Lecture_6_effect_modification

Strategies to evaluate interaction
The
absolute difference or attributable risk model (additive) The relative difference or Ratio model (multiplicative)
Multiplicative Interaction – the association of Non-white race and lower CD4 counts on Mortality Observed Mortality CD4 > 200 White 2.3 Nonwhite 4.2 Joint expected RR
Additive Interaction – the association of older age and lower CD4 counts on Mortality Observed Mortality CD4 > 200 Age < 35 Age > 35 1.9 5.0 Joint expected AR
Additive versus Multiplicative
Additive
is used more for public health assessments and multiplicative is used more in prediction models Mantel-Haenszel and logistic/Cox regression are based on multiplicative approach Statistical interaction on either scale, but especially multiplicative, does not demonstrate biological interaction Also issues with noncollapsibility of the odds ratio (see RG&L for more info.)
R11-R00 = R10-R00+R01-R00
RD11 = RD10+RD01
RD11 - RD10- RD01 = interaction contrast = 0 if no ditivity
Calculating additive interaction when only relative measures are given
20.0
Relative Risk
Age > 35 No
Age > 35 Yes
10.0
70.0
Is there an additive effect?
Age CD4 200 CD4 200 CD4 200 CD4 200 > < 35
Mortality Relative Rate Risk 1.9
>
< <
> 35
< 35 > 35
5.0
26.5 29.5
Is there any evidence of multiplicative interaction?
Observed vs. expected
Examples
Age,
CD4 and mortality Are they confounders? Are they effect modifiers?
Example--Interaction
A. Risk/Rate of Y B. Z+ Z+ ZZC.
Z+
ZXX+ XX+ XX+
In In
A, there is no interaction. B, the presence of Z strengthens the association between X and Y, but does not change its direction In C, the presence of Z changes the direction of the association between X and Y
Definition of Interaction
Based
on homo or heterogeneity of effects - effect of a putative risk factor A on the risk of an outcome Y is not homogeneous in strata formed by a third variable Z (the effect modifier) Base on comparisons between observed and expected joint effects when the observed joint effect of A and Z differs from that expected on the basis of the independent effects of A and Z
Finding effect modification in your data
What interactions should I look at?
Viewpoint
1: We should not expect effects to be the same in all strata. We should examine effect modification on as many axes as possible Viewpoint 2: Average effects are good enough. Only look for effect modification if it would be interesting if you didn’t find it.
CD4 < 200
23.4
30.4
Joint observed RR
Observed White Non-white RR CD4 > 200 Is there any evidence of multiplicative interaction?
CD4 < 200
Calculating additive interaction when only relative measures are given
Attributable risk versus relative risk
AR
is a measure of the association based on the absolute difference between two risk estimates (risk difference) Relative risk is the risk of developing the disease in the exposed compared to the unexposed Odds ratio is the ratio of the odds of developing the disease in the exposed compared to the unexposed
Effect modification/ interaction
Interaction or effect modification
Two
or more risk factors modify the effect of each other with regard to the occurrence or level of a given outcome Also known as effect modification Synergistic (positive interaction) – potentiates the effect of the exposure of interest Antagonistic (negative interaction) – diminishes or eliminates the effect of the exposure of interest
Is there an additive effect?
Example where multiplicative interaction is present
Smoking or non Smoking Age < 35 No
Age < 35 Yes
Incidence of Lung cancer 10.0
Race
CD4 > 200 White
Mortality Rate 2.3
Relative Risk
CD4 > 200 Non-white 4.2 CD4 < 200 White
23.4
CD4 < 200 Non-White 30.4
Is there any evidence of multiplicative interaction?
Assessing additive interaction
Assessing multiplicative interaction
10.0
Example where multiplicative interaction is absent
Smoking or non Smoking Age < 35 No Age < 35 Yes Age > 35 No Age >35 Yes Incidence of Lung cancer 15.0 30.0 20.0 40.0 Relative Risk
Additive versus Multiplicative
Additive
– the AR (RD) in those exposed to Factor A varies as a function of a third variable. Multiplicative – when the relative difference (ratio) in the risk of an outcome Y between subject exposed and those not exposed to a putative risk factor A differs as a function of a third variable
CD4 < 200
26.5
29.6
Age > 35
Joint observed AR
Observed Age < 35 Attrib Mort CD4 > 200 CD4 <
Is there any evidence of additive interaction?
Mortality by race and CD4 count
Homogeneity and heterogeneity of effects
When you stratify and risk varies by strata, then effect modification exists
Example of additive but not multiplicative interaction
If ICR ≠ 0, implies non-additivity If ICR>0, then superadditive If ICR<0, then subadditive
Confounding versus Interaction

Sometimes the same variable may be both a confounder and an effect modifier Confounding makes it difficult to evaluate whether a statistical association is also causal Interaction is part of the web of causation Do not adjust for a variable that is both a confounder and an effect modifier (reporting an average measure may be meaningless) – stratify instead