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!!!
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
Conclusion
1, When covariates adjust needed, a choice is to use L Regression
2, Other methods could be used too