nuisance that needs to be eliminated (by adjusting, matching, restriction, etc.)
Effect Modification(also known as “interaction”)
• When the measure of effect differs between strata– Can apply to RR or risk difference (AR) measures
• Presumed additive or multiplicative effect model depends on biology of disease and factor
• Synergy: when effect exceeds that expected under the chosen model– RR (A+B) >> RR (A) + RR (B)– RR (A x B) >> RR (A) x RR (B)
Schematic of additive modelfor case control data (Szklo & Nieto, 2000)
BL BL BL BL BL
“A” “Z” “Z” “Z”
“A” “A”
Excessjoint
increase
Additive model effects:Expected = OR(A) + OR(Z) - 1.0
OR=1.0
2.03.0
4.0
7.0
Expected Observed
RR estimates in strata: “guidelines” for heterogeneity[Szklo & Nieto 2000]
Suspected E-M factor absent
Suspected E-M factor present
Adjust or report strata RR’s
2.3 2.6 Adjust
2.0 20.0 Report
0.5 3.0 Report (qualitative diff)
3.0 4.5 Maybe both
Is there an associationbetween risk factor (X)and disease (Y)?YES
Is it affected by Bias?
No
Estimate magnitudeand direction of
effect on RR
Are STRATUMRR’s different from“crude”RR?
YESStratum RRs are similarto each other: Confounding: Adjust for stratum factor
Stratum RRs are statistically different from each other:Interaction/effect modificationreport strata RRs, don’t adjust
Yes
No
No confounding by Strata factor
Stratified analysis flow chart
Considerations
• Collect data on potential confounders– if you don’t get it you can’t control for it
• Try to reason what the potential effect of confounding might be – Magnitude and direction (as with bias)– Coffee drinking and MI: smoking may be a
positive confounder because smokers are at increased risk of MI
Generally speaking...
• A “strong” association is less likely to be explained by confounding than a weak one
• For an observed association to be the sole result of confounding by another factor:– the factor must have a stronger association with
disease than the one observed– if RR= 10.0 for smoking and Lung ca, then a
confounder would need RR> 10.0
Logistic Regression
• Allows simultaneous adjustment for several confounders (also allows “interactions”)– multiple variables to predict disease status
(dichotomous outcome)• Odds ratios can be obtained directly from
the regression coefficients• “Standard” method seen in most case-
control study analyses (matched and unmatched analyses)
Conclusion
• What is confounding? – How do we recognize, evaluate and control it?
• What is effect modification?– How do we recognize and evaluate it?– Why is it important?– [also know as “interaction”, “effect measure
modification”, etc.]