2. Negussie D. 2020
Residual confounding
Unknown confounders (non-measurable/ undetectable)
Controlling for one of several confounding variables does
not guarantee that confounding is completely removed.
Residual confounding may be present when:
the variable that is controlled for is an imperfect surrogate of
the true confounder,
other confounders are ignored, the units of the variable used for
adjustment/stratification are too broad
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Statistical significance in assessing confounding
It is inappropriate to relay only on statistical significance
Rather knowledge of slight association of the confounder to the
outcome and exposure may be important
If statistically significant is taken into account use of conservative P-
value as large as 0.20 may be better
Such conservative P-value may differentiate small differences in
proportion of confounders
Rather OR/RR of < 0.7 [preventive] or >1.3 [risk condition] in the
sample may be better than looking at the P-value.
[This since we look the association only in the sample]
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4. Negussie D. 2020
Identifying a confounder
Statistically, a confounder also should fulfill the following
Once analysis using multivariate or Mantel-Hanzel way of
stratification is done, an adjusted result will come
This adjusted result should be compared with the crude result
If the difference is much high (clinical significant), then it is
confounded result
RR/ORpooled different from RR/ORAdjusted
Adjusted estimate ≠ Crude estimate
5. Negussie D. 2020
Mediator and Confounding
Not every factor that is associated with both the exposure and
the disease is a confounding variable.
It could be a mediating variable
Statistically, a mediator has similar criteria, except for it
[mediator] is part of the pathway mechanism.
A mediator is also associated with both the dependent and
independent variables but is part of the causal chain between
the independent and dependent variables.
Difficult to distinguish statistically, but only differentiated
based on biological knowledge of the process of action.
6. Negussie D. 2020
Mediation
As a confounder, it is associated to both the exposure and
the outcome but is a path of action.
It is distinguished by careful consideration of causal
pathways.
Knowledge of biological plausibility about the mediator is
necessary
Atherosclerosis
Cigarette fibrinogen
mediator
Exposure outcome
7. Negussie D. 2020
Cont…
Therefore, a mediator is part of the pathway
Once a third variable is determined for its superiusness
characteristics, it should also be tested for it mediator effect.
Mediator effect of a third variable is determined by biological and
contextual knowledge of the relationship.
If a mediator is known, it should be reported in the discussion as a
finding of the research.
However, confounding effect may not be described, but avoid its
occurrence [adjusting it].
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Interaction
The term is used to describe a situation of two or more risk
factors modify the effect of each other with the outcome
(more by statisticians)
This phenomenon is also known as effect modification
and is distinguished from the phenomenon of confounding
(more by epidemiologists)
Effect modification / interaction is a condition that should be
identified and described
However, confounder is a condition (a variable) that should 8
9. Negussie D. 2020
Homogeneity/ heterogeneity
The term homogeneity indicates that the effects of a risk factor are
homogeneous or similar in strata formed by another factor .
Heterogeneity of effects, therefore, implies that these effects are
not similar.
ie. effect of a variable on an outcome is different in the presence
and absence of a third variable
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Strategies to evaluate interaction
A. Assessment of Homogeneity of Effects
1. Detection of Additive Interaction: The Absolute difference or
Attributable Risk Model
2. Detection of Multiplicative Interaction: The Relative inference or
or Ratio Model
B. Comparing Observed and Expected joint Effects;
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A.1. Detection of Additive Interaction
When the attributable risk in those exposed varies as a
function of a third variable
That is to calculate the attributable risk for those exposed
on each stratum
It can also be examined graphically too.
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Cont...
The absolute excess risk of Y attributable to A do not differ
according to exposure to Z,
Therefore, Z has no interaction or effect modification
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The attributable risk for A is larger for those exposed than for those not
exposed to Z, denoting heterogeneity of the absolute effects of A.
(ie. Z has effect modification on A for the outcome)
Cont...
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15. Negussie D. 2020
Graphical Presentation
Interaction is absent on the left, because
the absolute difference between
presence and absence of Z is similar
ie. When Z absent, 40-10 = 30
While Z present, 60-30 = 30
Interaction is present on the right panel
because the absolute difference between A+
and A-is higher when Z is present
ie. When Z absent, 40-10 = 30
While Z present, 90-30 = 60
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16. Negussie D. 2020
A.2. Detection of Multiplicative Interaction
The relative risk for A is the same for those exposed and not exposed
to Z.
Relative risk for the disease among exposed to A was similar between
those exposed and not exposed to Z; RR= 2.00
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Cont…
The relative risk for A is larger among those exposed to Z, indicating that
the effects of A measured by the relative risk are heterogeneous
according to exposure to Z.
The relative risk of the disease among exposed to A was different among
those exposed and not exposed to Z; RR of 2.0 Vs 5.0
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Graphical Presentation It is done on logarithmic scale coordinate
Interaction is absent on the left, because the
relative difference of A between presence and
absence of Z is similar
ie. When Z absent, 20/ 10 = 2
While Z present, 30/ 15 = 2
Interaction is present on the right panel because the
relative difference between A+ and A-is higher when Z
is present.
Ie. When Z absent, 20/ 10 = 2
While Z present, 90/15 = 6
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19. Negussie D. 2020
B. Comparing Observed and expected joint effect
When the observed joint effect differs from expected
joint effect.
Expected joint effect can be estimated by assuming the
two factors are independent
Like for homogeneity, it is based on the conceptual
framework for both
1. Additive models (absolute difference)
2. Multiplicative models (relative difference) 19
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Joint effect difference
When there is no interaction
The joint effect of risk factors A and Z equals the sum
of their independent effects
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No interaction
21. Negussie D. 2020
Cont…
When there is positive interaction (synergism), the
observed joint effect of risk factors A and Z is greater than
that expected on the basis of summing the independent
effects of A and Z
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Positive interaction (Synergism)
22. Negussie D. 2020
Cont…
When there is negative interaction (antagonism), the
observed joint effect of risk factors A and Z is smaller than
that expected on the basis of summing the independent
effects of A and Z
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Negative interaction (antagonism)
23. Negussie D. 2020
Study designs and interaction
Cohort study (and other prospective studies)
Incidence, attributable risk and relative risks are measurable
Therefore, both additive and multiplicative effect is
measureable
Case-control studies
Able to measure odds ratio (indirect measure of RR)
but difficult to measure attributable risk
So only multiplicative effect is measureable
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Expd ORA+Z+ = Obs ORA+Z- x Obs ORA-Z+
25. Negussie D. 2020
Quantitative vs. Qualitative Interaction
1. Quantitative interaction:
The association between a factor and the outcome exists
and is of the same direction in each stratum of the third
variable
1. Qualitative interaction:
It occurs when the effect of a factor on the outcome is in
opposite direction in one of stratum of the third variable
compared to the other stratum
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Cont…
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A, Qualitative interaction:
there is crossover: that is, RRA+/A- > 1.0
and ARA+/A- > 0 when Z (effect modifier)
is present, and RR < 1.0 and AR < 0
when Z is absent.
B, Quantitative interaction:
the RR > 1.0 and AR > 0 when Z is
present, and RR = 1.0 and AR = 0
when Z is absent.
27. Negussie D. 2020
Summary
Do both crude analysis and stratified analysis
Assess for difference in effect estimate between strata
If there is difference in effect estimate between strata,
then there is interaction effect.
On the other hand, compare the estimated effect vs the
observed joint effects, if much difference consider for the
presence of interaction.
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