Unit 8: Confounding
and effect (measure)
and effect (measure)
modification
Part 2
Dr. Borenstein
5 M lti
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5. Multivariate analysis: Analysis
Stratified analysis does not allow for simultaneous
adjustment of many variables because cell sizes
get too small and are unstable
Most often, we adjust for many confounders at
once
Variables such as age, gender, race, and
education are often incorporated into a model with
the exposure to establish the independent effect
of
the exposure after adjusting for other variables
Multivariate analysis is a tool to adjust for multiple
Multivariate analysis is a tool to adjust for multiple
variables simultaneously.
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Multivariate analysis, con’d
Involves modeling the relation between E
and D by means of a mathematical
equation
In the equation, the outcome (D) is
considered the dependent
variable
The exposure(s) of interest, other strong
The exposure(s) of interest, other strong
risk factors for the D and one or more PCF
are considered independent (predictor,
are considered independent
(predictor,
explanatory) variables.
Before including a variable in a
Before including a variable in a
model,
We conduct stratified PCFE and PCFD
and also stratified MH crude and adjusted
analysis to discern if each variable should
be introduced into the mathematical
model.
Multivariate analysis equation
Multivariate analysis equation
(general form)
Y =
α
+
β
1
X
1
+
β
2
X
2
+ . . . +
β
n
X
n
+
+
γ
X X
+… +
X
1
X
2
β
=coefficients from mathematical model
X=independent variable
Y=outcome (state you wish to predict)
Outcome = intercept + exposure (X
1
)+ confounder (X
2
) + …
+ confounder(X
n
)
+
+ interaction term (effectmodification) for
+
… + interaction term (effectmodification) for
exposure
X1
* confounder
X2
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Multiple regression model
Outcome = continuous (BP cholesterol level Ab titers)
Y =
α
+
β
1
X
1
+
β
2
X
2
+ . . . +
β
n
X
n
Outcome = continuous (BP, cholesterol level, Ab titers)
The coefficients of each independent (X) variable are
directly interpretable in relation to the outcome
The presence of each variable in the model means that
we know their relation to Y independent of the other
variables
Commonly used for crosssectional data, cohort data
looking at baseline or longitudinal change (also
incorporates random effects)
Many variations of the multiple regression model
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Logistic regression model
Outcome = natural log odds of disease
Outcome
natural log odds of disease
Log (odds of disease)=
α
+
β
1
X
1
+
β
2
X
2
+..+
β
n
X
n
Coefficients (
β
) can be directly converted to the
odds ratio, which describes the independent
association of that parameter with the outcome
Commonly used for casecontrol (frequency or
unmatched) and crosssectional data. Can be
used for cohort data if time to event is not
used for cohort data if time to event is not
important and can adjust for followup time.
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 Summer '08
 Staff
 Regression Analysis, Epidemiology, Medical statistics, standard population, direct adjustment

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