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Lecture 10: interaction and effect measure modification
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Terms in this set (31)
Outline
1. Definitions
a. biological and statistical interaction
b. Effect measure modification
2. scale (additive vs. multiplicative)
3. assessing EMM/statistical interaction
a. heterogeneity of effects
b. joint effects
4. assessing EMM/statistical interaction in CC studies
5. quant vs. qual EMM/interaction
6. EMM/interaction vs. confounding
7. Public health interaction
Biological interaction
1. two causes or E interact on biological level to cause disease or O
2. presence of interaction based on measurements called stats interaction, may not reflect true bio interaction
Example
RR of O w/ E1 = 7.3
RR of O w/E2 = 3.4
RR of O w/E1 and E2 = 59.4
approaches to assessing EMM
1. heterogeneity of effects
2. independent versus joint effects (statistical interaction)
1. Heterogeneity (or homogeneity) of effects (definition)
1. whether effect is homogeneous or heterogeneous when stratified on EM
a. effect of E on O is not homogeneous in strata formed by EM
b. effect different at different levels
2. Statistical interaction (independent vs. joint effects)
1. Obs. joint effect of two E's is same or different than expected from independent effects
2. types of joint effects
a. synergism
b. antagonism
3. measure effect on two scales
a. additive
b. relative (multiplicative)
Synergism
1. Obs. joint effects greater than expected from individual effects
2. A+Z= A+Z+more than expected
Antagonism
1. Obs. joint effect smaller than expected from ind. effects
2. A+Z = A+Z which is less than expected
Additive interaction
1. Attributable risk model
a. effect measured on additive scale (difference in measures / ARs)
2. Risk difference used as measure of effect
a. stat model = linear regression
multiplicative interaction
1. relative risk model
a. effect measured on relative scale (RRs, ORs)
2. risk ratio used as measure of effect
a. stat model = odds
association between E and O modified by X (graphs two lines parallel + slopes, two lines different slopes). What happens to rate difference and rate ratio with increase in E
1. two parallel lines
a. rate differences stay constant (10%-5%=5% ; 90%-85%=5%)
b. rate ratio decreases (10/5 = 2 ; 90%/85%=1.05)
2. two lines different slopes
a. rate difference increases (10%-5%=5% ; 100%-50%=50%)
b. rate ratios stay constant (10/5=2 ; 100/50=2)
Decision tree for conf and EM
STEPS
1. calc crude and stratified estimates and compare
Are estimates the same?
1. No
a. EM present, report stratified estimates
2. YES
a. calc. adjusted estimate with MH method and compare to original estimate
Are they the same?
1. NO
a. confounding, report adjusted
2. YES
a. no confounding, report crude
Homogeneity of effects (assessing Additive, not present example)
What type of graphs/scale?
stratify on potential EM (Z)
1. Z- and A - ; IR = 10 ; AR = 0
2. Z- and A+ ; IR = 20 ; AR = 10
3. Z+ and A- ; IR = 30 ; AR = 0
4. Z+ and A+ ; IR = 40 ; AR = 10
Because ARs associated with A are not modified by Z, Additive interaction not present
linear: parallel +ve slopes
Homogeneity of effects (assessing Additive, present example)
what type of graph/scale?
stratify on potential EM (Z)
1. Z- and A - ; IR = 5 ; AR = 0
2. Z- and A+ ; IR = 10 ; AR = 5
3. Z+ and A- ; IR = 10 ; AR = 0
4. Z+ and A+ ; IR = 30 ; AR = 20
Because ARs associated with A are modified by Z, Additive interaction present
linear: Different +ve slopes
Homogeneity of effects (assessing multiplicative, not present example)
what type of graph/scale?
stratify on potential EM (Z)
1. Z- and A - ; IR = 10 ; RR = 1
2. Z- and A+ ; IR = 20 ; RR = 2
3. Z+ and A- ; IR = 25 ; RR = 1
4. Z+ and A+ ; IR = 50 ; RR = 2
Because ARs associated with A are not modified by Z, no multiplicative interaction
Log scale: parallel +ve slopes
Homogeneity of effects (assessing multiplicative, present example)
what type of graph/scale?
