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Calculating expected frequencies

For the risk ratio -

i  =   ( a + b )( a + c )λMH
( c + d ) + [ ( a + b )λMH ]
Estimation of i assuming a common risk ratio is straightforward using the formula given to the right. You can now see why you need to compute the common risk ratio before testing for interaction - it is necessary because the value of the common ratio is used to assess whether interaction is present or not. But remember - if interaction is present, then your common risk ratio is no longer meaningful.
 

For the odds ratio -

i   =   Pi± 
Pi2 - 4 ωMHMH - 1) (a + b) (a + c)
2 (ωMH - 1)
where
    Pi = MH - 1) [(ai+bi) + (ai+ci)] + ni.

Estimation of the i assuming a common odds ratio is a bit less straightforward. We give the appropriate formula to the right. Again we use our Mantel-Haenszel estimate, this time of the common odds ratio. Note however that we have a ± sign in the equation which means that we will get two answers to the formula. We choose the answer that gives positive values to the other expected values.