an illustration of rate difference estimation with sas in logistic regression
DESCRIPTION
An Illustration of Rate Difference Estimation with SAS in Logistic Regression. Yun Guo. Outline. Statistical methods for RD RD with logistic regression SAS realization Conclusion. Statistical methods. Wald/t approximation—no covariate adjust CMH (weighted estimate)-adjust strata - PowerPoint PPT PresentationTRANSCRIPT
An Illustration of Rate Difference Estimation with SAS
in Logistic Regression
Yun Guo
Outline
• Statistical methods for RD
• RD with logistic regression
• SAS realization
• Conclusion
Statistical methods
• Wald/t approximation—no covariate adjust• CMH (weighted estimate)-adjust strata• Logistic Regression-adjust both
Statistical methods
• Logistic regression
,where, x is covariate, s is factor, t is treatment, sub i is indexing subject
(1)
exp( )
1 exp( )i i i
ii i i
x s tp
x s t
(2)
RD with logistic regression
• Odd Ratio through Logistic Regression
Simply subtract among different levels of factor
Say t(t=1) vs. t(t=0),
1 0log( ) log( ) log( ) exp( )1 1t t
p pOR
p p
RD with logistic regression
• Rate through Logistic Regression (say subject i=1)
1
0
1 0
exp( )
1 exp( )
exp( )
1 exp( )
i it
i i
i it
i i
t t
x sp
x s
x sp
x s
RD p p
(3)
Intercept, covariate as well as factor, not gone!!!!
RD with logistic regression
• How about the variance of estimate?
1
0
1 0
exp( )
1 exp( )
exp( )
1 exp( )
var( ) var( )
i it
i i
i it
i i
t t
x sp
x s
x sp
x s
RD p p
(4)
Very messy!!!
RD with logistic regression
Hereafter subscript 1/0 of est p index treatment.
Statistical methods
• Marginal approach (sum over all samples)
Statistical methods
Statistical methods
• To conclude, we have following 4 steps• 1, establish logistic regression • 2, get estimated rates, covariance of estimates,
estimated RD• 3, set up Delta method• 4, get CI
SAS realizationEXAMPLE DATA
SAS realizationPREPARE DATA
SAS realizationSTEP 1: Logistic regression
SAS realizationSTEP 1: Logistic regression
SAS realizationSTEP 1: Logistic regression
COV
EST
SAS realizationSTEP 2: RD estimate
SAS realization
Step 3: Delta method
Step 4: CI
Conclusion
1, When covariates adjust needed, a choice is to use L Regression
2, Other methods could be used too
Thank you!