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# Equivalence Tests for Extensions of McNemar's Test

Ok,
I need to perform a customized test on SAS wrt to the extension of McNemar's Test. I have actually done McNemar's Test on SAS...pretty simple. And the ext. of the test is similar in the sense we deal with a two by two table. However we flip the null and alternative hypothesis but anyways I will spit out some basic info and see if we can go from there.
Here is the test statistic. Notice its two dimensional.
L_0=(p_11+p_12)-theta_0*(p_11+p_12)=p_12+(1-theta_0)p_11-theta_0*p_21

L_1 is similar. We just switch the theta_0 with theta_1

Var(S_0)=[p_12*(1-p_12)+((1-theta_0)^2)*p_11*(1-p_11)+((theta_0)^2)p_21(1-p_21)+2*theta_0*p_12*p_21-2(1-theta_0)p_12*p_11+2*theta_0(1-theta_0)p_21*p_11]

Var(S_1) is similar just switch the theta_0 with theta_1.

The point estimate of theta is (p_11+p_12)/(p_11+p_21)

Now note that theta_0 and theta_1 are some fixed value that are created according to our significance level. The rest of the info is gathered from the 2X2 table.
If the two tests are deemed to be equivalent then they lie within the interval (theta_0, theta_1)

note: L_0/s.e.(L_0) is a standard normal.

I am also dealing with a compound null hypothesis thus the p-value is the sum of the two tail probabilities L_0/s.e.(L_0) and L_1/s.e.(L_1)

Any help is appreciated. Thanks
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