I would appreciate assistance with a gllamm or xtmelogit code for the model described below for combining multiple 2 by 2 results of a binary diagnostic test with binary reference test outcome:
The # of positive test results from the ith study in the disease grp is y_i1
and for the normal grp y_i0, follow binomial distributions such that
y_ij ~bin(N_ij, eta_ij)
where N_ij is the # of test results in the group and
eta_ij is the true rate of positive results.
D_i and S_i are random-effects that describe how accuracy and implicit threshold , respectively, vary by studies such that:
D_i = logit(eta_i1) - logit(eta_i0)
S_i = logit(eta_i1) + logit(eta_i0)
D_i is normally distributed with mean A+B*S_i and variance sigma_D^2
S_i is normally distributed with mean S and variance sigma_S^2
Thanks for your assisstance.
Sincerely,
Ben
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