stratify on potential EM (Z)
1. Z- and A - ; IR = 10 ; RR = 1
2. Z- and A+ ; IR = 20 ; RR = 2
3. Z+ and A- ; IR = 25 ; RR = 1
4. Z+ and A+ ; IR = 125 ; RR = 5
Because ARs associated with A are modified by Z, multiplicative interaction
Log scale: Different +ve slopes
Test of homogeneity of stratified ORs
Ho: strength of assoc. is homogenous across all strata (OR1=OR2=OR3)
Ha: not homogeneous
Joint Effects (additive interaction, not present)
1. observed (a,b,c,d) IRs
= 10, 30, 20, 40
2. observed (a,b,c,d) ARs
= 0, 20, 10, 30
Joint Expected AR = b+c = 30
Joint observed AR = d = 30
Since joint AR is the same than expected by adding individual AR's, there is no additive interaction
Joint Effects (additive interaction, present)
1. observed (a,b,c,d) IRs
= 10, 30, 20, 60
2. observed (a,b,c,d) ARs
= 0, 20, 10, 50
Joint Expected AR = b+c = 30
Joint observed AR = d = 50
Since joint AR is the different than expected by adding individual AR's, there is additive interaction
Joint Effects (multiplicative interaction, not present)
1. observed (a,b,c,d) IRs
= 10, 30, 20, 60
2. observed (a,b,c,d) RRs
= 1, 3, 2, 6
Joint Expected RR = b*c = 6
Joint observed RR = d = 6
Since joint RR is the same than expected by multiplying individual RR's, there is no multiplicative interaction
Joint Effects (multiplicative interaction, present)
1. observed (a,b,c,d) IRs
= 10, 30, 20, 90
2. observed (a,b,c,d) RRs
= 1, 3, 2, 9
Joint Expected RR = b*c = 6
Joint observed RR = d = 9
Since joint RR is different than expected by multiplying individual RR's, there is multiplicative interaction
assessing interaction via multiple regression
1. three treatments, three lines, different slopes
2. include interaction term to regression model
(b13, b12)
3. two predictors interact if the effect on the response variable of one predictor depends on the value of the other
EMM in CC studies (approaches)
1. heterogeneity of effects
a. cant assess additive interaction (incidence not measured)
b. can assess multiplicative
2. assessing observed/expected joint effects
a. additive and multiplicative
Additive interactions (CC studies)
1. Exp OR = ObsORb + ObsORc-1.0
2. if Obs > Exp, additive effect
multiplicative interactions (CC studies)edf
1. Exp OR = ObsORb * ObsORc
2. if Obs > Exp, multiplicative effect
interaction in matched CC
1. cant do additive (neither homogeneity or joint), multiplicative (joint)
a. b/c incidence rates not available
b. b/c OR expressing independent effect not available after matching
c. ""
2. CAN ONLY DO MULTIPICATIVE (HOMOGENEITY)
a. ORs for E and O are available for CC pairs according to effect modifier
quantitative interaction
1. effect so f A on outcome are different according to Z, directions of assoc. between A and outcome are same in both Z strata
a. qual. interaction seen on both scales (add and mult)
Qualitative interaction
effects of A on outcome are in different directions, depending on presence/absence of Z, assoc. in one strata formed by Z but not in the other
reciprocity of interaction
1. A modifies the effect of Z, then Z modifies the effect of A
a. doesnt matter which is the explanatory/principle variable...
Reasons for interaction (heterogeneity)
1. random variability
2. confounding
3. bias
4. differential intensity of E
Public Health interaction
1. determining # cases of disease occurring in pop and depend on proportion of pop. in which factors occur jointly
a. like additive interaction (attributable risks)
Why is EM important?
1. understand causation
2. identify high risk groups; target intercentions
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