Slide13. Logistic Regression

Multivariable Binary Logistic Regression
Overview:
Basic Concept of subgroup analysis assessing role of 3rd variable
Detecting confounding and interaction based on sub-group analyses
Detecting confounding and interaction using SPSS
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22.3 Conducting subgroup analysis assessing the role of the 3rd factor
in SPSS
The VA randomized trial of coronary artery bypass surgery (CABG) vs.
standard medical therapy in patients with stable angina pectoris.
Dataset CABG.sav contains the following variables:
•
•
•
Primary study endpoint:
– All cause mortality at 6 years (Status6) (dead=1 / alive=0)
Primary study exposure
– Treatment (Surgery=1; Medical Treatment=0)
Covariates
– Left main disease (LMD) (yes=1/no=0)
– Angiographic risk (Angrisk) (low=0/high=1)
– Clinical risk (Clinrisk) (mild=1/moderate=2/ high=3)
– Diabetes (Diabetes) (yes=1/ no=0)
Peduzzi P, Kamina A, Detre K. Twenty-two-year follow-up in the VA Cooperative Study of Coronary
Artery Bypass Surgery for Stable Angina. Am J Cardiol (1999) 83 (2) 301-4
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Assessing over all effect of surgery (all patients).
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Crude (unadjusted) effect of CABG (All patients)
Over-all (unadjusted) OR for surgery and mortality = 0.73, p=0.081
indicating that the effect of surgery is marginally significant to improve
mortality.
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Sub-group analysis by LMD
(with or without left main disease)
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Among patients with
LMD (LMD=1)
Among patients with
No LMD (LMD=0)
a
Mortality at 6 years * CABG Crosstabulation
Count
Mortality at
6 years
Total
Count
Treatment
CABG
Alive
Died
Non CABG
235
76
311
a. Left Main Disease = Absent
CABG
223
61
284
a
Mortality at 6 years * CABG Crosstabulation
Total
458
137
595
Mortality at
6 years
Total
Treatment
CABG
Alive
Died
Non CABG
23
20
43
CABG
38
10
48
Total
61
30
91
a. Left Main Disease = Present
Different?
It appears that surgery improved mortality only among patients with LMD vs those without LMD
So let’s seek an evidence for the interaction (p-value for interaction) to numerically assess
ORLMD = 0.846 differs from ORno-LMD =0.303.
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Testing for interaction using a binary logistic regression
ORno-LMD
ORint
P=0.043 for the interaction
indicates that LMD seems to modify association of surgery and
Mortality. Let’s calculate two stratified OR’s of mortality and surgery
by LMD based on this result.
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How to interpret Exp(B) of a logistic regression with an interaction term
ORno-LMD
ORint
Exp(B) for Treatment among patients without LMD= 0.846 =ORno-LMD
Exp(B) for Treatment among patients with lmd = ORLMD
= ORno-MD X ORint
= 0.846 * 0.358 = 0.303. (this matches with the result of the sub-group
analysis)
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Now let’s see what happen, if you adjust OR for LMD instead of
detecting the interaction.
This is LDM
adjusted OR of
death by
treatment.
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Checking for confounding
•
Definition of confounder: Association of outcome and exposure
differs when another variable (covariate) is considered (i.e.,
adjusted).
Thus in order to assess if the third factor is confounding factor, we will
compare adjusted OR and un-adjusted OR.
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Using Logistic Regression to detect confounding by the effect of
LMD
Model excluding LMD
Unadjusted OR of death by treatment = 0.731
Model adjusting for LMD
OR of death by treatment adjusted for LMD= 0.720
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Does Diabetes Confound the Effect of Mortality and Surgery by
comparing crude and M-H adjusted OR’s?
Two OR’s are similar, thus we conclude that LMD is not confounding
the effect of treatment (surgery vs non-surgery).
Note: This is in fact expected, because in RCT, randomization provided
similar proportion of patients with LMD between surgery and control
groups, thus, LMD is not associated with exposure. In order to be a
confounder, it must associates with both exposure and outcome.
Confounding is not much of an issue in RCT, but interaction can well
exist.
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Example of assessing an interaction
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