compare two lower confidence interval of odds ratio?

[phson]

Dear all,

 

I have a problem with comparing two lower confidence intervals of odds ratio. The detail is follow:

 

I have:

 

lci1 = e^[ln(a*d/b*c)-1.96*square root(1/a+1/b+1/c+1/d)]

 

lci2 = e^[ln(a*(d-1)/b*(c+1) - 1.96*square root(1/a+1/b+1/(c+1)+1/(d-1)]

 

I want to approve lci1 > lci2 with all 0 < a,b,c,d < N

 

I have progammed this problem in computer. As the result, it is true ( lci1 > lci2 ). We want demonstrate this inequation in mathematisc style. Could you please help me?

 

Thank you in advance!

Best,

 

 

 

[phson]

I support more condition for this issue

 

a,b,c >=1 ; d >=2

 

a+b = D1; c+d = D2 (D1 and D2 are constant)