logistic regression analysis of matched data
DESCRIPTION
Logistic Regression Analysis of Matched Data. THE GENERAL LOGISTIC MODEL. S. Logit form of logistic model: Logit P( X ) = + i X i. Logit form:. Special Case: No Interaction, I.e., all = 0. EVW LOGISTIC MODEL FOR MATCHED DATA. - PowerPoint PPT PresentationTRANSCRIPT
Logistic Regression Logistic Regression Analysis of Analysis of
Matched DataMatched Data
THE GENERAL LOGISTIC MODEL
Logit form of logistic model:
Logit P(X) = + iXi
Pr(D=1| X1,..., Xp) = P(X ) = 1
1 + exp[ + iXii=1
p
]
Logit form:
Special Case: No Interaction, I.e., all = 0.
OR = exp [ ] = e
EVW LOGISTIC MODEL FOR MATCHED DATA
Logit P(X) = + E + 1iV1i + 2iV2i + EkWk
E = (0, 1) exposure
V1i’s denote dummy variables used to identify matching strata
V2j’s denote potential confounders other than matching variables
Wk’s denote potential effect modifiers
(usually other than matching variables)
Adjusted OR Comparing E=1 vs. E=0 Controlling for the V’s and W’s
Special Case: No Interaction, I.e., all = 0.
OR = exp [ + kWkk
]
OR = exp [ ] = e
logit P(X) = + E + 1iDii=1
62
+ 21GALL
logit P(X) = + E + 1iDii=1
62
+ 21GALL
logit P(X) = + E + 1iDii=1
62
+ 21GALL
OR(adj) = exp []
exp
OR(adj) = exp [2.209] = 9.11
logit P(X) = + E + 1iDii=1
62
+ 21GALL
OR(adj) = exp [2.209] = 9.11
logit P(X) = + E + 1iDii=1
62
+ 21GALL
where the Di denote 62 dummy variables for the 63 matched sets
logit P(X) = + E + 1iDii=1
62
OR(adj) = exp [2.209] = 9.11
logit P(X) = + E + 1iDii=1
62
+ 21GALL
H0: OR(adj) = 1 = 0
OR(adj) = exp [2.209] = 9.11
H0: OR(adj) = 1 = 0
logit P(X) = + E + 1iDii=1
62
+ 21GALL
OR(adj) = exp [2.209] = 9.11
H0: OR(adj) = 1 = 0
OR(adj) = exp [2.209] = 9.11
= (2.76, 30.10)
logit P(X) = + E + 1iDii=1
62
+ 21GALL
exp [ 1.96s]
OR(adj) = exp [2.209] = 9.11
(2.76, 30.10)
(2.76, 30.10)
INTERACTION MODEL: 63 matched pairs
Note: Previous model was a no interaction model
OR(adj.) = exp [ + 1GALL ]
Logit P(X) = + E + 1iDi + 21GALL + 1EGALL62
95% CI for OR involving interaction?
e.g., What is the 95% CI for
?OR(adj.) = exp [ + 1GALL ]
GENERAL 100(1) CI FORMULA IN A LOGISTIC MODEL FOR MATCHED DATA
100(1 - )% CI for OR (adj.):
exp [ L Z1 -
2
Var (L) ]
OR(adj.) = exp [ L ] where L = + kWkk
VARIANCE FORMULA
Var (L) = Var () + Wk2Var (
k)
k
+ 2 Wk2Cov (,
k)
k
+ 2 Wk2Cov (
k,k)
k
?
k °
OR(adj.) = exp [ L ] where L = + kWkk
Example: 95% CI formula
exp [ L 1.96 Var (L) ]
OR(adj.) = exp [ + 1GALL ]
L = exp [ + 1GALL ]
Var (L) = Var () + (GALL)2Var (1)
+ 2(GALL)2Cov (,1)