Transcript An Illustration of Rate Difference Estimation with SAS in

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
(1)
,where, x is covariate, s is factor, t is treatment,
sub i is indexing subject
exp(   xi   si   ti )
pi 
1  exp(   xi   si   ti )
(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),
p
p
log(OR)  log(
)t 1  log(
)t  0  exp( )
1 p
1 p
RD with logistic regression
• Rate through Logistic Regression (say
subject i=1)
exp(   xi   si   )
pt 1 
1  exp(   xi   si   )
exp(   xi   si )
pt  0 
1  exp(   xi   si )
RD  pt 1  pt  0
(3)
Intercept, covariate as well as factor, not gone!!!!
RD with logistic regression
• How about the variance of estimate?
pt 1
exp(   xi   si   )

1  exp(   xi   si   )
pt  0
exp(   xi   si )

1  exp(   xi   si )
var( RD)  var( pt 1  pt  0 )
Very messy!!!
(4)
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 realization
EXAMPLE DATA
SAS realization
PREPARE DATA
SAS realization
STEP 1: Logistic regression
SAS realization
STEP 1: Logistic regression
SAS realization
STEP 1: Logistic regression
COV
EST
SAS realization
STEP 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!