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
![Page 1: An Illustration of Rate Difference Estimation with SAS in Logistic Regression](https://reader035.vdocuments.us/reader035/viewer/2022062221/56813a7e550346895da2775c/html5/thumbnails/1.jpg)
An Illustration of Rate Difference Estimation with SAS
in Logistic Regression
Yun Guo
![Page 2: An Illustration of Rate Difference Estimation with SAS in Logistic Regression](https://reader035.vdocuments.us/reader035/viewer/2022062221/56813a7e550346895da2775c/html5/thumbnails/2.jpg)
Outline
• Statistical methods for RD
• RD with logistic regression
• SAS realization
• Conclusion
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Statistical methods
• Wald/t approximation—no covariate adjust• CMH (weighted estimate)-adjust strata• Logistic Regression-adjust both
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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)
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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
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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!!!!
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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!!!
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RD with logistic regression
Hereafter subscript 1/0 of est p index treatment.
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Statistical methods
• Marginal approach (sum over all samples)
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Statistical methods
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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
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SAS realizationEXAMPLE DATA
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SAS realizationPREPARE DATA
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SAS realizationSTEP 1: Logistic regression
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SAS realizationSTEP 1: Logistic regression
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SAS realizationSTEP 1: Logistic regression
COV
EST
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SAS realizationSTEP 2: RD estimate
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SAS realization
Step 3: Delta method
Step 4: CI
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Conclusion
1, When covariates adjust needed, a choice is to use L Regression
2, Other methods could be used too
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Thank you!