an illustration of rate difference estimation with sas in logistic regression

20
An Illustration of Rate Difference Estimation with SAS in Logistic Regression Yun Guo

Upload: kanoa

Post on 05-Jan-2016

55 views

Category:

Documents


2 download

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 Presentation

TRANSCRIPT

Page 1: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

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

Outline

• Statistical methods for RD

• RD with logistic regression

• SAS realization

• Conclusion

Page 3: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

Statistical methods

• Wald/t approximation—no covariate adjust• CMH (weighted estimate)-adjust strata• Logistic Regression-adjust both

Page 4: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

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)

Page 5: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

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

Page 6: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

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!!!!

Page 7: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

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!!!

Page 8: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

RD with logistic regression

Hereafter subscript 1/0 of est p index treatment.

Page 9: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

Statistical methods

• Marginal approach (sum over all samples)

Page 10: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

Statistical methods

Page 11: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

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

Page 12: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

SAS realizationEXAMPLE DATA

Page 13: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

SAS realizationPREPARE DATA

Page 14: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

SAS realizationSTEP 1: Logistic regression

Page 15: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

SAS realizationSTEP 1: Logistic regression

Page 16: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

SAS realizationSTEP 1: Logistic regression

COV

EST

Page 17: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

SAS realizationSTEP 2: RD estimate

Page 18: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

SAS realization

Step 3: Delta method

Step 4: CI

Page 19: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

Conclusion

1, When covariates adjust needed, a choice is to use L Regression

2, Other methods could be used too

Page 20: An Illustration of Rate Difference Estimation with SAS in Logistic Regression

Thank you!